Guide
Measurement and traceability

The chain behind the number

What has to be true, from the sensor to the display, for a measured number to mean what it says, and what ties it, link by link, to the definition of its unit

+ Guide · Measurement and traceability

The chain behind the number.

From the air in a blood-pressure cuff to a constant of nature, this guide follows the stages inside an instrument and the calibrations above it, and ends with what makes a measured number trustworthy.

+ The central question

What has to be true, from the sensor to the display, for a measured number to mean what it says, and what ties it, link by link, to the definition of its unit?

Starts at:school science: fractions, ratios, squares and square roots; no electronics or statistics assumed.Ends at:read a calibration certificate, an uncertainty budget and a device's accuracy claim, and say what makes a measured number trustworthy. Built around:the redefinition of the SI that took effect on 20 May 2019, followed down the traceability chain from the Planck constant to the cuff of a blood-pressure monitor.

The mirror shows that a careful measurement can be wrong in a way no one sees. A measurement is a comparison, so a measured number is only as good as the reference it was compared with, and each reference is only as good as the one it was compared with in turn. That chain of comparisons raises the question this guide answers: What has to be true, from the sensor to the display, for a measured number to mean what it says, and what ties it, link by link, to the definition of its unit?

One instrument recurs throughout: an automated upper-arm blood-pressure monitor. The channel that measures the pressure of the air in its cuff runs from a small silicon sensor through an amplifier, a converter and firmware to the number on its display (Chapter 1). The monitor shows that pressure in millimeters of mercury, written mmHg, the unit in which medicine states blood pressure. One millimeter of mercury is fixed by convention at 133.322 387 415 pascals. The pascal is the unit of pressure in the SI, the International System of Units that nations agree on (Chapter 3).

In measurement, the measurand is the quantity a measurement is meant to find; for the monitor's pressure channel, it is the pressure of the air in the cuff. The monitor gives two kinds of number. Its reading is the cuff pressure it shows. Its estimate is a different quantity, reached by a different route: the systolic and diastolic blood pressure that its software works out from small oscillations in that cuff pressure.

A reference is whatever a measurement is compared with, from the marks on a ruler to a gauge of known accuracy or a standard kept by a national laboratory. In a calibration a laboratory compares an instrument with a reference under stated conditions and records how the two relate. Uncertainty is the stated size of the doubt that remains about a result, given in the result's own unit.

Two chains end in every displayed number, the monitor's reading among them. The first runs inside the instrument through six stages, sense, condition, digitize, compute, connect and decide, each named by what it does. A sensor senses the quantity and turns it into an electrical signal, and circuits condition that signal by amplifying and filtering it. A converter digitizes the signal into numbers, firmware computes the result from those numbers, and the instrument connects the result to a display or a record. Finally a person or a program decides what to do with it. Each stage adds error. A correction can remove the part of that error that is known, and what remains can be bounded but never removed (Chapter 2).

The second chain runs outside the instrument, as a series of calibrations. Each calibration compares an instrument with a better reference and adds an uncertainty of its own, so the uncertainty only grows down the chain, from the definition of the unit to the instrument on the bench. The first link below the definition is a national metrology institute, the laboratory that keeps a country's measurement standards. The institute realizes the unit: it builds a physical standard from the unit's definition. Since 20 May 2019 every SI unit has been defined through seven constants with fixed values. The kilogram was the last unit defined by an object, and since that date it has rested on the Planck constant (Chapters 3 and 19).

A measured number means what it says when three conditions hold. First, both chains are known and unbroken. Second, the number's uncertainty is stated and is smaller than the margin that the decision based on the number allows. Third, tests show that the instrument stays within that uncertainty between calibrations. A number that an algorithm derives from the readings, such as the monitor's estimate, needs one more proof, because calibration covers only the readings. The maker must therefore validate the derived number by comparing it with the same quantity measured by a reference method, an established way of measuring it. For the monitor's estimate, a clinical study makes that comparison (Chapter 24).

How to read this guide

The reader starts in Part I with what a measured number is: a comparison with a reference, an error and the doubt about it, and a unit that nations agree on. In Part II the signal passes through the instrument's stages, from the sensor to the firmware, and each stage adds error. In Part III the doubt is stated in numbers: from repeated readings, through the uncertainty budget that combines the sources of doubt, to the plus-or-minus on a certificate and the decision a test makes. In Part IV each reference is calibrated against a better one, from the factory bench up to a national laboratory. At the top of that chain, in Part V, the definition of the kilogram changed from a metal object to a fixed value of the Planck constant, a constant of nature.

In Part VI a maker proves a measurement in a product, and in Part VII the measuring system is treated as a whole. In Chapter 28, the last of Part VII, the reader follows the chain link by link from the Planck constant to the cuff and reaches the answer to the central question. In Part VIII the reader learns who builds the chain in 2026, and in Part IX what rules apply to measuring instruments and medical devices as of November 2026.

Three kinds of reader can take shorter routes. An engineer new to measurement who has never written an uncertainty budget can read Parts I to III and Part VII, or take the shortest path through Chapters 1, 4 to 9, 11, 13, 24, 25 and 28. A founder or product lead who needs to know what an accuracy claim promises and what a calibration program needs can read Chapters 1, 13, 16, 17, 24 to 26 and 28 first. A regulatory or quality professional can start with Chapters 14 to 17, then 22 to 24, 26, 30 and 31.

The mathematics stays at school level: ratios, percentages, powers of ten, squares and square roots. Beyond that, only two tools appear, each worked step by step with real numbers. The first is the root-sum-of-squares, which combines independent uncertainties by adding their squares and taking the square root of the sum. The second is decibels, a scale for the ratio of two signals. Four kinds of box recur:

In the plates, every color has a meaning and none is decoration. The number the instrument reports, such as the monitor's reading in mmHg, is always lapis blue, and one orange mark in each plate points at the detail that matters most. Every other class of thing keeps one color throughout: green for the quantity being measured, plum for references and standards at every link of the calibration chain, and teal for the signal inside the instrument, analog or digital. Deep red marks noise and error, violet marks uncertainty as an interval, a distribution or a budget, and ochre marks limits and decisions, such as a specification or a tolerance. The algorithm's estimate of blood pressure has a color of its own, so that it is never drawn like the reading. A key strip under every plate lists only the colors that plate uses.

The color key

+ Part I · Foundations

What a measured number is.

A bathroom scale, a clinical thermometer and a blood-pressure monitor look nothing alike, and each does the same thing: it compares. Each sets the quantity in front of it against a reference built into it, and someone once set that reference against a better one. Before any electronics or standards, this part fixes three ideas that the rest of the guide depends on. Chapter 1 shows what a measurement is, a comparison with a reference, and introduces the blood-pressure monitor that the guide follows to its end. Chapter 2 separates the error of a reading from what anyone can know about that error, its uncertainty. Chapter 3 shows why nations must agree on a unit before any two numbers can be compared.

+ The questionWhat is an instrument doing when it shows a number?

The sensor measures air, not blood

An automatic blood-pressure monitor reports a person's blood pressure, and its sensor never touches the blood: it measures the pressure of the air in the cuff. Texas Instruments, known as TI, is a maker of chips, and it publishes a reference design for such a monitor, a worked example of its circuit, its parts and its software. In that design a pump inflates the cuff around the upper arm until the pressure reaches a target, and a valve then opens to let the air out. A tube carries the air pressure from the cuff to a small silicon sensor on the monitor's circuit board. Everything the monitor later displays, the cuff pressure and the blood pressure alike, is worked out from that one air pressure as it falls.

The sensor in TI's design is the 2SMPP-03, a gauge-pressure sensor for air only, rated from 0 to 50 kPa, as Omron's data sheet describes it. A gauge-pressure sensor measures a pressure against the pressure of the air around it (Chapter 4). A kilopascal, kPa, is a thousand pascals, the SI unit of pressure (Chapter 3). With every heartbeat the artery under the cuff pushes against it, so the falling cuff pressure carries small pulsations, one for each beat, which this guide calls oscillations. In a typical monitor the oscillations measure from less than 1 mmHg to 3 mmHg, by the figures of Freescale, another chip maker. From them the monitor works out a blood pressure that its sensor never meets (Chapter 4).

Every measurement is a comparison

The international definition of measurement rests on comparison. The International Vocabulary of Metrology, known as the VIM, defines measurement as the process of "experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity". A note to the definition gives its core in one sentence: "Measurement implies comparison of quantities or counting of entities." The VIM is the shared vocabulary of measurement, and the Joint Committee for Guides in Metrology, the JCGM, publishes it. As of November 2026 the edition in force is still the third, of 2012, although in January 2026 the JCGM sent a draft of the fourth edition to a vote.

A ruler shows the comparison plainly, because the length of a part is laid beside marks that stand for known lengths. The monitor compares in several steps that no user sees, and a measurement made this way, through a chain of signals and computations rather than against a scale, is called indirect. Its sensor compares the cuff pressure with the pressure of the air around the monitor (Chapter 4). Its firmware compares the sensor's signal with numbers stored at calibration, when the monitor's readings were set against those of a reference manometer, a pressure gauge whose own readings had been compared with a better standard still.

The number on the display is the last of these comparisons, so it can be no sounder than the ones before it. The opening pages showed what happens when one of those comparisons is never made: Perkin-Elmer's mirror matched its test instrument, and the check that no one carried out, between that instrument and an independent measure of length, decided the outcome. A further note to the VIM's definition lists what every measurement presupposes: a description of the quantity suited to the intended use of the result, a measurement procedure, and "a calibrated measuring system operating according to the specified measurement procedure". The monitor needs all three. Its quantity must be described well enough to say what is measured, its procedure must say how the cuff is inflated and read, and its measuring system must have been calibrated against a reference.

Measurand, indication and result

The measurand is the "quantity intended to be measured", in the VIM's definition. The word "intended" carries weight, because an instrument can measure a quantity close to the one intended without measuring the intended quantity itself. The monitor's pressure channel senses its own measurand, the gauge pressure of the air in the cuff at each moment of the deflation. Its blood-pressure output has a different measurand: the person's systolic and diastolic pressures in the artery under the cuff, the highest and lowest pressures of each heartbeat. Specifying a measurand requires knowing the kind of quantity and the body that carries it, as a note to the definition adds. Both measurands are pressures, but one is carried by air in a cuff and the other by blood in an artery.

An instrument's indication is the "quantity value provided by a measuring instrument or a measuring system", in the VIM's words. An indication and the value of the quantity being measured "are not necessarily values of quantities of the same kind", a note warns, and the monitor shows why. In TI's design the sensor's output runs from about 0 to 30 mV over 0 to 40 kPa, as TI states, so the sensor's indication is a voltage. The converter's indication is a count, a whole number. Only the display's indication is a pressure in mmHg, and each change of kind on the way rests on a relation that someone had to establish and that can be wrong.

In the VIM's definition, a measurement result is the "set of quantity values being attributed to a measurand together with any other available relevant information". A note adds that a result "is generally expressed as a single measured quantity value and a measurement uncertainty". A quantity value is a number together with its unit, so a complete result carries three things: a number, its unit and its uncertainty.

A home monitor shows its value alone, such as 150 and its unit. The VIM's note on the measurement result allows the value alone when the uncertainty is negligible for the purpose, and says that in many fields this is the common way. The monitor's maker states a limit of error in the manual. Microlife, a monitor maker, gives that limit for one of its home monitors as "pressure within ± 3 mmHg". Such a limit tells the user how far any reading may stray, but not how far a particular one did. Chapter 2 shows why a limit of error is not an uncertainty, and Part III shows how an uncertainty is worked out.

Six stages from the cuff to the display

The monitor's cuff-pressure channel, which the guide follows from here to its last chapter, passes through six stages, each named by what it does: sense, condition, digitize, compute, connect, decide. Each stage changes the signal, and each can add an error. In TI's reference design a named part does the work of each stage.

To sense, the 2SMPP-03 uses a bridge of piezoresistors, resistors formed in silicon that change their value when the silicon flexes under pressure. TI drives the bridge with a constant current of 100 µA, the drive that Omron rates it for, and pressure unbalances the bridge so that a small voltage appears at its output (Chapter 4). To condition, an instrumentation amplifier, TI's INA350, multiplies that voltage by 50. An instrumentation amplifier is built to measure a small difference of voltage such as the bridge's output (Chapter 6). A filter then passes the oscillations to a path of their own. It weakens the signal below 1.7 hertz, or cycles per second, and above 5.9 hertz, and so it blocks the steady level that the cuff pressure gives (Chapter 6).

To digitize, a 12-bit converter turns the amplified voltage into a count by comparing it with a reference voltage of 2.5 V (Chapters 7 and 8). The converter writes each count as 12 binary digits, or bits, and twelve doublings give 4,096 possible counts. It is built into TI's MSPM0L1306 microcontroller, a chip that combines a small processor with circuits such as the converter. To compute, the firmware converts counts into pressure with coefficients set at calibration, and it runs the algorithm that turns the oscillations into blood pressure (Chapter 9). TI's own software for the design "leaves the blood pressure algorithm section blank", so the maker of each monitor supplies its own.

To connect, the monitor shows the result on its display, which steps in whole millimeters of mercury in Microlife's monitors, and an instrument may also store or send its results (Chapter 9). To decide, someone acts on the number: a production test passes or fails the monitor (Chapter 13), and the user or a doctor acts on the blood pressure it reports.

01 — The cuff-pressure channel, from sense to decide

The quantity being measuredReferences and standardsThe signal in the chainLimits and decisionsReadingFocal detail

The reading and the estimate

The six stages produce two outputs, and the guide keeps them apart in every chapter. The reading is the cuff pressure in mmHg, and a chain of calibrations ties it to the SI. The monitor is compared with a reference manometer and the manometer with a better standard, and the chain reaches a pressure balance, a piston loaded with masses, which sets a pressure from the weight of the piston and its masses divided by the piston's area. Through those masses the chain reaches the kilogram (Chapters 14 and 15). The estimate is the systolic and diastolic blood pressure, which the firmware's algorithm derives from the oscillations. The oscillations are always largest when the cuff pressure equals the mean arterial pressure, the average pressure in the artery over a heartbeat, as Renesas, a third chip maker, states. The rules that lead from that point to systolic and diastolic values are each maker's own (Chapter 9).

02 — One cuff pressure, two outputs

References and standardsThe signal in the chainLimits and decisionsThe algorithm's estimateReadingFocal detail

The two outputs are checked against different references. OIML, the intergovernmental body that writes model rules for measuring instruments, sets a limit for the reading of an automated monitor: within ±3 mmHg or 2 % of the reading, whichever is greater, with the pressure rising or falling, at any temperature from 10 to 40 °C. OIML's test replaces the cuff with a rigid metal vessel of 500 ml and compares the monitor with a reference manometer at steady pressures, so no oscillation reaches the sensor during the test. For the estimate, OIML sets a separate requirement, which the maker meets through a clinical investigation on people (Chapter 24). Microlife states that its home monitor's blood-pressure values correspond to the Korotkoff method, which finds blood pressure from the sounds heard through a stethoscope over the artery. The reading is defined against a manometer, and the estimate against a method that a person carries out.

Because the pressure test brings no oscillations to the sensor, it never exercises the algorithm, and a monitor can meet OIML's limit at every test pressure and still report blood pressures that are wrong. In 2021 PTB, Germany's national metrology institute, proposed a new OIML guide for testing monitors with simulators that reproduce real oscillations. Its proposal argued that "any verification of the pressure measurement alone completely ignores the second step", the algorithm's step from oscillations to blood pressure.

+ The questionIf no one can know the true value, what does it mean for a reading to be wrong?

Two monitors, both within their limit

Two monitors can read the same cuff pressure 6 mmHg apart, and both can be within their limit. The monitors of two makers, Microlife and A&D, read the cuff pressure to within ±3 mmHg by the makers' own figures, and OIML allows an automated monitor ±3 mmHg or 2 % of the reading, whichever is greater (Chapter 1). At a steady 120 mmHg, 2 % of the reading is only 2.4 mmHg, so the 3 mmHg branch applies. One monitor may then show 117 mmHg and another 123 mmHg, and each meets its limit, though only at its edge (Chapter 13). A tester who wanted to say which of them is wrong would need the true pressure in the cuff, and no one has the true pressure.

The air in the cuff has one definite pressure, but no one can know it exactly. In the VIM's words, a true quantity value is one "consistent with the definition of a quantity", and a note to that definition adds that, in the approach built on errors, the true value is "considered unique and, in practice, unknowable". The true value cannot be known exactly because every instrument compares the pressure with some reference, and every reference carries a doubt of its own. A tester who calls a reading wrong therefore compares it with a reference whose value is known well enough for the purpose. The tester then faces two questions: how far the reading lies from the reference, and how well anyone knows that distance. The first is the reading's error, and the second is its uncertainty.

Error is a difference from a reference

Measurement error is a difference with a sign: in the VIM's words, the "measured quantity value minus a reference quantity value". A note to the definition warns that error "should not be confused with production error or mistake", so an instrument's error is not a fault that someone made. A monitor that shows 152 mmHg while a reference manometer shows 150 mmHg has an error of +2 mmHg, and one that shows 148 mmHg has an error of −2 mmHg. In OIML's test procedure for automated monitors, the tester records exactly this difference, the monitor's reading minus the reference's, at a series of steady pressures.

Instruments in everyday use do not all read within 3 mmHg of a reference. A'Court and colleagues at the University of Oxford measured how many do in a cross-sectional survey of the sphygmomanometers, the instruments with a cuff that measure blood pressure, in use at 38 general practices in England. The team tested them between January and July 2009 and published the survey in 2011, and the National Institute for Health Research funded it. The testers compared each instrument with a reference pressure meter at 250, 200, 150, 100 and 50 mmHg. They fully tested 584 instruments, and 503 of them, or 86 %, read within 3 mmHg of the reference at every point. Another 77 instruments, 13 %, showed at least one reading 4 to 9 mmHg off, and 4 instruments, fewer than 1 %, showed one 10 mmHg or more off. Thirty-six of the 308 digital instruments failed.

Every one of those errors is a comparison with a reference meter, and no tester knows an error better than the reference that found it. The authors do not state how accurate their reference meters were, so an instrument recorded as 3 mmHg off could have been somewhat more or somewhat less off, by an amount that the reference meter's own doubt sets. The second question, how well anyone knows the error, therefore cannot be skipped.

Systematic and random error

Error has two parts, which differ in how each behaves when a measurement is repeated. In the VIM's words, a systematic error "in replicate measurements remains constant or varies in a predictable manner", while a random error "varies in an unpredictable manner". An estimate of a systematic error is called a bias in the VIM. The monitor's pressure channel produces both kinds. A single 2SMPP-03 sensor may have an offset, its output with no pressure applied, anywhere within 4.0 mV of the typical value, by Omron's figures, and whatever one sensor's offset is, it shifts every reading in the same direction by the same amount. TI's amplifier and the circuits around it add noise, less than 10 µV from peak to peak at the amplifier's input by TI's figure, and the noise moves each reading by a different amount in no predictable direction (Chapter 5).

The two parts call for different remedies. An engineer can remove a known systematic error with a correction, and in the method of the GUM, the international guide to uncertainty (Chapter 11), the correction comes before any uncertainty is stated: the GUM's working assumption is that a result "has been corrected for all recognized significant systematic effects". A monitor can remove its sensor's offset in this way. Before a measurement, its firmware reads the sensor open to the air, stores that reading and subtracts it from every later reading, as an Omron patent describes (Chapter 17). No correction can remove a random error from a single reading, but the firmware can reduce its effect by averaging many readings (Chapters 5 and 10).

In a real instrument, errors that keep their sign from one test pressure to the next reveal a systematic error. Ramírez-Barrera and colleagues measured errors of this kind in a bench study published in 2021. They worked at the Instituto Tecnológico Metropolitano, ITM, in Medellín, Colombia, and calibrated four aneroid sphygmomanometers, the mechanical dial gauges used with a stethoscope, chosen at random from different brands. ITM funded the work, and no author worked for a maker. The team followed OIML R 16-1, the model rule that OIML replaced with R 148 in 2020, and compared each gauge with a digital reference manometer in two rising and two falling series. The fourth gauge read low at every point the authors report, by 0.235 to 2.710 mmHg, so it carried a systematic error.

03 — One gauge's error and its doubt, against the limit

References and standardsNoise and errorUncertaintyLimits and decisionsFocal detail

Accuracy, trueness and precision

Accuracy, trueness and precision, three words that everyday speech uses loosely, mean three different things in measurement. Measurement accuracy is, in the VIM's words, the "closeness of agreement between a measured quantity value and a true quantity value of a measurand", and a note to the definition adds that accuracy "is not a quantity and is not given a numerical quantity value". By the same note, a monitor is called more accurate when its error is smaller.

A monitor has good trueness when the average of an unlimited number of its repeated readings lies close to a reference value. Over so many readings the random errors average out, while a systematic error stays in every one, so trueness responds to systematic error and not to random error. A monitor has good precision when its repeated readings agree closely with each other, in the VIM's words the "closeness of agreement between indications or measured quantity values obtained by replicate measurements". Engineers usually state precision as a standard deviation, the usual measure of how widely values scatter about their average (Chapter 10). A note to the definition warns that "measurement precision" is sometimes "erroneously used to mean measurement accuracy".

04 — Trueness and precision at one pressure

References and standardsNoise and errorReadingFocal detail

Precision depends on what stays the same between the repeated readings, so it is stated under one of two sets of conditions that the VIM defines. Under repeatability conditions, the same operators use the same procedure, measuring system, operating conditions and location over a short period. Under reproducibility conditions, the locations, operators and measuring systems differ. A production tester who reads one monitor several times in a minute measures its repeatability. An engineer who compares monitors from different lines, tested by different people at different sites, measures their reproducibility. The first spread shows how closely one monitor repeats itself, and the second how closely monitors agree across lines, people and sites.

Makers use the word accuracy differently. When Microlife and A&D state an accuracy of ±3 mmHg, they give a limit within which the error must lie, and that limit is a number, while the VIM's accuracy has none. Such a limit is a maximum permissible measurement error in the VIM's term, and OIML's ±3 mmHg is a limit of the same kind. The limit tells a user how wrong a monitor is allowed to be. It does not tell how wrong one particular monitor is.

Resolution is not accuracy

An instrument's resolution, the smallest change it can show, sets no limit on its error. In the VIM's words, resolution is the "smallest change in a quantity being measured that causes a perceptible change in the corresponding indication", and a note adds that noise or friction can limit it. A display's resolution is the "smallest difference between displayed indications that can be meaningfully distinguished", usually its last step.

An analytical balance shows the difference between resolution and accuracy. The Sartorius CPA224S displays to 0.1 mg, repeats within 0.1 mg and departs from a straight line by less than 0.2 mg, twice its display step, by its maker's figures. Shimadzu's figures for its AUW220D balance follow the same pattern. A balance that shows a tenth of a milligram can therefore be wrong by two tenths, and Chapter 8 sets the monitor's 1 mmHg display step against its ±3 mmHg limit in the same way.

Uncertainty states what is known

A second term answers the second question, how well anyone knows a reading's error. Measurement uncertainty is, in the VIM's words, a "non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used". In the GUM's plainer words, the uncertainty of a result "reflects the lack of exact knowledge of the value of the measurand". A monitor's error at one reading is a single number with a sign, and no one ever knows it exactly. The uncertainty of that reading is a stated width of doubt around the result, without a sign, and an engineer can work it out and write it down.

Uncertainty has many sources, and the monitor supplies an example of most of those the GUM lists. A tester may define the measurand incompletely, by reading a cuff pressure without saying at which moment of the deflation. The engineer may know the conditions imperfectly, such as the sensor's temperature. The display has a finite resolution, the reference manometer used at calibration has an inexact value, the firmware's method rests on approximations, such as a straight line through a curved response, and repeated readings vary. An uncertainty expressed as a standard deviation is a standard uncertainty, in the GUM's term. The engineer finds one by statistics on repeated observations in a Type A evaluation, and from any other information, such as a data sheet or a certificate, in a Type B evaluation (Chapters 10 and 11).

Neither the monitor that shows 117 mmHg nor the one that shows 123 mmHg can be called wrong from its display alone, because each reading's error is unknown. A calibration laboratory can measure each monitor's error at a test pressure against a reference and state an uncertainty with it, and only that pair of numbers shows whether a monitor is likely to be within its limit.

+ The questionWhy does a kilogram in Bengaluru equal a kilogram in Gaithersburg?

A treaty signed in Paris

A kilogram has no size of its own in nature: it is as large as the people who use it agree it is. Every measurement compares a quantity with a reference (Chapter 1), and a unit is the reference that every other reference shares. Two laboratories that each kept their own idea of the kilogram could weigh the same object and report numbers that differ, and neither number would be wrong by its own reference. A kilogram in Bengaluru equals a kilogram in Gaithersburg because India and the United States both belong to one treaty, the Metre Convention, and refer to one definition. In practice a national laboratory makes a unit from its definition, a step that metrologists call realizing it, and the national laboratories keep comparing their results (Chapter 21).

The Metre Convention gave its member governments a permanent structure for deciding matters of measurement units, and it is still in force. Representatives of seventeen states, the United States among them, signed it in Paris on 20 May 1875. The treaty's purpose "was the creation of an international organization called the BIPM", the International Bureau of Weights and Measures, as the BIPM describes it.

Three bodies and a laboratory

The signatories set up three bodies under the Convention, and each has its own task. The General Conference on Weights and Measures, the CGPM, decides the units by its resolutions. It gathers delegates from every Member State and normally meets every four years. There are 69 Member States as of October 2026, by the BIPM's count, and 34 Associate States and Economies take part without full membership. The International Committee for Weights and Measures, the CIPM, has eighteen members, each from a different State. It meets every year, works under the CGPM's authority and is advised by ten Consultative Committees. The BIPM is the laboratory and secretariat, based at the Pavillon de Breteuil in Sèvres, near Paris, with the task to "ensure worldwide unification of measurements".

The agreement is still open to change, and the CGPM changes it by vote. The 28th CGPM met at Versailles from 13 to 15 October 2026 and passed seven resolutions. In one of them the delegates ask the CIPM to work toward a proposal for a new definition of the second, to be presented at the 29th meeting in 2030. They voted on a direction, and the second itself is unchanged.

05 — Who agrees on the units

References and standardsFocal detail

India has been a Member State since 11 January 1957. Its national metrology institute is the CSIR National Physical Laboratory, CSIR-NPL, in New Delhi, which keeps the country's national standards and passes their values on to calibration laboratories. Since 14 October 1999 CSIR-NPL has also taken part in the CIPM's arrangement under which national institutes accept one another's calibration certificates, a mechanism that Chapter 21 describes.

Seven base units and what is built from them

The CGPM maintains the SI, the International System of Units. The SI has seven base units: the second for time, the meter for length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for amount of substance and the candela for luminous intensity. Every other SI unit is a derived unit, built from these by multiplying and dividing them. The BIPM lists 22 derived units with special names of their own, among them the newton for force, the joule for energy, the volt, the ohm and the pascal for pressure. The BIPM sets the system out in the SI Brochure, now in its 9th edition of 2019, version 4.01 of June 2026.

A prefix scales a unit by a power of ten. The prefix kilo multiplies by a thousand, so the sensor's rated 50 kPa is 50,000 pascals. The SI's 24 prefixes run from quecto, a factor of 1 in 10³⁰, to quetta, a factor of 10³⁰. The 27th CGPM added the four outermost of them, ronna, ronto, quetta and quecto, in 2022. A vote of delegates extended the list of prefixes, just as votes of the CGPM had fixed each of the units.

The CGPM also decides what each unit's definition rests on, and the meter and the kilogram once rested on metal. In September 1889 its first meeting sanctioned international prototypes of the meter and the kilogram, and national copies followed: India keeps copy No. 57 of the kilogram at CSIR-NPL. The CGPM replaced the meter's metal definition in 1960 and the kilogram's in 2018. Since 20 May 2019 all seven base units have rested on seven defining constants with fixed values, among them the Planck constant (Chapter 19). The kilogram's prototype still exists, but the kilogram no longer depends on it.

The pascal, the unit of the reading

The SI unit of the monitor's reading is the pascal, and because pressure is force divided by area, a pascal is one newton of force spread over one square meter. The newton, the SI's unit of force, is a kilogram meter per second squared. Dividing it by a square meter leaves a kilogram per meter per second squared, which is how the BIPM writes the pascal in base units. A cuff pressure of 20 kPa therefore means that the air pushes with 20,000 newtons on every square meter of the cuff's inner wall. A square meter holds 10,000 square centimeters, so the same pressure is 2 newtons on every square centimeter.

06 — The pascal, and the millimeter of mercury beside it

References and standardsLimits and decisionsReadingFocal detail

Medicine does not state blood pressure in pascals. It uses the millimeter of mercury, mmHg, whose name comes from the mercury-column sphygmomanometer, in which the pressure holds up a column of mercury. The unit's value is fixed by convention at 133.322 387 415 Pa, as the World Meteorological Organization records it in its code register. A reading in mmHg therefore involves no mercury and no column, only a fixed multiple of the pascal.

A unit kept outside the SI's lists

The SI Brochure no longer lists the millimeter of mercury. The BIPM dropped the unit from the Brochure's 9th edition, in 2019, and ISO, the International Organization for Standardization, dropped it the same year from ISO 80000-4, its standard on the quantities of mechanics. Pražák and colleagues record both changes in a letter published in 2020, which they wrote as metrologists working in a research project co-funded by the European Union. Version 4.01 of the Brochure, issued in June 2026, also leaves the unit out: its one table of non-SI units lists the bar, equal to 100 kPa, and the decibel, but not the millimeter of mercury. In the Brochure's chapter on non-SI units, the BIPM recognizes that "some non-SI units are widely used and that this is expected to continue for many years".

Law, not the SI, keeps the millimeter of mercury in medicine. Non-SI units "do not hold any special status within the SI", in the words of the BIPM's news item on version 4.01, of 4 June 2026. The EU's units directive, 80/181/EEC, has listed the millimeter of mercury since an amendment of December 1984 among the units "permitted in specialized fields only", for "blood pressure and pressure of other body fluids", and its annex forbids prefixes with the millimeter of mercury.

OIML allows a monitor to show blood pressure in kPa or in mmHg, and in its two Recommendations for sphygmomanometers, both of 2020, it gives every limit in both units, such as ±0.4 kPa paired with ±3 mmHg. OIML pairs each limit with a rounded value in the other unit, not with an exact conversion, so the two forms of one limit can differ.

+ Part II · The signal chain

Where error enters.

Between a physical quantity and the number on a display lie six stages, each named by what it does: sense, condition, digitize, compute, connect, decide. In the blood-pressure monitor, the sensor turns the air pressure in the cuff into a few millivolts, the electronics amplify and filter them, a converter turns them into counts, and firmware turns the counts into millimeters of mercury on the display and in the stored record. Each stage can add an error, and noise is not a stage of its own but something that every stage adds. This part follows the cuff-pressure channel through the first five stages: sensing in Chapter 4, noise in Chapter 5, conditioning in Chapter 6, sampling and quantization in Chapters 7 and 8, and computing and connecting in Chapter 9. The sixth stage, the decision, comes in Chapter 13, once Part III has stated how sure each reading is.

+ The questionHow does a pressure, a temperature or a light level become a voltage, and what else comes in with it?

A pressure becomes a few millivolts

Between an empty cuff and a cuff at 40 kilopascals, which is 300 mmHg, the sensor in Texas Instruments' reference design for a blood-pressure monitor changes its output by only about 30 millivolts (Chapter 1). A millivolt is a thousandth of a volt. The sensor is Omron's 2SMPP-03, and TI drives it with a constant current of 100 microamperes, written 100 µA, a ten-thousandth of an ampere. Omron gives the sensor's bridge of resistors a resistance of 20 kilohms, written 20 kΩ. A voltage is the current times the resistance, so 100 µA through 20 kΩ sets 2 V across the bridge. The 30 mV is about fifteen thousandths of those 2 V, since 30 divided by 2,000 is 0.015. Every later stage of the monitor works with this small change, and every error the sensor adds travels with it to the display.

Like every sensor, the 2SMPP-03 is a transducer, a device that turns one physical quantity into another, here a pressure into a voltage. The transducer sets how large the signal is, and also which other quantities enter the measurement alongside the one intended. The force sensor of a weighing instrument is a transducer too: OIML, the intergovernmental body that writes model rules for measuring instruments, defines a load cell as a "measuring transducer that will produce an output in response to an applied load".

The cuff is part of the sensor

The sensor never touches the blood, so the cuff, its tube and the air inside them belong to the sensing system as much as the chip does. A pump fills the cuff around the upper arm with air, and a tube carries the pressure of that air to the sensor inside the monitor (Chapter 1). The 2SMPP-03 measures gauge pressure: it compares the pressure on one side of its chip with the pressure of the surrounding air on the other, so its reading is the cuff's pressure above the pressure of the room. Omron rates the sensor for use with air only, so air must carry the pressure from the cuff to the chip, and the chip can respond only to what the air brings it.

The air also carries a much smaller signal at the pace of the heart. The artery under the cuff swells a little with every heartbeat and pushes on the cuff, so the air pressure rises and falls slightly with each beat. These small rises and falls are the oscillations. They ride on the much larger, slowly falling pressure of the cuff, and together the two make the oscillometric signal. Typical oscillations measure less than 1 mmHg to 3 mmHg, by the figures that Chua and Siew, two engineers at the chip maker Freescale, give in a 2005 application note on a digital blood-pressure meter. The cuff pressure is the monitor's reading, and the systolic and diastolic values are the estimate that its firmware derives from the oscillations (Chapter 9).

07 — The cuff, the tube and the oscillometric signal

The quantity being measuredThe signal in the chainThe algorithm's estimateReadingFocal detail

A bridge of four resistors

The chip turns pressure into a voltage through piezoresistance, the change in a material's electrical resistance when the material is strained, that is, stretched or compressed. The 2SMPP-03 is a MEMS sensor, short for microelectromechanical system, in which the moving part and the resistors are made in the same piece of silicon. Pressure strains the silicon, and the strain changes the resistances. Four of the resistors are joined in a square called a bridge. The current enters at one corner and leaves at the opposite one, so it divides between two paths of two resistors each, and the other two corners are the outputs. When the four resistances are equal, each path divides the voltage across the bridge in half, so both outputs sit at the same voltage and the voltage between them is zero.

A bridge responds to a difference between its resistances and ignores a change that all four share. Pressure changes the resistances unequally, the bridge loses its balance, and a small voltage appears between the outputs. A change that moves all four resistances by the same fraction leaves each path dividing the voltage in half, so the bridge stays balanced and that change adds nothing to the difference. Both outputs stay close to 1 V, half of the 2 V across the bridge, while the signal is only their difference of a few millivolts. The amplifier that follows must measure that difference of millivolts while ignoring the 1 V that both outputs share (Chapter 6).

The current or voltage that powers a bridge is its excitation, and Omron states every output figure for the 2SMPP-03 at an excitation of 100 µA, the current that TI's design supplies. The offset is the output with no pressure applied, typically −2.5 mV, and one sensor's offset may lie anywhere within 4.0 mV of that value. The span is the output at full scale minus the output at zero, typically 42.0 mV for the sensor's full scale of 50 kPa, which is about 375 mmHg. A sensor's sensitivity is the change in its output for a given change in the quantity it measures, and it differs from a diagnostic test's sensitivity, which Chapter 24 explains. For the 2SMPP-03 it is the span divided by the range, 42.0 mV over 375 mmHg, or 112 µV for each millimeter of mercury, where a microvolt is a millionth of a volt.

08 — A bridge turns pressure into millivolts

The signal in the chainUncertaintyFocal detail

How other transducers compare

A bridge can be powered by a current or by a voltage, and its maker states its output per unit of whichever excitation it uses. The 2SMPP-03 takes a current, so Omron states its span at 100 µA. TDK's C32/2 takes a voltage. The C32/2 is a die, a bare silicon chip that carries a bridge, and TDK sells it for medical devices among other uses. Its sensitivity is ratiometric to the supply, as TDK states it, which means that its output grows in proportion to the supply voltage (Chapter 6). TDK gives that output per bar, a unit of pressure equal to 100 kPa. HBK, a maker of load cells, states the rated output of its PW6D in millivolts for each volt of excitation, because the PW6D takes a voltage too. The table adds two transducers of other kinds, a platinum resistance thermometer and a photodiode, with figures from TI's guide to such thermometers and from an article on low-light measurement by Analog Devices, a maker of amplifiers and converters.

The two silicon sensors, from different makers, put out a similar share of their excitation at full scale. Omron's span of 42.0 mV is about 21 thousandths of the 2 V across its bridge, and TDK's 215 mV per bar over a range of 0.4 bar is 86 mV, about 17 thousandths of its 5 V supply. HBK's 2.0 mV for each volt is 2 thousandths, or 10 mV at 5 V. The silicon sensors' share is therefore about 8.5 to 10.5 times the load cell's at its full load, since 17 divided by 2 is 8.5 and 21 divided by 2 is 10.5, so for the same excitation these silicon bridges give the amplifier the larger signal. Not every monitor uses a bridge. In one Omron Healthcare patent, granted in 2013, the pressure sensor's capacitance changes with pressure, and an oscillator circuit turns that capacitance into a frequency for the processor to read.

The thermometer and the photodiode each need a circuit to turn what they sense into a voltage. The Pt100 is a platinum sensor of 100 Ω at 0 °C. Its resistance rises by about 0.39 Ω for each degree: the standard IEC 60751 sets a coefficient of 3.9083 thousandths for each degree, as TI reports it, and 3.9083 thousandths of 100 Ω is about 0.39 Ω. A current turns that resistance into a voltage, and the current also heats the sensor (Chapter 6). In a photodiode, light generates a current, and an amplifier turns the current into a voltage through a resistor whose value sets the gain. In an example by Analog Devices, a photocurrent of up to 125 nanoamperes, billionths of an ampere, passes through a resistor of 80 megohms, written 80 MΩ, and gives up to 10 V, since 125 nA times 80 MΩ is 10 V.

What else comes in with the pressure

A sensor responds to more than the quantity it is meant to measure, and any other quantity that changes its output is an influence quantity. For the 2SMPP-03, a silicon bridge, the largest in Omron's figures is temperature. Omron names another: the board the sensor is mounted on may influence its output, so mounting is an influence quantity too.

The 2SMPP-03's offset can move with temperature by several times the accuracy that a monitor must meet. Omron states how far the offset and the span move between 0 and 85 °C, relative to 23 °C, in percent of full scale, written %FS: a share of the whole 375 mmHg range rather than of the reading. At 85 °C, where the change is widest, a typical sensor's offset has moved by 2.0 %FS, and any one sensor's offset may have moved by anywhere from −3.0 to 7.0 %FS, which Omron sums up as ±5.0 %FS about the typical change. The same sensor's span may have moved by −2.0 to 4.0 %FS, which Omron sums up as ±3.0 %FS about a typical change of 1.0 %FS. Omron does not state that the sensor compensates for temperature. The largest offset change in Omron's figures, 7.0 %FS, is 7.0 % of 375 mmHg, about 26 mmHg, more than eight times the ±3 mmHg to which monitor makers such as Microlife and A&D state their cuff-pressure accuracy (Chapter 8). Even Omron's summary figure of 5.0 %FS is about 19 mmHg, so a monitor built on this sensor must compensate for temperature or correct for it.

09 — Temperature moves the bare sensor

Noise and errorLimits and decisionsFocal detail

A warming of 10 K can move a reading by a monitor's whole accuracy limit, as TDK's figures for its die show. TDK gives the C32/2's span a typical temperature coefficient of −2.1 thousandths per kelvin, where a kelvin is the same step as a degree Celsius. Over 10 K the span therefore falls by 10 times 2.1 thousandths, which is 21 thousandths, or about 2.1 %. In a monitor that used the die without compensation, the reading at a cuff pressure of 150 mmHg would fall by 2.1 % of 150 mmHg, about 3 mmHg, the whole of a ±3 mmHg limit.

The effect of temperature can be compensated on the sensor's chip, corrected in firmware or, for the offset, removed by zeroing. Where the sensor is not compensated on its chip, the monitor's firmware can correct the reading from a measured temperature (Chapter 9). Zeroing the sensor just before each measurement removes the offset's share of the effect, as long as the sensor's temperature holds steady while the measurement lasts.

Even at a steady temperature, the 2SMPP-03's output does not follow the pressure exactly, and Omron gives two figures for how far it departs. The output departs from a straight line by up to 1.3 %FS, which is 1.3 % of 375 mmHg, about 4.9 mmHg, and that departure is the sensor's nonlinearity. At any one pressure, the output with the pressure rising and the output with it falling differ by up to 0.2 %FS, about 0.75 mmHg, and that difference is the sensor's hysteresis.

Omron gives no figure for the 2SMPP-03's repeatability, and none for its long-term stability, the drift of the output over months of use. TDK does give a long-term figure for its die. The long-term stability of the C32/2's offset is typically 0.15 % and at most 0.3 % of the die's normalized full-scale output of 120 mV, measured to TDK's own test standard. The typical 0.15 % of 120 mV is 0.18 mV. A bar, 100 kPa, is about 750 mmHg, so the die's typical sensitivity of 215 mV per bar is about 0.29 mV for each mmHg, and 0.18 mV is about 0.6 mmHg. An engineer who chooses Omron's sensor has no such figure from its maker and must establish one by testing. During the monitor's life, periodic checks against a reference must cover the drift that Omron does not state (Chapter 17).

+ The questionWhat is noise, where does it come from, and why can it never be removed?

A resistor that makes a voltage

A resistor lying on a bench, connected to nothing, produces a voltage. The voltage is small and never still: it wanders at random about zero, so its average is zero, while its size is not. This voltage is thermal noise, also called Johnson noise, and its source is the random motion that heat gives to the charges in every conductor. John Johnson of Bell Telephone Laboratories measured it with a vacuum-tube amplifier and reported in 1928 that a statistical fluctuation of electric charge "exists in all conductors", producing a random variation of voltage between their ends. In the same issue of the journal, Harry Nyquist of AT&T calculated the effect from thermodynamics and statistical mechanics and found that his results agreed with the experiments.

In a measuring instrument, noise is any part of the signal that the measured quantity did not cause, and thermal noise is the part that no design can remove. No resistor is free of it: "it is not possible to obtain resistors that do not have Johnson noise", in the words of a tutorial by Analog Devices, a maker of amplifiers and converters. A designer can control only its size. A resistor makes noise power in proportion to its resistance, to its absolute temperature, counted in kelvins, and to the bandwidth, the range of frequencies over which the signal is measured. The Boltzmann constant, which converts a temperature into an energy, sets the scale.

Thermal noise follows this rule closely enough for a laboratory to measure the Boltzmann constant with it. In 2011 Benz and colleagues measured the constant from the noise of a 100 Ω resistor held at the triple point of water, the one temperature at which ice, liquid water and water vapor exist together. They worked at NIST, the US national metrology institute, with partners at other institutes, and reached a relative standard uncertainty of about 12 parts in a million, where relative means a share of the measured value. Since 20 May 2019 the SI has fixed that constant of nature at an exact value (Chapter 19).

Because the noise averages to zero, makers state its size as an rms value, short for root mean square. The rms value is the square root of the average of the squared values, and for noise it equals the standard deviation, the usual measure of how widely values scatter about their average (Chapter 10). Makers also state noise from peak to peak, the distance between the highest and the lowest values over a stated time. Random noise has no fixed maximum, so by Analog Devices' convention the peak-to-peak figure is 6.6 times the rms value, a size the noise exceeds only 0.1 % of the time. Dividing a peak-to-peak figure by 6.6 therefore recovers the rms value, the form in which noise figures can be compared and added.

Because the noise power grows in proportion to the bandwidth, the rms voltage grows with the square root of the bandwidth. Makers therefore state a noise density: the rms noise in a band 1 Hz wide, stated in volts per root hertz. A 1,000 Ω resistor at 25 °C has a density of 4 nV per root hertz by Analog Devices' figure, where a nanovolt is a billionth of a volt. The noise power also grows in proportion to the resistance, so the density grows with the square root of the resistance. The 20 kΩ bridge of Chapter 4 has twenty times the resistance of the 1,000 Ω resistor, so its density is the square root of 20, about 4.5, times 4 nV, or about 18 nV per root hertz.

Two more kinds, and interference

Two more kinds of noise join thermal noise, and they differ in how their density depends on the frequency. Shot noise has the same density at every frequency, as thermal noise has. It arises because a current is a stream of separate electrons whose arrival is random, and its density grows with the square root of the current, a rule Analog Devices states for the small current that flows into an amplifier's input. The other kind grows as the frequency falls and is called 1/f noise, read "one over f", where f stands for the frequency. In Analog Devices' definition its power is inversely proportional to the frequency, so halving the frequency doubles the noise power.

The cuff's pressure oscillations lie at a few hertz, low enough for 1/f noise to matter. Above a certain frequency the flat level of thermal and shot noise is the larger, and below it 1/f noise takes over. That crossover is the 1/f corner: about 1 to 10 Hz in the best low-noise, low-frequency amplifiers and up to about 100 Hz in general-purpose ones, by Analog Devices' figures. In TI's reference design for the monitor, the filter for the oscillations weakens the signal below 1.7 Hz and above 5.9 Hz (Chapter 6). The band between those two frequencies lies within the 1 to 10 Hz range of the best amplifiers' 1/f corners. A general-purpose amplifier's 1/f corner can lie well above the band, at up to about 100 Hz, and below that corner 1/f noise is the larger part.

The amplifier in TI's design, the INA350, shows how much 1/f noise adds in this band. By TI's figures, its density is 43 nV per root hertz at 1 kHz, where the density is flat, and its noise over 0.1 to 10 Hz, a band that contains the oscillations, is 4 µV from peak to peak. If the density stayed at 43 nV per root hertz all the way down, that band, 9.9 Hz wide, would hold 43 nV times the square root of 9.9, which is 3.15, about 135 nV rms. Multiplied by 6.6, that is 0.89 µV, about 0.9 µV from peak to peak. TI's 4 µV is about four and a half times as much, since 4 divided by 0.89 is about 4.5, and the excess is the amplifier's 1/f noise.

Because 1/f noise lies inside the signal's own band, no filter can remove it without removing the signal: it "cannot be filtered out", in the words of Kiely, an Analog Devices engineer, in a 2017 article. The remedies for 1/f noise therefore act where it arises, in the amplifier or in the sensor. An amplifier can remove its own in two common ways, as Analog Devices' engineers describe them. In chopping, a switch at the input, working many times a second, moves the signal up to the switching frequency, called the chopping frequency, and a second switch at the output brings the signal back to its own frequency. That second switch moves the amplifier's own offset and 1/f noise up to the chopping frequency, where a filter removes them. In auto-zero, the amplifier measures its own offset and subtracts it, and because the noise changes slowly at low frequencies, subtracting consecutive samples cancels the amplifier's low-frequency noise too. Analog Devices calls an amplifier that uses either technique, or both, a zero-drift amplifier.

Zero-drift amplifiers "only remove the 1/f noise of the amplifier", as Kiely puts it. The sensor's 1/f noise enters with the signal and is amplified with it. For the sensor, Kiely names a different remedy: exciting the sensor with an alternating supply rather than a steady one, which he calls AC excitation, for alternating current. The supply alternates in direction, and the outputs of the two phases are subtracted, which by his account removes the sensor's 1/f noise. In that subtraction an error that does not reverse with the supply, such as an offset, cancels, while the signal, which reverses, doubles.

10 — Where the pulse sits in the noise

The signal in the chainNoise and errorFocal detail

Interference is noise with an outside cause, and the electronics can reject some of it, but no filter removes the part that falls inside the oscillations' band. Mains wiring at 50 or 60 Hz couples a hum into the leads, and the hum, Analog Devices notes, reaches an amplifier's two inputs together, as a shared voltage that the amplifier of Chapter 6 is built to reject. A converter that samples the hum too slowly can still turn it into a slow false signal (Chapter 7).

The monitor also makes interference of its own: the motors of the pump that fills the cuff add noise while they inflate it, as Sanchez of Freescale notes in a 2007 application note on a monitor design. Movement of the arm presses on the cuff, and its pressure changes can fall in the oscillations' band, where no filter separates them from the signal. Microlife, a monitor maker, asks the user in its instructions to keep the arm still and not to talk during a measurement.

Signal against noise, in decibels

A noise matters only against the signal it accompanies, and engineers state one against the other as the signal-to-noise ratio, or SNR. They express it in decibels, written dB, a scale that counts tenfold steps. For a ratio of voltages each tenfold step adds 20 dB, and for a ratio of powers each tenfold step adds 10 dB, by the definitions in NIST's guide to the SI. Power grows with the square of voltage, so the two definitions give the same number of decibels for the same signal: a voltage ratio of 10 is a power ratio of 100, two tenfold steps of 10 dB each, which again makes 20 dB.

A voltage ratio of 100 is therefore 40 dB, and 1,000 is 60 dB. Ten doublings multiply a ratio by about 1,000, so each doubling of a voltage ratio adds about a tenth of 60 dB, about 6 dB. A level in decibels must always state its reference level, NIST adds, but an SNR needs no outside reference, because it is the ratio of two quantities measured in the same channel.

In the monitor, the smallest oscillation, not the cuff pressure, sets the noise target, the most noise the electronics may add, because the firmware derives its estimate from the oscillations (Chapter 4). TI expects the smallest oscillation at its amplifier's input to measure 100 µV from peak to peak. The circuits that first take the sensor's signal, led by the amplifier, are the channel's front end, and TI states that the front end's input-referred noise is under 10 µV from peak to peak. Input-referred means expressed as if the noise entered at the amplifier's input alongside the sensor's signal. The ratio of the two figures is 100 divided by 10, which is 10, one tenfold step or 20 dB, so even the smallest oscillation is at least ten times the size of the noise.

11 — Decibels count tenfold steps

The signal in the chainNoise and errorFocal detail

Averaging, and what it cannot remove

When noise is random, an average of several readings reduces it, and the reason is the sum of squares from the solved example. A sum of N readings holds N copies of the signal, which add to N times the signal, and N independent noises, which add as the square root of the sum of their squares. N equal squares sum to N times one square, so the noises grow only by the square root of N. Dividing the sum by N therefore keeps the signal and divides the noise by the square root of N. The rule holds for a moving average, which averages the latest N readings each time a new one arrives, as TI states in one of its converter data sheets.

In decibels, averaging two samples improves the SNR by 3 dB and averaging four improves it by 6 dB, by Analog Devices' figures. Sixteen readings divide the noise by four, two doublings or 12 dB, and a hundred divide it by ten, one tenfold step or 20 dB. Each gain costs time, because a hundred readings take a hundred times as long as one, and a signal that changes during the average shrinks along with the noise. The monitor's firmware therefore balances noise against response time (Chapter 9), and the same rule applies to repeated readings at one pressure (Chapter 10).

Averaging cannot reduce an error that is the same in every reading, because the average returns such an error whole, as it returns the signal. It will not correct a converter's integral nonlinearity, a fixed error of the converter's own, as Analog Devices notes (Chapter 8), and an offset or a span error passes through the average unchanged. Averaging divides random noise by the square root of N and leaves every fixed error where it was.

12 — Averaging shrinks noise, not bias

The quantity being measuredNoise and errorReadingFocal detail

The noise floor sets the smallest signal

The noise floor is the level of noise below which no change can be told apart from it. A designer cannot remove the floor but chooses where it lies against the smallest signal the channel must see. A narrower bandwidth lowers the floor, because rms noise grows with the square root of the bandwidth. A filter does not stop noise exactly at its corner frequency, the frequency at which it begins to weaken the signal, so some noise above that frequency still passes. The simplest low-pass filter, which passes slow signals and weakens fast ones, is one resistor and one capacitor. Its noise bandwidth, the width of a sharp-edged band that would pass the same noise power, is 1.57 times its corner frequency, by Analog Devices' figure. A narrower band also slows the channel's response, and a band narrower than the signal removes part of the signal itself.

A smaller resistance or a lower temperature reduces thermal noise, and an amplifier with a low 1/f corner reduces the low-frequency rise. None of these reaches zero, because thermal noise follows from the temperature of every conductor and the Boltzmann constant fixes its scale. In TI's design the floor is under 10 µV, a tenth of the smallest oscillation, and the amplifier's noise sets it, at about 11 times the bridge's thermal noise in the solved example.

+ The questionWhat does the electronics between the sensor and the converter do to the number?

Every count is a fraction of the reference

The monitor's converter turns the amplified signal into a number by comparing it with a steady voltage, so each count it reports is a fixed fraction of that voltage. The part that holds the comparison voltage is the voltage reference, and in Texas Instruments' reference design for a blood-pressure monitor it is the ATL431LI, which holds 2.5 V. The 12-bit converter divides the 2.5 V into 4,096 steps, twelve doublings (Chapter 1), and 2.5 V divided by 4,096 is about 0.61 mV a step (Chapter 8). The number on the display is therefore the signal's voltage divided by the reference's voltage, and the reference acts as the instrument's internal standard: whatever it does, every reading follows in proportion.

In TI's design the bridge current and the reference come from separate sources, so each must hold its value on its own between calibrations. TI drives the bridge with a constant current of 100 µA, set by holding 0.249 V across a 2.49 kΩ resistor whose value may differ by up to 0.1 %, its tolerance. The sensor's output follows the current and the converter's count follows the 2.5 V reference, so a drift in the current moves the output, and a drift in the reference moves the scale against which the output is counted.

The amplifier measures a difference

The bridge's output is a difference of a few millivolts between two terminals that both sit about 1 V above the bridge's lower end (Chapter 4). An instrumentation amplifier, or in-amp, is built to measure exactly such a difference and to multiply it by a set factor, its gain. It is a precision gain block that must reject volts of common-mode signal, the voltage that both inputs share, while it amplifies signals of microvolts, in Analog Devices' description. TI's design uses the INA350 at a gain of 50, so the 16.8 mV that a cuff pressure of 150 mmHg adds at the bridge becomes 0.84 V at the amplifier's output.

How well an in-amp ignores the shared voltage is its common-mode rejection ratio, or CMRR, stated in the decibels of Chapter 5. The INA350 reaches at least 85 dB and typically 95 dB by TI's figures. At 20 dB for each tenfold step, 10 dB is a factor of the square root of 10, 3.16, and 5 dB the square root of 3.16, 1.78, so 85 dB is 10,000 times 1.78, about 17,800. A change of 1 V in the shared voltage therefore looks like 1 V divided by 17,800, about 56 µV, between the inputs, which at the sensor's 112 µV for each mmHg is about 0.5 mmHg. A steady common-mode voltage gives a steady error, which the zero reading taken before each measurement removes (Chapters 2 and 17). A changing one passes into the reading as noise in the same proportion.

The amplifier adds two errors of the kinds the sensor also has. A gain error multiplies every reading by a factor slightly off the nominal one. For the INA350 it is at most 0.6 %, and typically 0.082 % at a gain of 50, by TI's figures. At 150 mmHg these come to 0.6 % of 150, 0.9 mmHg, and about 0.12 mmHg. The INA350's offset adds the same voltage to every reading, at most 1.2 mV and typically 0.2 mV. Referred to the input (Chapter 5), 1.2 mV divided by the sensor's 112 µV for each mmHg is about 11 mmHg, and 0.2 mV is about 1.8 mmHg. Both look large beside a ±3 mmHg limit, but each is fixed for a given amplifier at a given temperature, so the zero reading removes the offset, and the span coefficient that calibration stores for each unit removes the gain error (Chapter 9).

Calibration does not remove the change of either error with temperature, its temperature coefficient. The INA350's offset drifts by 0.37 µV for each degree on average, the mean of 140 amplifiers whose drift TI plots in its data sheet. Across the 30 °C from 10 to 40 °C in which a monitor must meet its limit (Chapter 1), that is 0.37 µV times 30, about 11 µV, or about 0.1 mmHg. The zero reading takes out the offset's drift as long as the temperature holds during the measurement, but the gain's drift stays in the reading until the next calibration. Such residual drifts, and the voltage reference's drift, the drift of the scale itself, still belong in the monitor's uncertainty.

One sensor, two paths

No single gain serves both parts of the oscillometric signal of Chapter 4, which the amplifier's output carries together. At 150 mmHg the output holds about 0.84 V of cuff pressure and oscillations of 5 to 15 mV from peak to peak, the 100 to 300 µV at the amplifier's input multiplied by 50. One mmHg of oscillation, 112 µV at the input, becomes 5.6 mV, so on the converter's steps of 0.61 mV the shape of a 1 mmHg oscillation would rest on only about 9 counts. More gain on the whole signal would not help. TI sets 70 dB as the oscillations' target, three and a half tenfold steps, or 1,000 times 3.16, about 3,200 times, and at that gain the 16.8 mV of cuff pressure at 150 mmHg would become about 53 V, about twenty times the converter's 2.5 V.

Designers therefore feed two paths from one sensor. A filter passes some frequencies and weakens others, and its corner frequency marks where the weakening begins. In Chua and Siew's 2005 meter for Freescale, the cuff pressure, which changes at under 0.04 Hz, goes straight to the converter. The oscillation, at about 1 Hz, passes a two-stage high-pass filter, which weakens the slow cuff pressure and keeps the faster oscillation, and then an amplifier with a gain of 150. A band-pass filter also weakens what is faster than the oscillation. TI's oscillation path is a band-pass filter with corner frequencies at 1.7 Hz and at 5.9 Hz.

A filter also weakens the signal near its corner frequency, so the gain that follows must allow for the loss. Freescale's filter weakens the 1 Hz oscillation by 10 dB, a factor of 3.16. The meter's integrated sensor, which carries its own amplifier on the chip, gives 12 to 36 mV for 1 to 3 mmHg, and divided by 3.16 these leave the filter as 3.8 to 11.4 mV. The gain of 150 then brings them to about 0.57 to 1.7 V.

TI's design splits its gain between two amplifiers. The in-amp's gain of 50 is 100 halved, 40 dB less about 6 dB, or 34 dB, and the amplifier built into the microcontroller adds about 32 dB after it, so the two stated gains make about 66 dB. TI does not state the gain of the rest of the path, and it sets a total target of 70 dB or more across 0.5 to 7 Hz. That band reaches beyond the filter's corner frequencies at 1.7 and 5.9 Hz, and the oscillations reach below the lower one: a pulse rate of 40 to 180 beats a minute, the range A&D states for one of its monitors, divided by 60 seconds is 0.67 to 3 Hz. Each corner of the filter, set by one resistor and one capacitor, weakens frequencies gradually beyond it, so the filter weakens a slow oscillation without removing it, and the gain must allow for that loss as well.

Taken as a gain of 70 dB, about 3,200 times, the target brings the 100 to 300 µV oscillations to about 0.32 to 0.95 V, a large share of the converter's 2.5 V. One mmHg of oscillation, 112 µV at the input, then becomes about 0.35 V, or about 580 counts of 0.61 mV instead of 9.

On the cuff-pressure path a monitor can place a low-pass filter, which keeps slow signals and weakens fast ones, ahead of the converter. There it limits the noise bandwidth of Chapter 5 and guards against aliasing, the false slow signal that a converter makes from a fast one it samples too slowly (Chapter 7). TI does not describe the cuff-pressure path separately, so Chapter 11 works its budget on the assumption that the cuff pressure reaches the converter at the in-amp's gain of 50. One sensor feeds two paths, and each path is shaped for one of the two numbers the monitor reports: the cuff-pressure path for the reading, and the oscillation path for the estimate that the firmware derives (Chapter 9).

13 — One sensor, two paths

The signal in the chainThe algorithm's estimateReadingFocal detail

A shared source cancels

A design can avoid depending on a separate reference by letting one source serve both the sensor and the converter. A measurement made this way is ratiometric: the converter compares the sensor's output with a reference derived from the sensor's own excitation, so a change in the excitation moves both sides of the comparison by the same fraction and the count stays the same. In a precision weigh scale that Analog Devices describes in a circuit note, the converter's reference inputs take their voltage from the load cell's sense lines, the pair of wires that carry the excitation voltage back from the cell. That connection creates "a ratiometric configuration that is immune to low frequency changes in the power supply excitation voltage", in Analog Devices' words. By Analog Devices' account the design then needs no precision reference.

Some blood-pressure designs and their sensors use the same principle. Chua and Siew's meter feeds its sensor and the pair of resistors that sets its converter's reference from one 5 V supply, so supply variations do not affect its accuracy, by their account. The sensitivity of TDK's C32/2 die and the output of NXP's MPX2050 are ratiometric to the supply, in their makers' descriptions: each scales with the supply, so a design that also derives its reference from that supply can cancel the change. TI's monitor design, with its separate sources, is not built this way.

A ratiometric design still needs a part that holds its value, but a different part. In a resistance-thermometer circuit that TI describes in a guide, the current that flows through the sensor also flows through a reference resistor, whose voltage serves as the converter's reference. Each voltage is the same current times a resistance, so the current, with its accuracy and drift, cancels from their ratio, and the result depends only on the two resistances, as TI states. The reference resistor's accuracy and drift do not cancel, so the stable part of that design is a resistor instead of a voltage.

14 — A separate reference, and a shared one

References and standardsThe signal in the chainNoise and errorReadingFocal detail

The current that measures also heats

The excitation that makes a sensor's signal also puts heat into the sensor, and the warming is an error of its own, called self-heating. For this reason most excitation currents for resistance thermometers should stay below 1 mA, by TI's guide to them. The temperature rise is the power the current dissipates divided by a dissipation constant, the power that warms the element by one degree. By TI's figures that constant ranges from about 2.5 mW for each degree for a small thin-film element to 65 mW for a large wire-wound one, a milliwatt being a thousandth of a watt.

The power is the current squared times the resistance, so a current of 1 mA in a 100 Ω Pt100 dissipates 1 mA times 1 mA times 100 Ω, or 0.1 mW. That warms the small element by 0.1 divided by 2.5, about 0.04 °C. The Pt100's resistance rises by about 0.39 Ω for each degree (Chapter 4), so the small element's warming adds 0.04 times 0.39 Ω, about 0.016 Ω, and the element reads about 0.04 °C high, an error the sensor makes by being measured.

The monitor's pressure sensor heats itself in the same way. The 2SMPP-03 consumes 0.2 mW by Omron's rating, exactly the power of 100 µA flowing through its 20 kΩ bridge, 100 µA times 100 µA times 20,000 Ω, and twice the Pt100's 0.1 mW. Omron states no temperature rise for the sensor. Because the current is constant, the heating stays nearly the same at every pressure, so it shifts the sensor's temperature once instead of moving with the reading. The temperature effects of Chapter 4 then act on that shifted temperature, and a zero reading taken under the same excitation as the measurement carries the same heating.

+ The questionHow often must a changing signal be measured, and what goes wrong when it is measured too slowly?

A wobble with no heart in it

Mains hum completes 50 cycles a second, and a converter reads it 49 times a second, a rate assumed for the arithmetic and not the rate of any monitor. The readings then rise and fall once a second, the pace of a heart beating 60 times a minute, although no heart produced them. Between two readings a forty-ninth of a second passes, and in that time the hum completes one full cycle and a forty-ninth of the next. Each reading therefore catches the hum a forty-ninth of a cycle later in its swing than the reading before. After 49 readings the lag adds up to a whole cycle, so the readings trace one slow rise and fall each second.

15 — Hum read too slowly becomes a heartbeat

The signal in the chainNoise and errorFocal detail

The false wobble falls where the monitor's firmware looks for the oscillations of Chapter 4, the small rises and falls that each heartbeat adds to the cuff pressure. The oscillations lie at low frequencies: about 1 Hz in Chua and Siew's 2005 meter for Freescale, a chip maker (Chapter 6). A filter in a 2001 patent by Colin, a monitor maker, passes the oscillations in a band of, for example, 1 to 10 Hz, the oscillation band. A wobble at 1 Hz from the hum lies inside this band, and nothing in the readings tells it apart from an oscillation. This distortion is aliasing: a frequency too fast for the readings appears in them as a slower one, its alias. Aliasing is generally not recoverable, as Unser of EPFL, the Swiss federal institute of technology in Lausanne, states in a 2000 review of fifty years of sampling theory, so once the readings hold the false wobble, the firmware in general cannot remove it.

The wobble's arithmetic assumes a converter whose every reading records the input at one instant. A sample-and-hold circuit takes such readings: it follows the input, then disconnects a small capacitor from it and holds that capacitor's voltage while the converter works. The moment of disconnection fixes the instant that the reading records, and the speed of that disconnection is the circuit's most essential dynamic property, by the account of Analog Devices, a maker of converters. A converter that instead averages the input over each conversion records no single instant. For such a converter the same arithmetic still gives where the hum lands, but the converter's own averaging decides how much of the hum remains.

Twice the highest frequency

The number of readings that a converter takes each second is its sampling rate, and a converter avoids aliasing only if this rate is at least twice the highest frequency in its signal, as Analog Devices states for engineers. The rule rests on the sampling theorem, which Shannon showed in a paper of 1949 and Unser quotes: a signal containing no frequencies above a stated limit is completely determined by readings spaced one over twice that limit apart. For a limit of 10 Hz, the readings fall a twentieth of a second apart. Twice the highest frequency in the signal is the Nyquist rate, the lowest sampling rate the theorem allows.

In this rule the signal is everything that reaches the converter, not only the part the designer wants. The oscillations of the published designs lie below about 10 Hz, so they alone would need twice 10, or 20 readings a second. Hum from the mains at 50 or 60 Hz also reaches the converter unless something removes it first (Chapter 5), and with the hum included the theorem requires twice 60, or at least 120 readings a second. A converter that reads more slowly does not lose the hum but moves it to another frequency.

Where the hum moves can be predicted from a rule that holds for any tone, a signal at a single frequency. A tone read at a given sampling rate has images at every whole multiple of the sampling rate, plus or minus the tone's own frequency, and the readings cannot tell the tone apart from its images, as Analog Devices states. Readings can represent frequencies only up to half the sampling rate, the theorem's limit, so by this image rule a tone above half the sampling rate always has an image below half that rate, where the readings show it as an alias. At 49 readings a second, the 50 Hz hum has an image at 50 − 49 = 1 Hz, inside the oscillation band.

The published designs read fast enough to keep the hum's alias out of the oscillation band. A monitor that Lopez of Freescale describes in a 2012 application note takes one sample every 10 ms, which is 100 readings a second, so half its rate is 50 Hz. Hum at 50 Hz then appears at 100 − 50 = 50 Hz and hum at 60 Hz at 100 − 60 = 40 Hz, both far above the oscillation band. Oh and colleagues at Hanyang University in Seoul built a prototype monitor, reported in 2008, that read its sensor 75 times a second, which places the hum at 75 − 50 = 25 Hz or 75 − 60 = 15 Hz, again outside the band. A filter in the firmware can remove an alias at 25 Hz, because that alias, unlike the 1 Hz alias at 49 readings a second, does not share a frequency with the oscillations.

16 — Where the mains hum lands at three sampling rates

The signal in the chainNoise and errorFocal detail

A filter before the converter

Designers keep a fast tone from aliasing by weakening it before the converter reads it, with a low-pass filter, which passes frequencies below its corner frequency and weakens those above it (Chapter 6). Placed ahead of the converter for this purpose, the filter is an anti-alias filter. Filtering before sampling is the standard practice, as Unser notes, and an anti-alias filter is used in almost all applications of sampling converters, the kind that read the input at single instants, as Analog Devices states.

The simplest low-pass filter, built from one resistor and one capacitor, weakens frequencies above its corner frequency gradually rather than removing them, so it lets part of the hum through. Lopez's design places such a filter, with its corner frequency at 10 Hz, ahead of the buffer amplifier, the stage that isolates the sensor from the circuit after it. Lopez does not call it an anti-alias filter, but it does that work in part, and the design's 100 readings a second place the hum that passes it at 50 Hz, outside the oscillation band.

Oh and colleagues used a converter of the averaging kind, and no analog filter at all. They digitized their sensor's output with TI's ADS1222, a 24-bit converter. The ADS1222 is a sigma-delta converter, which takes no instantaneous samples: it averages the input over each conversion through a digital filter of its own (Chapter 8). Such a converter internally reads far faster than the signal needs, so by Analog Devices' account a simpler analog anti-alias filter is enough ahead of it. Oh and colleagues wrote that an analog filter between the sensor and the converter was not necessary, but they did not say how their converter's own filter treated the hum.

The filter inside such a converter can remove almost all of the hum when the designer sets the converter's output rate to suit the mains. Analog Devices makes the AD7190, a sigma-delta converter, for weigh scales. At an output rate of 50 readings a second, its filter places deep notches, frequencies that it blocks almost completely, at 50 Hz and at every multiple of 50 Hz, and the converter then rejects 50 Hz hum by at least 96 dB, by Analog Devices' figure. At 20 dB for each tenfold step of amplitude (Chapter 5), 96 dB is 96 ÷ 20 = 4.8 tenfold steps, so the hum shrinks by a factor of about 63,000 before it can alias. A notch helps only when it sits on the mains frequency.

A converter that reads a slow signal can let the timing of its readings vary far more than one that reads a fast signal. Aperture jitter is the variation, from one sample to the next, in the instant the sample-and-hold's switch opens, by Analog Devices' definition. The error that jitter causes grows with the signal's frequency and the jitter multiplied together, by Analog Devices' formula. In its example, a converter that reads a signal of 100 MHz, or 100 million cycles a second, to the quality of a 14-bit converter needs jitter below 0.1 ps, where a picosecond, written ps, is a millionth of a millionth of a second. The monitor's oscillation band lies below 10 Hz, and 100 MHz divided by 10 Hz is about ten million. At the same quality, a converter reading the oscillation band could therefore let its timing vary about ten million times as much, 0.1 ps times ten million, or about a microsecond. The timing of each reading is not where the monitor's error enters.

Once a beat

The monitor samples its signal a second time, far more slowly than its converter does. The algorithm of Chapter 9 needs the size of each oscillation and the cuff pressure at which it occurred. Plotted against the falling cuff pressure, the sizes of the oscillations trace their envelope, which rises to a peak and falls again. Each heartbeat produces one oscillation, so however fast the converter reads, the firmware receives one point on the envelope per beat. The heart, not the converter, sets this second sampling rate.

The deflation of the cuff sets how far the pressure falls between points, and the published rates lie at 2 to 3 mmHg a second, the rate in Colin's patent. Microlife, another monitor maker, states a deflation of 3 mmHg a second for its WatchBP Office monitor in manual mode, and it recommends 2 to 3 mmHg a second for auscultation, listening to the artery with a stethoscope. India regulates automated blood-pressure monitors under their formal name, automated sphygmomanometers, and its rule for them sets 0.3 to 0.4 kPa a second, or 2.25 to 3.0 mmHg at 133.322 Pa to the millimeter of mercury, for devices used for auscultation (Chapter 30). For a device in which the pulse controls the deflation, letting the pressure fall one step at each pulse, the rule sets 0.3 to 0.4 kPa for each pulse.

A monitor's two rates answer different questions, so they must be read together. The converter's rate decides whether the hum aliases into the oscillation band, and the deflation rate, with the heart rate, decides how finely the envelope is known. Lopez gives a sampling period without a deflation rate, and Colin and Microlife give deflation rates without a sampling rate, so a designer who copies any one of them still has to choose the other rate.

17 — The envelope is sampled once a heartbeat

The signal in the chainThe algorithm's estimateReadingFocal detail

The pressure step between two points is the deflation rate multiplied by the time between two beats, so it depends on the patient's heart, which the monitor does not control. At 80 beats a minute the beats fall 60 ÷ 80 = 0.75 s apart, so at 3 mmHg a second the cuff falls 3 × 0.75 = 2.25 mmHg between them. Celler and colleagues at the University of New South Wales in Sydney set their simulator to that heart rate in a 2018 study funded by the Australian Research Council. They tested six automated monitors on the simulator, analyzed 304 recordings from 102 patients, and made their reference recordings at a deflation of 2 to 3 mmHg a second. A&D, another monitor maker, specifies its UA-651 for pulse rates from 40 to 180 a minute. Those rates place the beats 1.5 s and a third of a second apart, which at 3 mmHg a second leaves 4.5 and 1.0 mmHg between points.

These steps limit the estimate, the systolic and diastolic pressures that the algorithm of Chapter 9 derives, and not the cuff-pressure reading. The peak of the envelope usually falls between two points, so the firmware locates the peak, and every pressure it derives from it, only as finely as the steps allow. Chapter 11 works out the reading's uncertainty, and a clinical study on patients tests the estimate (Chapter 24).

+ The questionA 24-bit converter divides its range into nearly seventeen million steps. How many of them carry information?

Codes, steps and the least significant bit

A 24-bit converter can produce 16,777,216 codes, 2 multiplied by itself 24 times, and each code stands for one narrow band of input voltage. Converters of that size are offered for blood-pressure designs. Renesas, a chip maker, offers a 24-bit sigma-delta converter on versions of its RL78/H1D microcontroller, a family that Renesas describes as well suited to healthcare devices, especially blood-pressure monitors. The monitor followed in this book uses a 12-bit converter with only 4,096 codes, and that converter still adds almost nothing to the uncertainty of the reading (Chapter 11). A bit count alone therefore does not decide how good a reading is: what a bit is worth depends on the signal, the noise and the display.

A converter compares its input with a reference voltage and returns a whole number, the code or count, that says what fraction of the reference the input is. The converter writes each code as a row of binary digits, or bits, each a 0 or a 1, and every added bit doubles the number of codes. The span of input that one code stands for is the converter's step, and it equals the full range divided by the number of codes. The step is also called the least significant bit, or LSB, because a change of one in the code's last bit stands for one step of input.

The step halves with every added bit, and at 24 bits it is as small as the noise of one ordinary resistor. For a range of 10 V the step is 2.44 mV at 12 bits and 596 nV at 24 bits, which is 0.06 parts per million of the range, by the table of Analog Devices, a converter maker. That 596 nV equals the thermal noise of a 2.2 kΩ resistor in a 10 kHz band at 25 °C, as the same table notes (Chapter 5). The noise of that single resistor, ahead of a 24-bit converter, would move its code by about a step.

In the monitor, one step of the converter corresponds to about a tenth of a millimeter of mercury in the cuff. In TI's design the converter's reference is 2.5 V, and its 4,096 codes give a step of about 0.61 mV. The amplifier ahead of the converter multiplies the bridge's output by 50, so one step corresponds to 12.2 µV at the bridge. At the sensor's typical 112 µV for each millimeter of mercury (Chapter 4), one step is therefore 0.109 mmHg of cuff pressure. The reference, the gain and the sensor fix the size of each step, and the step says nothing yet about how close the reading is to the pressure in the cuff.

Half a step either way

Within one step the converter cannot tell one input from another, so every reading carries an error of up to half a step in either direction. This quantization error, plotted against the input, is a sawtooth in Analog Devices' model. As in Chapter 2, the error is the reading minus the input. While the input rises through a step the code holds still, so the error falls from plus half a step to minus half a step and then jumps back, and every value in between is equally likely.

The sawtooth spreads the error evenly between its limits, a flat distribution (Chapter 11). The rms value of such an error is the step divided by the square root of 12, about 0.29 of a step, by Analog Devices' account. For the monitor, half a step is about 0.055 mmHg and the rms error 0.031 mmHg, the figure that the engineer enters for the converter in Chapter 11, where the errors of all the stages are combined. The model is not precise but is accurate enough for most applications, Analog Devices adds. It fails when the signal's frequency and the sampling rate are in a simple ratio, because the error then repeats in a pattern instead of scattering as noise.

18 — Two quantizations: the converter count and the display step

The signal in the chainNoise and errorUncertaintyReadingFocal detail

The quantization error alone sets the best signal-to-noise ratio, the SNR of Chapter 5, that a converter of a given number of bits can reach. For a sine wave that fills the converter's range, that best SNR is 6.02 dB for each bit plus 1.76 dB, which Analog Devices calls the theoretical performance of a perfect converter. Each extra bit halves the step, and halving the step halves the amplitude of the error, a ratio of 2 that is worth 6.02 dB. An ideal 12-bit converter therefore reaches 6.02 dB times 12, plus 1.76 dB, or 74.0 dB, and an ideal 24-bit converter 146.2 dB. No real converter reaches its ideal figure, because its own circuits add noise to the quantization error, and also distortion, which appears as harmonics of the signal.

Effective bits and noise-free bits

Makers therefore state what a real converter delivers, in bits of two kinds. The first starts from SINAD, the signal-to-noise-and-distortion ratio: the signal's rms amplitude divided by the rms amplitude of everything else in the converter's output, noise and distortion together, added as the square root of the sum of their squares (Chapter 5). Running the ideal formula backward turns SINAD into the effective number of bits: SINAD minus 1.76 dB, divided by 6.02 dB. A converter with 11.1 effective bits therefore adds as much noise and distortion as a perfect converter of 11.1 bits would. IEEE, the Institute of Electrical and Electronics Engineers, fixes converter terms in its standard, IEEE 1241-2023, and the definitions and formulas here are Analog Devices' versions. The 12-bit converter of TI's monitor design reaches up to 11.1 effective bits by TI's figures, about one bit short of twelve. Twelve doublings give 4,096 levels and 11.1 doublings about 2,200, so the monitor's converter behaves like a perfect one with about 2,200 levels rather than 4,096.

The second measure counts only the codes that hold still. In Analog Devices' formula, the noise-free resolution is the full range divided by the peak-to-peak noise, which is 6.6 times the rms noise (Chapter 5), with that ratio counted in bits: the resolution at which the output code does not flicker. Effective resolution divides the range by the rms noise instead, so it comes out about 2.7 bits higher, because 6.6 is about 2 multiplied by itself 2.7 times. "Noise-free bits" is a makers' term, used by Analog Devices and by TI. Both resolutions fall short of 24 bits even in Analog Devices' AD7190, a 24-bit converter for weigh scales, at its quietest setting, a gain of 128 and 4.7 readings a second. Its noise is then 8.5 nV rms, its effective resolution 23 bits and its noise-free resolution 20.5 bits, so noise leaves only about 1.5 million distinguishable levels among its 16.8 million codes.

A signal that fills only part of the range uses fewer codes still. In a weigh-scale example worked by Analog Devices, the load cell gives 10 mV at full load, about an eighth of the 78 mV between the AD7190's input limits of ±39.06 mV at that gain. The peak-to-peak noise is 6.6 times 8.5 nV, or 56.1 nV, and 10 mV divided by 56.1 nV gives 178,250 noise-free counts, or 17.4 bits. Of the 16,777,216 codes the converter can produce, about 1 % carry information in that design, and the rest describe noise or inputs the signal never reaches. The monitor's converter is the opposite case. The input-referred noise of the monitor's front end is under 10 µV from peak to peak by TI's figure (Chapter 5), less than one step of 12.2 µV. Noise therefore moves the code of a steady pressure by less than one step, and in this design the step, not the noise, limits the resolution.

19 — How many codes carry information

The signal in the chainNoise and errorReadingFocal detail

Linearity, dither and oversampling

Bits describe how finely a converter divides its range, not whether the divisions sit in the right places. In Analog Devices' definitions, integral nonlinearity, or INL, is the largest departure of the converter's actual transfer characteristic, the relation between each input and its code, from a straight line. Differential nonlinearity, or DNL, is the largest departure of any one step from its ideal size. A DNL worse than minus one step means that some step has no width at all, so its code never appears, and Analog Devices calls it a missing code.

Averaging can resolve finer than one step only if a little noise reaches the input, as Analog Devices states. A perfectly steady input that lies between two codes gives the same code every time, and averaging identical codes cannot reveal what lies between them. Dither, in Analog Devices' definition, is external noise added to the converter's input. About half a step rms of broadband noise, noise spread over a wide band of frequencies, tends to randomize the quantization error, by Analog Devices' figure. Noise much beyond about one step reduces the converter's SNR in proportion, so dither helps only in small amounts.

Averaging is the principle of oversampling: reading far faster than the signal needs and averaging the readings down. Four times as many readings give one more bit, and sixteen times as many give two, by Analog Devices' rule, because four readings halve the random noise (Chapter 5), a gain of 6 dB, one bit's worth. The converter in TI's design can oversample by 128 times in hardware. Since 128 is 2 multiplied by itself seven times, and each bit takes two doublings, it adds 3.5 bits in principle, taking 12 bits toward 15.5, provided that the input carries enough noise to act as dither.

The sigma-delta converter, also called delta-sigma, relies on oversampling more than any other kind of converter. In Analog Devices' description, the converter's loop combines the input with the output of a 1-bit converter driven by the loop's own result and feeds the sum to an integrator, a circuit whose output rises or falls at a rate set by what it receives. The integrator ramps up or down until the average of the 1-bit stream equals the input, and the loop shapes the quantization noise so that most of it falls outside the band of interest. A digital filter then turns the fast 1-bit stream into slower readings of many bits, a stage that loses no information by Analog Devices' account. That filter is why a sigma-delta converter averages over each conversion rather than taking instantaneous samples (Chapter 7).

Resolution against accuracy

Bits measure resolution, the smallest change a reading can show (Chapter 2). No bit count says how close the reading is to the pressure in the cuff, which is accuracy, and monitor makers state the two figures separately. Microlife, a monitor maker, gives its BP B3 Basic and WatchBP Office monitors a resolution of 1 mmHg and a static accuracy within ±3 mmHg for a steady cuff pressure. Under India's rule for automated sphygmomanometers, the display's scale interval is 1 mmHg (Chapter 30). The rule's maximum permissible error for the cuff pressure, the largest error it allows, is ±3 mmHg or 2 % of the reading, whichever is greater. At 150 mmHg, 2 % is 3 mmHg, so both branches give 3 mmHg, and a monitor may show 150 mmHg while the cuff holds any pressure from 147 to 153 mmHg, three display steps either way.

The display is itself a second quantization. The converter's step of 0.109 mmHg is about a ninth of the display step, so the firmware rounds about nine codes into each displayed millimeter of mercury. Rounding to 1 mmHg leaves an error of up to 0.5 mmHg either way, about nine times the converter's own half-step. The display therefore adds far more to the reading's uncertainty than the converter does, and the engineer counts it as a separate entry in Chapter 11.

A display can also show digits that the channel behind it cannot produce. Freescale's 2005 meter (Chapter 4) used an 8-bit converter whose 241 steps span 0 to 300 mmHg, a step its authors give as 1.24 mmHg. Those 241 steps join 242 codes, so a display of whole millimeters of mercury driven from them could show at most 242 values between 0 and 300. Of the 301 whole numbers in that range, 59, which is 301 minus 242, would never appear, the first of them 3, 8, 13 and 18 mmHg. Every reading would look exact to its last digit while the channel moved in steps about a quarter larger than that digit.

20 — Resolution against accuracy at 150 mmHg

The signal in the chainUncertaintyLimits and decisionsReadingFocal detail

The widest difference between resolution and accuracy in the chain lies in the sensor. Before calibration, the bare sensor's errors, combined, give a standard uncertainty of about 26 mmHg, a figure that the engineer works out in Chapter 11 from the sensor maker's limits. That is about 240 converter steps, behind a display that steps in single millimeters of mercury. The converter's 12 bits resolve far more finely than the reading is known, and only the calibration coefficients, numbers measured for each unit and stored in the firmware, bring the reading within the limit (Chapter 9).

+ The questionWhat can firmware add to a measurement, and what can it hide?

A meter that subtracted 1,024

A blood-glucose meter can measure correctly and still report a wrong number. At a blood glucose of 1,024 mg/dL and above, the FreeStyle InsuLinx meter would display and store in memory a result 1,024 mg/dL below the measured one, as its recall notice stated. One mg/dL is a milligram of glucose in a deciliter, a tenth of a liter, of blood. A measured 1,066 mg/dL would thus appear as 42 mg/dL, in the example that the trade journal MD+DI gave when it reproduced the notice. Abbott Diabetes Care began recalling the meters in the US in April 2013. Abbott's own reason for the recall, as FDA recorded it, was only that at rare, extremely high glucose levels, 1,024 mg/dL and above, the meter may provide an inaccurate reading.

A falsely low result at such a level could delay the treatment of severe hyperglycemia, a blood glucose far above normal, and this could lead to serious injury or death, as MedWrench, a website for medical-equipment technicians, warned in its report of the recall. FDA classified the recall as Class I, the most serious of its three recall classes, on 9 May 2013. A fault in code is present in every meter that runs the code, so the recall covered 335,273 meters by FDA's record.

The meter's code, not its sensor, made the error. FDA recorded the cause as "Software design". The number 1,024 is 2 multiplied by itself ten times, a boundary in binary counting (Chapter 8), but what the code did wrong is stated neither in FDA's record nor in the notice. The remedy was itself code: a software update from Abbott's website, or a replacement meter. Firmware, the code that an instrument runs, is therefore a stage of the measuring chain like the sensor and the converter, the compute stage of Chapter 1's six. It can add an error that appears only at inputs that a calibration may never apply.

Coefficients for each unit

The monitor's firmware must first turn counts into millimeters of mercury, and it cannot use one set of numbers for every unit, because no two sensors are alike. One of Omron's 2SMPP-03 sensors may have an offset anywhere within 4.0 mV of the typical −2.5 mV, and a span anywhere within 5.5 mV of the typical 42.0 mV (Chapters 4 and 11). The firmware therefore holds calibration coefficients, numbers measured for each unit and stored in its memory. Two of them carry most of the correction: a zero, the output taken as no pressure, and a span coefficient, the unit's own sensitivity, its change in output for each millimeter of mercury (Chapter 4).

The monitor obtains its two coefficients in different ways, because it can measure its zero again at every use, while the span coefficient needs a known pressure that only a reference supplies. Shenzhen CHK Technology, a Chinese monitor maker, requires each sensor to be calibrated in the method of its 2010 patent application. A program sets the gain and offset of the amplifier on the chip, so that zero pressure falls at one-eighth of the converter's codes and full scale at seven-eighths. The monitor then corrects its zero each time the sensor is switched on.

The air around the monitor supplies the zero's known pressure. In 1980 Omron, then named Omron Tateisi Electronics, filed a patent for a monitor that exposes its sensor to the atmosphere before measuring, stores the reading taken then as a correction and subtracts it from every later reading. Between calibrations the zero also serves as a check that the monitor makes on itself (Chapter 17).

The span coefficient comes from a calibration against a reference (Chapter 14), usually during manufacture, with known static, or steady, pressures applied at a series of values over the range, as Grotov, an individual inventor, describes the common practice in a patent granted in 2019. In Welch Allyn's service manual for the Ambulo 2400, an ambulatory monitor that the patient wears through the day, a technician applies 250 mmHg and then 15 mmHg from a reference and then drains the system to zero. The monitor's later tests must agree with the reference within ±3 mmHg.

21 — Two calibration points give one unit its own line

References and standardsThe signal in the chainNoise and errorReadingFocal detail

Designs differ most in where they correct for temperature. Omron states no temperature compensation for its 2SMPP-03, although it sums up the effect of temperature between 0 and 85 °C as ±5.0 %FS on the offset and ±3.0 %FS on the span (Chapters 4 and 11). Freescale's integrated sensors, the MPXV5050GP and the MP3V5050, carry the correction in circuits on the chip, as Freescale describes them. CHK requires in its patent that temperature drift be compensated, without saying where or how, and Grotov writes only that a monitor may include a thermistor, a resistor whose value changes with temperature, or another temperature sensor. A design built on a bare bridge must therefore state where its temperature correction is made: in the sensor, in the circuit or in the firmware.

From oscillations to an estimate

Before any algorithm runs, the firmware separates the oscillations from the cuff pressure and reduces the noise. It does both with digital filters, calculations run on the stream of readings, and a filter that reduces noise does so at the cost of time, because it averages over a longer stretch of readings. In the monitor, a filter that averages over more than a beat would average away the oscillations as well.

A converter at its quietest setting can be too slow for a pulse. Analog Devices' AD7190 converter, at a gain of 128, has 8.5 nV rms of noise at 4.7 readings a second, against 295 nV at 4,800 a second, about 35 times more, since 295 divided by 8.5 is 34.7. At the slower rate its filter needs four conversion periods to settle after a step, and 4 divided by 4.7 readings a second is 0.85 s. That is longer than one beat at 80 a minute, which lasts 60 divided by 80, or 0.75 s.

Two designs filter in the firmware. Oh and colleagues' prototype monitor (Chapter 7) read its sensor 75 times a second and separated the oscillations in software with a digital high-pass filter whose corner frequency was 0.5 Hz. Microchip's reference monitor smooths its readings with a moving average run twice, which weakens the signal above 3.5 Hz, as the trade magazine Electronics For You reports. In both designs the firmware decides how much noise is removed at the cost of time, although in Oh and colleagues' design the converter's own filter also decides how much mains hum remains (Chapter 7).

The algorithm then turns the envelope of Chapter 7 into the estimate: the systolic pressure, the highest pressure in the artery during a heartbeat, and the diastolic pressure, the lowest. It rests on a published principle: the oscillations are always largest when the cuff pressure equals the mean arterial pressure, in Renesas's words (Chapter 1). Systolic pressure is read where the amplitude of the oscillations grows suddenly, and diastolic pressure where its rapid decline begins, as Freescale placed them in a 2005 note.

The common fixed-ratio method reads systolic and diastolic pressure where the envelope falls to a population-based fraction of its peak, one fraction, or ratio, on each side of it, as Chandrasekhar and colleagues at Michigan State University describe it. In a 2019 study of the popular published algorithms, they used a mathematical model and pressures recorded inside the arteries of 21 patients, and the US National Institutes of Health funded the work.

Each maker sets its own ratios. TI gives ranges for them in its monitor design, 0.30 to 0.75 for systolic pressure and 0.45 to 0.90 for diastolic, but it marks its table of values as for reference only and leaves the algorithm section of its software blank. Chandrasekhar and colleagues call commercial algorithms proprietary, and Celler and colleagues (Chapter 7) describe them as "closely guarded trade secrets that are not subject to independent critique and validation". By these accounts, the ratios inside a finished monitor are not published.

The ratios also rest on the peak, and the peak is less simple than the principle suggests. Chandrasekhar and colleagues found that the cuff pressure at the largest oscillation is a weighted average of systolic and diastolic pressure, with weights of 0.45 and 0.55. They also found that the true ratios varied between patients over a range of 0.5 to 0.6. A single population ratio therefore fits some patients and misses others.

The ratio a maker chooses moves its monitor's systolic estimate. In a 2018 study, Celler and colleagues tested six finished monitors on a simulator, which gave every monitor the same pulses. In their analysis, the systolic ratio that best matched auscultation, the stethoscope method, was 0.565. Three monitors from Chinese makers behaved as if they used a ratio of about 0.46 and overestimated systolic pressure by 6.2 mmHg on average. The other three, one German and two Japanese, behaved as if they used about 0.65 and underestimated it by 4.8 mmHg. Above the cuff pressure of the largest oscillation, where systolic pressure is read, the envelope grows as the cuff pressure falls, so a smaller ratio is reached at a higher cuff pressure and gives a higher systolic reading. On the same simulated pulses, the two groups' average systolic errors lay 6.2 plus 4.8, about 11 mmHg, apart.

The estimate is defined against a reference method on people, not against a manometer (Chapter 24). Microlife, for example, ties its home monitor's estimate to the Korotkoff method (Chapter 1), phase I of the sounds for systolic and phase V for diastolic pressure.

22 — One envelope, three systolic ratios

The algorithm's estimateFocal detail

The record and what it inherits

The last computing steps are rounding and units, and each is a quantization of its own. The firmware rounds its counts to the display's 1 mmHg (Chapter 8). A monitor that can also show kilopascals must convert, and the conversion rounds a second time. Under India's rule for automated sphygmomanometers, the display's scale interval, the step between two shown values, is 0.1 kPa or 1 mmHg (Chapter 8). The two steps are not equal: at 133.322387415 Pa to the millimeter of mercury (Chapter 3), 0.1 kPa, which is 100 Pa, is 0.75 mmHg.

Firmware that rounds in one unit and then converts the rounded value into the other rounds twice, and the second rounding can move the shown digit. A cuff pressure of 150 mmHg is 150 times 133.322 Pa, or 19.998 kPa, shown as 20.0. A cuff pressure of 149.6 mmHg is 19.945 kPa and should show 19.9, but rounded first to 150 mmHg it shows 20.0, one step of the display too high.

23 — What the firmware does between the converter and the display

References and standardsThe signal in the chainThe algorithm's estimateReadingFocal detail

A reading becomes a record when the firmware stores it, and the record keeps every error the code made. The InsuLinx meter stored its wrong results in memory as well as showing them, so the stored history carried the same false values as the display. The monitor of Omron Healthcare's patent first filed in 2009 keeps its measurement data in nonvolatile memory, such as flash memory, which holds its contents when the power is off, so a stored value remains, right or wrong. Welch Allyn's Ambulo 2400 reports "SE 1" when it has no main calibration, and "HE 37" or "HE 18" when it is not calibrated or its calibration is corrupted, so its firmware checks the coefficients it depends on.

The memory itself can fail, and a monitor can report the failure rather than hide it. An error may occur at power-up in the NIBP EEPROM of Welch Allyn's patient monitors, as the maker describes in a 2012 bulletin. The name joins NIBP, non-invasive blood pressure, with EEPROM, a nonvolatile memory chip. When the error occurs, the monitor's display reads "NIBP Not Functional. Call for service." Welch Allyn states that the error does not constitute a risk to the patient, but it does not state what the memory holds.

From the memory the record passes to a phone, a clinic's system or a health record, and each link copies what the firmware computed without any means of checking it against the cuff. Software that computes a measured number therefore needs verification as a link of the chain in its own right. The International Electrotechnical Commission, the IEC, publishes the standard for that work, IEC 62304, Medical device software – Software life cycle processes. As of October 2026 the IEC lists it as the 2006 edition with its 2015 amendment and lists no second edition. Two consultancies describe a second edition in draft, and they disagree on how far the draft has progressed. The companion guide on medical device software and AI, The next patient, the next update, follows that life cycle in full. The accuracy of the firmware's corrections is also a requirement of the monitor's design (Chapter 25).

+ Part III · Uncertainty

How sure, in numbers.

A calibration laboratory writes a second, smaller number after a ± sign beside every pressure it reports. In 2020 a São Paulo laboratory issued a certificate for the pressure channel of a patient simulator, an instrument used to test blood-pressure monitors, and on it the line for 150 mmHg carries ±0.09 mmHg. With that number the laboratory states how sure it is of its own result. A monitor's displayed reading carries the same kind of doubt, although the monitor prints none. Each stage of the signal chain in Part II adds an error of its own to the cuff-pressure reading, and the engineer can state in numbers the doubt that those errors leave. In Chapter 10 the engineer works out how widely repeated readings scatter, and in Chapter 11 combines every source of error from the cuff to the display into one figure. In Chapter 12 the engineer reads what the ± on a certificate promises, and in Chapter 13 the maker's test engineer turns a reading near a limit into a pass, a fail or a result that the test cannot decide.

+ The questionHow do you state the scatter of repeated readings as one number?

Ten numbers for one pressure

Ten readings of one steady pressure give ten slightly different numbers on the monitor's channel. The engineer holds the air in a rigid vessel at 150.0 mmHg and connects the vessel to the monitor's tube and to a reference manometer, a gauge far more accurate than the monitor (Chapter 14). The reference shows that the pressure holds steady, yet the sensor, the amplifier, the converter and the firmware return a slightly different value at each reading. In the method of the GUM, the international guide to uncertainty, repeated readings are assumed to differ because the influence quantities of Chapter 4, the conditions besides the pressure that act on a measurement, are never held completely constant.

The ten readings are assumed: a computer program generated them, because no published figure for this scatter in a commercial monitor could be found. The program drew them at random and rounded each value to 0.1 mmHg. That rounding step is an assumption too. It stands for readings that the engineer takes from the firmware before the display rounds them to whole millimeters of mercury, a rounding that would give most of them the same number and hide the scatter. In the order drawn, the ten readings are 150.9, 149.7, 150.2, 150.1, 150.3, 149.4, 149.8, 149.7, 149.6 and 149.7 mmHg.

The mean and the spread around it

From the ten readings the engineer wants two numbers: a best value for the pressure, and a measure of how widely the readings spread around it, which says how closely one reading is likely to repeat another. The best estimate of a quantity from independent readings is their arithmetic mean, or average, by the GUM's rule. The engineer adds the ten readings, which come to 1,499.4 mmHg, and divides the sum by 10 to obtain a mean of 149.94 mmHg. The mean lies 0.06 mmHg below the reference's 150.0 mmHg. The program put no systematic error into the readings, so chance alone has moved the mean.

For the spread, the engineer starts from each reading's distance from the mean, its deviation. The ten deviations run from 0.54 mmHg below the mean to 0.96 mmHg above it, and positive and negative deviations always add to zero, so their sum cannot measure the spread. To obtain the standard deviation, the engineer squares each deviation, which makes every one positive, adds the squares and divides the total by one less than the number of readings. The square root of the result, which returns it to the readings' own unit, is the standard deviation. The divisor is 9 rather than 10 because the ten deviations must add to zero, so any nine of them fix the tenth, and that count of 9 is the degrees of freedom, in the GUM's term. For the ten readings the squares add to 1.744 mmHg², and the standard deviation comes to 0.44 mmHg.

The program drew the readings from a bell curve, the normal distribution of statistics. A bell curve makes values near its center more likely than values far from it, and it falls away in the same way on both sides. Its standard deviation sets its width, so a curve with a standard deviation of 0.4 mmHg is twice as wide as one with 0.2 mmHg. The program's curve was centered on 150.0 mmHg with a standard deviation of 0.4 mmHg, and both settings are assumptions, chosen to illustrate the method. The ten readings estimate that 0.4 mmHg as 0.44 mmHg, close but not equal, because ten draws sample the curve only coarsely.

24 — Ten readings of one pressure, and the spread around them

The quantity being measuredReferences and standardsUncertaintyReadingFocal detail

A mean is surer than one reading

When the engineer averages the ten readings, high and low readings partly cancel, so the mean varies much less than a single reading, which can land anywhere under the bell curve. How much the mean varies is measured by the standard deviation of the mean, which by the GUM's rule is the standard deviation of single readings divided by the square root of their number. The square root comes from Chapter 5's rule for adding independent noises: the sum of ten readings holds ten times the pressure but only the square root of 10 times one reading's scatter. Dividing the sum by 10 therefore divides the scatter by the square root of 10, about 3.16, and the mean's standard deviation is 0.44 divided by 3.16, or 0.14 mmHg. The mean's distance of 0.06 mmHg from the reference is less than half of that figure, so chance explains it.

Because of the square root, each extra reading improves the mean less than the one before. Four times as many readings halve the standard deviation of the mean, because the square root of 4 is 2: 40 readings would bring it from 0.14 to about 0.07 mmHg, and 160 readings to about 0.035 mmHg. To divide it by ten, the engineer needs a hundred times as many readings, since the square root of 100 is 10. Repetition therefore helps most at the start, and the engineer stops adding readings once the mean's standard deviation is small beside the other sources of error that the engineer combines with it in Chapter 11.

Working out the doubt by statistics on a series of readings, as the engineer has done here, is a Type A evaluation in the GUM's term, and ten readings is the count that two common rules of practice name. Europe's accreditation bodies, working together as the European co-operation for Accreditation, EA, warn that a Type A evaluation resting on fewer than ten readings needs its reliability considered. A balance's repeatability is tested by weighing one test weight not less than ten times under the US Pharmacopeia's chapter on balances, as Mettler-Toledo and Troemner, two companies that sell weighing equipment, describe it. Neither EA nor the two companies say that ten readings are enough for every purpose: EA treats fewer than ten as a reason for caution, and the pharmacopeia's chapter, as the two companies describe it, does not allow fewer. The engineer therefore takes ten as a floor, not as a count that suits every test.

The standard deviation of the mean applies only to a result that is itself a mean. A monitor in use takes one reading of the cuff pressure at each moment, so the doubt that scatter adds to that reading is the standard deviation of a single reading, 0.44 mmHg, and not the 0.14 mmHg of a mean of ten. UKAS, the UK's accreditation body, applies the same rule to a weighing in a worked example: it finds a repeatability of 8.7 mg from ten readings, and because the result is the mean of three, it divides 8.7 mg by the square root of 3 and obtains 5.0 mg. Ten readings estimate the scatter, and the number of readings averaged into the result sets the divisor.

How large is 0.4 mmHg?

The electronics alone scatter far less than 0.4 mmHg. In Texas Instruments' reference design for a blood-pressure monitor, the front end of Chapter 5 adds less than 10 µV of noise from peak to peak, by TI's own claim rather than a measurement. The figure is input-referred, expressed as if the noise entered at the amplifier's input beside the sensor's signal, which is about 112 µV for each millimeter of mercury (Chapter 4). Divided by 112 µV per mmHg, 10 µV of noise is below 0.09 mmHg from peak to peak. Dividing 0.09 mmHg by 6.6, the peak-to-peak factor that the converter maker Analog Devices uses (Chapter 5), gives about 0.014 mmHg as a standard deviation. The design's converter steps in about 0.11 mmHg, the quantization step of Chapter 8, so the front end's scatter is smaller than a single count of the converter that reads it.

Laboratory calibrations of mechanical blood-pressure gauges give a measured scatter for a whole instrument. In a bench study published in 2021, Ramírez-Barrera and colleagues at the Instituto Tecnológico Metropolitano in Medellín, Colombia, calibrated four aneroid sphygmomanometers, the mechanical dial gauges of Chapter 2. The institute funded the work, and none of the authors worked for a company. Ramírez-Barrera and colleagues report their scatter as a figure for a mean, not for a single reading. For the first instrument at 120 mmHg they report a Type A figure of 0.42 mmHg, which they compute as the standard deviation of the instrument's repeated readings divided by the square root of their number, the rule for the standard deviation of a mean.

25 — How large 0.4 mmHg is, beside what sources give

The signal in the chainNoise and errorUncertaintyLimits and decisionsReadingFocal detail

The assumed channel scatters about 29 times as much as its electronics, since 0.4 mmHg divided by 0.014 mmHg is about 29. If the whole channel scattered that much, almost all of its scatter would come from causes outside the front end and the converter, and no maker or study gives a figure for those causes in this channel. The generated mean's 0.14 mmHg is about a third of the aneroid gauge's 0.42 mmHg, and both are standard deviations of a mean. Ramírez-Barrera and colleagues do not state how many readings each mean contains, so the engineer cannot recover the aneroid gauge's single-reading scatter from their figure.

A repeatability test on the real channel would measure the channel's own scatter. In Chapter 11 the engineer combines the sources of error in the channel, and the electronics' noise is the only scatter for which a maker gives a figure. A measured scatter of the whole channel would enter there as a source of its own. At 0.44 mmHg it would be about as large as the largest source left after correction, the 0.46 mmHg that Chapter 11 derives from OIML's limit for the reference manometer. The engineer who runs the test therefore learns either that the channel repeats about as well as its electronics or that it has a source of scatter that no data sheet shows.

Repeatable is not the same as right

A small scatter shows that a channel repeats, not that it reads the true pressure. Every reading can lie the same distance from the true pressure, and the standard deviation measures distances from the mean, so an offset that every reading shares leaves the standard deviation unchanged. The aneroid gauges show the difference. The fourth of them, the gauge of Chapter 2's solved example, had a Type A figure of 0.28 mmHg at 120 mmHg, smaller than the first instrument's 0.42 mmHg. Yet at that pressure it read 2.43 mmHg below the reference, an error of −2.43 mmHg. The gauge repeated well and was still wrong by more than 2 mmHg, which is the difference between precision and accuracy that Chapter 2 named.

The engineer corrects an offset before counting any scatter, because in the GUM's method a result is assumed to have been corrected already for all recognized significant systematic effects (Chapter 2). The engineer therefore measures an error such as the fourth gauge's 2.43 mmHg by calibration and removes it by adjusting the gauge or correcting its readings (Chapter 14), and only then counts its 0.28 mmHg of scatter as part of the doubt. But the engineer does not correct an offset that chance has made, such as the generated mean's 0.06 mmHg below the reference. A correction based on it would shift every later reading by a chance amount instead of removing an error.

The engineer keeps a reading that lies far from the others unless the record shows a mistake. In the generated set, 150.9 mmHg lies 0.96 mmHg above the mean, more than twice the standard deviation. Yet the program drew it from the same bell curve as the other nine, so it belongs to the scatter. An engineer who left it out would understate the scatter, because the other nine readings have a standard deviation of only about 0.3 mmHg. A true mistake is different: blunders in recording or analyzing data can introduce a significant error of unknown size, and measures of uncertainty are not meant to account for such mistakes, as the GUM notes. The engineer therefore removes a reading written down as 159.0 instead of 150.9 mmHg because the record shows its cause, not because it lies far from the others.

The display step can hide the scatter

The monitor's display shows whole millimeters of mercury, and after rounding to that step only the readings that cross a boundary between two displayed values show any scatter. Rounded, the ten generated readings become 151, 150, 150, 150, 150, 149, 150, 150, 150 and 150 mmHg. Eight are identical, and only two, which happened to cross the boundaries at 150.5 and 149.5 mmHg, differ from them. The standard deviation of the rounded readings, 0.47 mmHg, lands close to the fine readings' 0.44 mmHg by chance, but it now depends on two readings instead of ten.

26 — What the 1 mmHg display does to the same readings

UncertaintyReadingFocal detail

A channel centered on 150.0 mmHg that scattered by only 0.2 mmHg would seldom cross either boundary, so ten displayed readings would usually all show 150, a standard deviation of zero from a channel that still scatters. Such a display hides the scatter, because its step of 1 mmHg is coarser than the scatter it would have to show (Chapter 8). For a Type A evaluation the engineer therefore takes readings finer than the display, either from the firmware's value before rounding, as the generated set assumes, or from a service mode if it shows a finer step. The engineer then counts the display's own step as a separate source of error, so that the rounding is counted once and in its own place (Chapter 11).

+ The questionHow do many small doubts combine into one, and which of them matters?

One method for every doubt

At one moment of a measurement, the air in the cuff of the blood-pressure monitor from the earlier chapters stands at 150 mmHg. Before the display can show 150, the sensor turns that pressure into a voltage, an amplifier multiplies the voltage, a converter turns it into a number, and the monitor's firmware converts the number into the reading on the display. Each stage can add an error of its own, and the engineer who designs the monitor cannot know any of those errors exactly, only how large each one may be. In Chapter 10 the engineer evaluated one source of doubt, the scatter of repeated readings. With the method of the GUM, the engineer combines that scatter with every other source into one statement of how sure the reading is, and can then see which source decides the result. The GUM, the international guide to uncertainty, takes its short name from its title, Guide to the expression of uncertainty in measurement. ISO published the GUM in 1993 in the name of seven international organizations.

The engineer works through the method in four steps. First, the engineer writes down the reading's measurement model: how the reading depends on the pressure in the cuff and on every error that each stage can add to it. Second, the engineer gives each of those inputs a standard uncertainty, which the GUM defines as an uncertainty "expressed as a standard deviation". Third, the engineer multiplies each standard uncertainty by a factor that converts it into millimeters of mercury, the unit of the display. Fourth, the engineer squares the converted values, adds the squares and takes the square root of the sum. That root is the reading's combined standard uncertainty, and the table that lists the inputs row by row, with what each one contributes, is the uncertainty budget.

Each standard uncertainty comes from one of two kinds of evaluation. In a Type A evaluation the engineer analyzes a series of observations statistically, as in Chapter 10 with repeated readings. In a Type B evaluation the engineer uses any other knowledge: a maker's data sheet, a calibration certificate, a limit set by a standard or the step of a display. Both kinds rest on probability distributions, as the GUM states, so a standard uncertainty derived from a figure in a data sheet is a standard deviation in the same sense as one computed from readings. An engineer can therefore add a maker's specification and a measured scatter in one budget.

From the cuff to the display

The budget's first inputs come from the sensor. A tube carries the pressure of the air in the cuff to the sensor inside the monitor. In its Low-Cost Blood Pressure and Heart Rate Monitor Reference Design, Texas Instruments uses the Omron 2SMPP-03, a small silicon sensor built as a bridge of piezoresistors (Chapter 4). A constant current of 100 µA drives the bridge, and pressure on the silicon unbalances it, so that a small voltage appears across the bridge's output. Omron gives the sensor's span as typically 42.0 mV for a full scale of 50 kPa, which is about 375 mmHg. The sensor therefore produces 42.0 mV divided by 375 mmHg, about 112 µV for each millimeter of mercury, and every later stage works with that small voltage.

Omron also gives the tolerance on each typical value, the amount by which a single sensor may differ from it. One sensor may have an offset anywhere within 4.0 mV of the typical value, and its span may lie anywhere within 5.5 mV of the typical 42.0 mV. Omron gives the remaining figures in percent of full scale, written %FS. The sensor's output departs from a straight line by 1.3 %FS at most, a departure called nonlinearity. At any one pressure, the output with the pressure rising and the output with it falling differ by no more than 0.2 %FS, and that difference is the sensor's hysteresis.

In TI's design an instrumentation amplifier multiplies the bridge's output by 50, one of the two gain settings TI gives. The front end adds an input-referred noise of less than 10 µV from peak to peak, by TI's figure (Chapter 5). A 12-bit converter with a 2.5 V reference then turns the amplified voltage into a count, and one count corresponds to about 0.11 mmHg at the cuff, the quantization step of Chapter 8. The converter can also oversample by 128 times in hardware, a way of resolving finer steps that Chapter 8 explains. The engineer can still take the coarser step of a single count, because even that step turns out to be small in the budget. The firmware converts counts into pressure with coefficients set at calibration (Chapter 9). The display then rounds the result to whole millimeters of mercury, the display resolution of 1 mmHg that Microlife, a monitor maker, states for two of its monitors.

The budget is judged against a limit on the cuff-pressure reading. OIML sets that limit in its rules for automated sphygmomanometers. A monitor must read the cuff pressure to within ±3 mmHg or 2 % of the reading, whichever is greater, at any point of its range, with the pressure rising or falling, and at any temperature from 10 to 40 °C. The two branches of the limit meet at 150 mmHg, where 2 % of the reading is exactly 3 mmHg, and the engineer works the budget at that pressure. Microlife and A&D, another maker, each state the same ±3 mmHg as the accuracy of the cuff pressure.

Temperature also moves the offset and the span. Omron sums up the effect between 0 and 85 °C as ±5.0 %FS on the offset and ±3.0 %FS on the span, and its table shows each figure as a spread around a typical shift. At 0 and 50 °C, either side of OIML's band of 10 to 40 °C, the table keeps the offset within 4.0 %FS and the span within 3.0 %FS of their values at 23 °C. Within OIML's band the two summary figures therefore cover the largest shifts in the table, and the engineer takes ±5.0 %FS and ±3.0 %FS as the limits of the two temperature rows.

27 — The cuff-pressure channel, stage by stage

References and standardsThe signal in the chainNoise and errorUncertaintyReadingFocal detail

Each figure becomes a standard uncertainty in mmHg

Most of those figures are limits, not standard deviations. When Omron gives the offset as within 4.0 mV of its typical value, it states only that the true offset of one sensor lies somewhere in that band, and it gives no reason to expect one value more than another. The GUM calls such a band a rectangular distribution, or a flat distribution: every value inside the limits is equally likely, and no value outside them is possible. The distance from the center of a flat distribution to either limit is its half-width.

The standard deviation of a flat distribution is its half-width divided by the square root of 3. The square root of 3 is about 1.732, so the standard deviation is about 0.58 times the half-width. The display gives the simplest case, because it rounds to whole millimeters of mercury. A reading of 150 mmHg therefore stands for any pressure from 149.5 to 150.5 mmHg, a half-width of 0.5 mmHg, and 0.5 divided by 1.732 gives a standard uncertainty of 0.29 mmHg. The sensor's hysteresis limit of 0.2 %FS is 0.2 % of 375 mmHg, or 0.75 mmHg, and 0.75 divided by 1.732 gives 0.43 mmHg. In OIML's test procedure a laboratory compares an automated monitor with a reference manometer, and OIML allows that reference a maximum error of ±0.8 mmHg. Divided by 1.732, that limit gives 0.46 mmHg.

28 — A limit as a flat distribution

References and standardsThe signal in the chainUncertaintyReadingFocal detail

Two other kinds of figure need divisors of their own. A calibration certificate needs no assumed distribution, because it states its uncertainty as a multiple of a standard deviation, and dividing by that multiple, usually 2, gives the standard uncertainty (Chapter 12). TI states its noise from peak to peak. The peak-to-peak value most commonly used is 6.6 times the noise's standard deviation, a size that the noise exceeds only 0.1 % of the time, as a tutorial by Analog Devices, a maker of amplifiers and converters, notes. The engineer therefore divides a peak-to-peak figure by 6.6 to obtain a standard deviation (Chapter 5).

Every row must be in millimeters of mercury, the unit of the display, but Omron gives the offset and the span in millivolts. The GUM calls the converting factor a sensitivity coefficient: the rate at which the result changes when one input changes. The sensor's sensitivity in Chapter 4's sense is 112 µV for each millimeter of mercury, and the coefficient for a voltage at the bridge is its inverse, one millimeter of mercury for each 112 µV. An offset half-width of 4.0 mV, divided by 0.112 mV for each millimeter of mercury, therefore becomes a half-width of about 35.7 mmHg, and 35.7 divided by 1.732 gives a standard uncertainty of 20.6 mmHg.

To refer the converter's step back to the cuff, the engineer divides one count, 2.5 V divided by 4,096 or about 0.61 mV, by the amplifier's gain of 50. That gives 12.2 µV at the bridge, and the sensor's coefficient turns it into 0.11 mmHg. TI's noise figure needs only the sensor's coefficient, because TI states it at the amplifier's input.

The span tolerance works differently, because an error in the span scales every reading in proportion. A span half-width of 5.5 mV is 13.1 % of the typical 42.0 mV, so at a reading of 150 mmHg the error can reach 13.1 % of 150 mmHg, about 19.6 mmHg. The coefficient of that row is the reading itself, and the same sensor therefore makes a larger error at 250 mmHg than at 150 mmHg. The temperature effect on the span scales with the reading in the same way.

Standard uncertainties add as squares

If the engineer added up the sensor's six limits, the total would describe a sensor in which every error sits at its limit, in the same direction, at the same moment. Independent errors seldom all act in the same direction: some push the reading up while others push it down. Omron gives each limit separately and states no link between a sensor's offset and its span, so the engineer treats the rows as independent. For independent errors the square of the combined standard deviation is exactly the sum of the squares of the separate ones. That fact is the reason for the method's fourth step, which is called the root-sum-of-squares.

Squaring also changes which rows matter, because a row twice as large as another counts four times as much in the total. The largest one or two rows therefore set the result, and the small ones contribute almost nothing. The row with the largest share of the total of squares is the budget's dominant contributor.

In the bare sensor, taken as Omron states it before any correction, each of the six limits, in millimeters of mercury and divided by 1.732, gives a standard uncertainty at 150 mmHg. They are 20.6 mmHg for the offset, 11.3 for the span, 10.8 for the temperature effect on the offset, 2.8 for the nonlinearity, 2.6 for the temperature effect on the span and 0.43 for the hysteresis, and the square root of the sum of their squares is about 26 mmHg. The offset dominates with 62 % of the total of squares, the span tolerance follows with 19 % and the temperature effect on the offset with 17 %. The bare sensor's 26 mmHg sits behind a display that steps in single millimeters of mercury, a plain case of the difference between resolution and accuracy that Chapter 8 described.

Auto-zero and calibration remove the largest rows

The monitor's firmware removes most of the sensor's error. Before each measurement the firmware can take the sensor's output at zero pressure as its zero, a step called auto-zero that Chapter 17 describes. It then subtracts that zero reading from every reading that follows, and the offset, present in both readings, cancels. The temperature effect on the offset cancels too, as long as the sensor's temperature holds steady between the zero reading and the measurement. Together the two rows, at 62 % and 17 %, make up 79 % of the bare sensor's total of squares.

In a calibration the monitor and a reference manometer then read the same pressures, and in the adjustment that follows, the firmware stores coefficients that make the monitor's readings agree with the reference's (Chapters 9 and 14). Together the two steps remove the span tolerance, 13 % of the typical span, from the budget, but the reference's own uncertainty enters in its place: OIML's limit of ±0.8 mmHg for the reference manometer, 0.46 mmHg as a standard uncertainty. The firmware can also reduce the nonlinearity with a table of corrections at several pressures, and the temperature effect on the span with a temperature correction. Neither Omron nor TI states how much error those two corrections leave behind, so the engineer lists those two residuals in the budget by name, without a number.

The hysteresis stays in the budget. The firmware applies a single correction at each pressure, but the sensor's output at that pressure can differ by up to 0.75 mmHg between rising and falling pressure, and the monitor must meet OIML's limit in both directions. A calibration made with the pressure moving one way leaves the readings taken the other way off by the whole difference, so the engineer takes 0.75 mmHg as the half-width of the hysteresis row. In their 2021 study of the uncertainty in calibrating four aneroid sphygmomanometers (Chapter 10), Ramírez-Barrera and colleagues take a hysteresis difference as the full width of a flat band instead. That choice fits a correction set midway between the two directions, and by halving the half-width it gives a standard uncertainty of about 0.22 mmHg here instead of 0.43 mmHg. The engineer keeps the larger figure, because neither Omron nor TI says where between the two directions a monitor's correction sits.

Taken together, the corrections change which rows decide the result. After auto-zero and calibration, the five rows that carry a number give a combined standard uncertainty of 0.70 mmHg, and three of them supply almost all of it: the reference manometer, the hysteresis and the display step. The converter step and the front end's noise add almost nothing.

29 — The doubts at 150 mmHg, drawn as squares

References and standardsNoise and errorUncertaintyFocal detail

Where the method stops

The root-sum-of-squares rests on two assumptions, and the first is that the inputs are independent. Two inputs that share a cause move together rather than at random, and the GUM deals with them in a separate clause on correlated inputs, in which each related pair adds a term of its own to the total of squares. The term can be large: in the GUM's book of worked examples, first published in 2026, counting the correlations between the inputs of a chemical analysis raises its total of squares by about a third.

The second assumption is that each input moves the result in proportion. In the GUM's words the rule is valid "to first order": it keeps only the part of each input's effect that is in proportion to that input. The GUM adds that this first-order rule is usually an adequate approximation. Amendment 1 to the GUM, published in 2026, adds a note for models that depart significantly from a straight line: for such a model the engineer can apply a Monte Carlo method, which the GUM's first supplement describes. A computer running the method draws a value for every input from its distribution, computes the result, repeats the draw many times over and reads the uncertainty from the spread of the results. As of October 2026 the JCGM lists the 2008 text of the GUM, with that amendment, as current.

Two limits of the method could apply to the monitor's budget, and neither does. The amendment concerns a model that departs from a straight line, and the monitor's model does not: each input moves the reading in proportion, with a coefficient of 1 for most rows and the reading itself for the two span rows. The GUM's first supplement adds a warning about a budget in which one flat input supplies almost all of the total of squares, because the combined result then keeps that flat shape instead of approaching a bell curve. The corrected channel's three leading rows are all flat, but none of them supplies even half of the total of squares: the reference manometer supplies 44 %, the hysteresis 39 % and the display step 17 %. Added together, three flat rows of comparable size give a distribution close to a bell curve, as EA states for any three or more such contributions (Chapter 12), so the supplement's warning does not apply to this budget.

The budget ends at the cuff-pressure reading. The monitor also reports systolic and diastolic values, which it computes from the oscillations in the cuff pressure with an algorithm (Chapter 9), so their error is not a row in this budget. Chapter 24 shows how a clinical study validates those values against a reference measured on patients rather than against a manometer.

+ The questionWhat does a "±" at about 95 % promise, and how do you read it off a certificate?

Two pages from a pressure laboratory

An accredited calibration laboratory prints a small number beside each reading it reports, and a real certificate shows what that number promises. On 9 February 2024 Mensor's calibration laboratory in San Marcos, Texas, calibrated a CPG2400 for the Washington State Patrol and issued a two-page certificate. The CPG2400 is a digital pressure gauge with a silicon pressure sensor, made by Mensor. The gauge reads absolute pressure, measured from vacuum rather than from the air around it (Chapter 4). Its range runs from 8 to 17 pounds per square inch, written psi, about 55 to 117 kPa. That is the range of the air's own pressure, so the gauge serves as a barometric reference and not as a reference for a cuff, but the engineer reads a cuff tester's certificate in the same way.

Mensor's laboratory applied 11 pressures, rising from 8 to 17 psi and falling back, and recorded each on its own line with the reference's value, the gauge's reading, the error as a percentage of the reading and the word "Pass". At about 15.2 psi on the rising side, for example, the reference stood at 15.19995 psi and the gauge read 15.2017 psi. Mensor gives the error as 0.0116 % of the reading, inside the gauge's limit of error of 0.030 % of the reading. Beside every line stands the small number, which grows from 0.00019 at 8 psi to 0.00038 at 17 psi. The heading of that column is not legible in the copy the patrol published, so the engineer reads its figures as psi, the unit of the reference and reading columns. Mensor explains the number in one sentence: "The combined and expanded uncertainty is reported at K=2 providing an approximate 95% confidence level."

Why the factor is 2

A combined standard uncertainty is one standard deviation, a measure of spread, while anyone who uses a reading needs a band that very probably holds the true value. The engineer obtains that band, the expanded uncertainty, written U, by multiplying the combined standard uncertainty by a number called the coverage factor, k. The chance that the band holds the true value is its coverage probability. The European co-operation for Accreditation, EA, requires accredited calibration laboratories to use k = 2, which gives a coverage probability of approximately 95 %.

In Chapter 11 the engineer ended with a combined standard uncertainty of 0.70 mmHg for the monitor's reading at 150 mmHg. Twice 0.70 mmHg is 1.4 mmHg, so that reading carries an expanded uncertainty of ±1.4 mmHg. Because U is the combined standard uncertainty multiplied by k, the step also runs backward: an engineer who receives a certificate divides its U by its k to obtain the standard uncertainty for a budget like Chapter 11's.

The 95 % rests on the bell curve of Chapter 10. A band with k = 2 reaches two standard deviations on each side of the reading. A bell curve holds 95.45 % of its values within that distance of its center, and exactly 95 % would need a factor of 1.96, as UKAS, the UK's accreditation body, notes. Laboratories therefore write "approximately" or give both figures. A São Paulo laboratory writes "aproximadamente 95,45%" on its certificate for a patient simulator, and NIST, the US national metrology institute, writes "approximately 95 percent (95.45 %)" in its example certificate for weights and measures laboratories. EA and UKAS call the figure a coverage probability and the two certificates call it a confidence level, but all of them attach it to the same factor of 2.

A factor of 2 gives about 95 % only under two conditions, which EA sets out: the result follows a bell curve closely, and its combined standard uncertainty is reliable. A result built from three or more contributions of comparable size approaches a bell curve, even when the contributions themselves are flat, as EA explains. The monitor's corrected channel in Chapter 11 meets the first condition, with three flat rows of similar size.

30 — From one standard uncertainty to a ± at about 95 %

UncertaintyReadingFocal detail

When the factor is not 2

When a standard uncertainty rests on few readings, the second condition fails and the factor grows, because a standard deviation computed from a few readings is itself uncertain. Chapter 10's ten readings showed this: drawn from a bell curve with a standard deviation of 0.4 mmHg, they estimated it as 0.44 mmHg. EA accepts the factor of 2 as reliable only if no contribution comes from a Type A evaluation of fewer than ten readings. Otherwise the engineer computes the result's effective degrees of freedom, a count derived with EA's formula from the degrees of freedom of each contribution, and reads k from EA's table. With 4 degrees of freedom the table gives k = 2.87, with 9 it gives 2.32 and with 10 it gives 2.28. As the count grows without limit, the factor falls to 2.00.

With few readings the table makes U larger. Chapter 10's ten readings meet EA's condition, so EA accepts k = 2 for their mean, although its table gives 2.32 for the 9 degrees of freedom of ten readings. Had the engineer taken k from the table instead, 2.32 times the mean's standard deviation of 0.14 mmHg would have given 0.32 mmHg, against the 0.28 mmHg that k = 2 gives.

Ramírez-Barrera and colleagues met the same effect in a real budget, in their bench calibrations of four aneroid gauges in Medellín, published in 2021 (Chapter 10). For the first gauge at 120 mmHg they report a combined standard uncertainty of 0.672 mmHg, 19.22 effective degrees of freedom and an expanded uncertainty of ±1.4 mmHg. They take k from the effective degrees of freedom, and EA directs the engineer to round 19.22 down to 19, for which its table gives 2.14. The product of 0.672 mmHg and 2.14 is 1.44 mmHg, which fits the printed ±1.4 mmHg, while k = 2 would have given 1.3 mmHg.

When one row, the budget's dominant contributor, supplies almost all of the total of squares, it also moves the factor away from 2. When that contributor is a Type A evaluation, its degrees of freedom set the factor through the same statistics as EA's table, as a worked example by UKAS shows. When it is a flat Type B limit, the result keeps the flat shape of Chapter 11 instead of approaching a bell curve, and UKAS works this case through with a digital voltmeter's limit. The monitor's corrected channel has no such row: its largest row supplies 44 % of the total of squares and two others supply most of the rest, so the factor of 2 serves it.

A certificate read line by line

The engineer reads a certificate as a series of checks, and each item on Mensor's certificate answers one of them. First the engineer confirms that the certificate describes the instrument in hand: Mensor names the issuer, its procedure and accreditation mark, the customer, and the gauge's serial number, sensor and range. Next the engineer finds the limit that the gauge was judged against, 0.030 % of the reading, because "Pass" means nothing without it. The two dates show how long the result is meant to serve: the calibration on 9 February 2024 and the recalibration due on 9 February 2025.

The as-found calibration is meant to describe the gauge as it arrived, but Mensor records that the zero was adjusted by 0.001 psi before it. Those readings therefore describe the gauge after a small adjustment, not exactly as it arrived, and the engineer keeps the adjustment and the calibration apart, as Chapter 14 does.

The word "Pass" rests on a rule that Mensor states: an asterisk would mark any point exceeding the limit of error on "simple acceptance regardless of uncertainty". "Pass" therefore compares the measured error alone with the limit and leaves the uncertainty out, a rule that Chapter 13 examines. None of the eleven lines carries an asterisk, and every error lies below 0.012 % of the reading, under half of the 0.030 % limit. The gauge passed at every point.

The engineer also follows the chain one link up from the gauge. Mensor names the reference it used, listed as DH CPD 8000, whose own calibration falls due in December 2024, and that reference is the next link (Chapter 15). Mensor also states its route of traceability: A2LA, the American Association for Laboratory Accreditation, accredits Mensor's laboratory, and A2LA had signed the arrangement in which the members of ILAC, the international cooperation of accreditation bodies, recognized one another's accreditations. On 1 January 2026 that arrangement passed into a single new one under Global ACI, which replaced ILAC and lists A2LA among the accreditation bodies it recognizes (Chapter 16).

31 — A pressure certificate, read line by line

References and standardsNoise and errorUncertaintyLimits and decisionsReadingFocal detail

A tester's certificate in the cuff's range

A patient simulator that tests monitors is calibrated in the cuff's own range. On 2 March 2020 LRM, the Laboratório de Referência Metrológica in São Paulo, calibrated the non-invasive pressure channel of a Rigel Uni-SiM, one such simulator, and issued a four-page certificate. LRM reports its results for non-invasive pressure in 13 lines, from 30 to 300 mmHg, with readings to 0.01 mmHg. For each it gives two pressures, the error between them in mmHg and in percent, the expanded uncertainty and k = 2.00. The uncertainty rises from 0.02 mmHg at 30 mmHg to 0.18 mmHg at 300 mmHg, and at 150 mmHg it is 0.09 mmHg. LRM states no limit and no conformity and says that its results refer only to the instrument calibrated, so the engineer receives measurements with their uncertainty and no verdict.

The certificate does not give the simulator's accuracy between calibrations, and for that the engineer turns to the maker. Rigel Medical's own manual for the Uni-SiM lists an accuracy of ±0.5 %FS beneath the entry for its digital manometer, a limit for the instrument in use. The manometer's range is 0 to 410 mmHg and the simulator's built-in pump covers 0 to 350 mmHg, but the manual does not say which full scale the percentage takes. The engineer therefore cannot tell whether the limit is 0.5 % of 410 mmHg, which is 2.05 mmHg, or of 350 mmHg, which is 1.75 mmHg. The certificate's 0.09 mmHg, by contrast, describes one calibration on one day. NIST states the difference in its example certificate: "The expanded uncertainty is not to be confused with a tolerance limit for the user during application."

The reference and the way each reading is formed decide how small a certificate's figures can be, because the reference's own uncertainty and the scatter of the readings both enter the budget (Chapter 11). The Meteorological Instrument Center of the Japan Meteorological Agency publishes a sample certificate for a barometer with its values masked. On that certificate the reference is a pressure balance, the piston loaded with masses that Chapter 15 describes. Each indication is the mean of six one-minute readings, a Type A evaluation, so averaging divides a single reading's scatter by the square root of 6, about 2.4 (Chapter 10).

One laboratory whose reference is itself a simulator claims far larger figures. In Chennai, an accredited calibration laboratory at IIT Madras uses a vital-sign simulator as its reference for the non-invasive blood-pressure channel of patient monitors, from 10 to 400 mmHg. Its scope of accreditation gives the smallest uncertainty it can claim there, its calibration and measurement capability (Chapter 16), as 9.56 % at the low end of the range and 0.93 % at the top, about 1.0 mmHg at 10 mmHg and 3.7 mmHg at 400 mmHg. Both lie far above the 0.09 mmHg that LRM printed at 150 mmHg with a standard manometer among its references.

Four to one

The engineer judges whether a certificate's U is small enough through one ratio. The test uncertainty ratio is the tolerance of the quantity tested, the limit its error must stay within, divided by the 95 % expanded uncertainty of the measurement that tests it, in ILAC's definition. In August 1988 the US Department of Defense wrote the four-to-one rule into its standard MIL-STD-45662A, whose clause on the adequacy of measurement standards reads: "the collective uncertainty of the measurement standards shall not exceed 25 percent of the acceptable tolerance for each characteristic being calibrated." An uncertainty of 25 % of the tolerance is a ratio of four to one.

The Department of Defense has since cancelled the standard, but civilian standards adopted its ratio: it passed into ANSI/NCSL Z540-1 in 1994, as Song of NIST records in a 1997 paper. The ratio is a practical substitute for controlling the risk of a wrong decision, as SIMCO, a calibration services company, describes it. A wrong decision becomes possible whenever a measured error lies within U of the limit, because the true error may then lie on the other side of it.

The successor standard replaced the ratio with the risk itself. In ANSI/NCSL Z540.3, published in 2006, NCSL International required that the probability of a false accept decision, accepting an instrument that is in fact outside its limit, "shall not exceed 2%", as Mimbs of NASA's Kennedy Space Center quotes it in a 2008 paper. The standard allowed a ratio of four to one or better when determining that probability was not practicable. NCSL International withdrew Z540.3 in October 2020 as superseded by ISO/IEC 17025:2017, the international standard for the competence of calibration and testing laboratories (Chapter 16).

The ratio remains in ILAC's guidelines of 2019, but the JCGM, the committee behind the GUM, warns in its guide on conformity assessment that such ratios "are sometimes ambiguously or incompletely defined". ILAC's guidelines add that a rule built on such a ratio must also specify what action to take, and one company's rule in Chapter 13 sets that action around the same 2 %.

For the monitor, the engineer sets the reference manometer against the ±3 mmHg limit. OIML allows the reference manometer a maximum permissible error of ±0.8 mmHg in its test procedure for automated sphygmomanometers. OIML states a limit rather than an uncertainty, but the engineer applies the ratio rules to it in the same way. Against ±3 mmHg, a reference within ±0.8 mmHg gives 3.75 to one, or 27 % of the tolerance, just short of the military four to one.

Germany sets a looser rule in its regulation on operating medical devices, the MPBetreibV: test equipment is accurate enough if its error limits and uncertainties do not exceed one third of those of the device tested. One third of 3 mmHg is 1 mmHg, so a reference within ±0.8 mmHg meets the German rule. The same reference fails four to one and meets one third, so the engineer records which ratio rule the test applies.

32 — Ratios against the ±3 mmHg limit at 150 mmHg

References and standardsUncertaintyLimits and decisionsReadingFocal detail

+ The questionWhen a reading lands near a specification limit, how should the decision be made?

A reading on the edge

A monitor on the production test reads exactly at the edge of its permitted error, and the test's own uncertainty reaches past the edge on both sides. The reference manometer holds the air in the test vessel at 150.0 mmHg, and the monitor's display shows 153, so the measured error is +3.0 mmHg. The maker's test engineer wrote this test and must now decide whether the monitor passes. The permitted error is ±3 mmHg or 2 % of the reading, whichever is greater, at any point of the range and with the pressure rising or falling, under R 149-1, OIML's rules for automated sphygmomanometers. India's rules for the same devices, Part VII-B, whose new text has been in force since July 2025, set the same limit (Chapter 30). Since 2 % of 150 mmHg is 3 mmHg, the two branches meet at 150 mmHg, as Chapter 11 showed, so the limit there is exactly 3 mmHg.

Above 150 mmHg the documents differ, so the engineer must name the one whose limit the test applies. OIML's and India's limit grows with the reading, to 5 mmHg at 250 mmHg, since 2 % of 250 mmHg is 5 mmHg. One maker, Zhuhai Yueja, states a flat cuff-pressure limit of ±3 mmHg at any measuring point under IEC 80601-2-30, the international standard for automated sphygmomanometers, whose 2018 edition is in force as of October 2026. The maker gives that limit in the summary of its 510(k), the premarket submission that Chapter 31 describes, and FDA, the US regulator, cleared that monitor. The summary is the maker's own document, and in it the maker names the standard for the monitor's performance testing without stating the edition. At 150 mmHg all three documents give 3 mmHg, so the monitor on the edge faces the same limit whichever one the engineer names.

The measured error of +3.0 mmHg is itself uncertain, and the engineer estimates by how much from the same kinds of error that a calibration laboratory counts. Chapter 11's five rows that carry a number describe the uncertainty of that error: the reference manometer, the hysteresis, the display step, the converter step and the noise. The German calibration service, DKD, counts rows of the same kind, among them the gauge's resolution and hysteresis, in the worked example of its guideline for calibrating pressure gauges. Doubled by Chapter 12's coverage factor of 2, the combined 0.70 mmHg of the five rows becomes an expanded uncertainty of 1.4 mmHg. The engineer takes that 1.4 mmHg as the expanded uncertainty of the error that the production test measures at 150 mmHg, an assumption that leaves out the two residuals that Chapter 11 named without a number. With about 95 % coverage, the monitor's true error then lies anywhere within 1.4 mmHg of the measured 3.0, from 1.6 to 4.4 mmHg, on both sides of the limit.

33 — One measured error, three acceptance limits

UncertaintyLimits and decisionsReadingFocal detail

Neither the limit nor the reading decides whether that monitor passes; the engineer needs a rule that says how the uncertainty counts. Calibration laboratories face the same question, and they answer it under ISO/IEC 17025, the standard against which they are accredited (Chapter 16). That standard defines a decision rule as a "rule that describes how measurement uncertainty is accounted for when stating conformity with a specified requirement", in the words that ILAC reproduces. The engineer's rule must relate two limits that ILAC keeps apart in its guidelines on decision rules; ILAC was the international cooperation of accreditation bodies until the end of 2025 (Chapter 16). The tolerance limit bounds the values that the property itself may take, here the monitor's true error. The acceptance limit bounds the measured values that the test will accept. A decision rule states where the acceptance limit sits relative to the tolerance limit, and for the monitor at +3.0 mmHg that position decides between pass and fail.

Simple acceptance shares the risk

Under the simplest rule the engineer passes every monitor whose measured error does not exceed the limit, so the acceptance limit equals the tolerance limit. ILAC calls this rule simple acceptance. The JCGM, the committee behind the GUM, describes the rule as important and widely used in its guide on conformity assessment, and notes that it is also known as shared risk. The monitor at +3.0 mmHg therefore passes, and whoever relies on it later carries the risk. Accepting an item that in fact lies outside its tolerance limit is a false accept, and under simple acceptance its probability may be as high as 50 %, by ILAC's guidelines. UKAS, the UK's accreditation body, places that 50 % at values on the tolerance limit, which is exactly where this monitor's reading lies: its true error is as likely to lie above the limit as below it.

Simple acceptance is common, and it suits a test whose uncertainty is small beside the limit. Mensor's laboratory states on the certificate of Chapter 12 that it applies "simple acceptance regardless of uncertainty". Taiwan's Bureau of Standards, Metrology and Inspection set a rule of the same kind for verifying mechanical sphygmomanometers in 2006: "the indication errors shall not exceed the maximum permissible error of verification", with no mention of the uncertainty of the test. Rules of that kind rely on a separate ratio rule for the reference, like those of Chapter 12. In legal metrology, the measurement that law regulates (Chapter 30), the usual criterion is an expanded uncertainty no larger than one third of the maximum permissible error, as the JCGM writes it, which is a ratio of three to one in Chapter 12's terms. A test uncertainty that small keeps the doubtful band narrow. That band holds the measured errors within one U of the limit, and at U's coverage probability of about 95 %, only for those could the true error lie on the other side of the limit.

The monitor's test does not meet that criterion. One third of 3 mmHg is 1 mmHg, while the test's 1.4 mmHg is 47 % of the limit, since 1.4 divided by 3 is 0.47. The doubtful band therefore runs from 1.6 to 4.4 mmHg, a wide stretch of the errors that a production line can produce. Inside that band the engineer must judge each monitor by its own measured value. The risk attached to one item is its specific risk, in the JCGM's term: the probability that this accepted monitor does not conform, or that this rejected one does.

The specific risk can be large even for a reading inside the limits, as the JCGM shows with an example from motor oil. The oil's viscosity, its resistance to flow, must lie between 12.5 and 16.3 square millimeters per second, written mm²/s, and the measured value is 13.6 mm²/s. The reading lies only 1.1 mm²/s above the lower limit, about 0.6 of its standard uncertainty of 1.8 mm²/s, and by the JCGM's figures the probability that the oil conforms is only about 66 %. Although the reading lies inside the limits, the chance that the oil lies outside them is therefore about one in three. For the monitor read on the limit itself, that chance is up to one in two.

A guard band moves the limit inward

To protect the user, the engineer moves the acceptance limit inside the tolerance limit. ILAC defines the guard band as the interval between a tolerance limit and the corresponding acceptance limit, and writes its width, w, as a multiple r of the expanded uncertainty: w = rU. A common choice is r = 1, so the guard band equals U.

ILAC states that with w = U the probability of a false accept is below 2.5 %. A reading at the acceptance limit lies one U inside the tolerance limit, so its true value lies beyond that limit only past the top of its 95 % band, where half of the 5 % outside the band lies. The JCGM writes the standard uncertainty as u, so that U = 2u, and gives the same case as w = 2u, with a false-accept probability of at most 2.3 % for a reading at the acceptance limit. The JCGM's figure is half of the 4.55 % outside a 95.45 % band, so the two figures differ only through Chapter 12's two conventions for coverage.

With w = U the engineer moves the monitor's acceptance limit from 3.0 to 1.6 mmHg, since 3.0 minus 1.4 is 1.6. A monitor whose measured error at 150 mmHg is 1.6 mmHg or less passes outright, because even the upper end of its uncertainty stays within the 3 mmHg limit. Near the limit the engineer need not force a pass or a fail, because ILAC allows statements with more than two outcomes in its guidelines. A measured result inside the guard band and below the tolerance limit is a "Conditional Pass". A result above the tolerance limit but below the tolerance limit plus the guard band, here 4.4 mmHg, is a "Conditional Fail", and only a result beyond 4.4 mmHg is a plain fail. A conditional result tells whoever relies on the monitor that the test cannot say on which side of the limit its true error lies.

The monitor at +3.0 mmHg falls exactly on the line between the two conditional outcomes, and ILAC's wording, "below" the tolerance limit for one and "above" it for the other, places it in neither. The engineer's rule must therefore say where a reading on a boundary goes, and ILAC expects the rule to be agreed before the measurements are taken.

A guard band set outward protects the person measured instead. In the JCGM's example of speed enforcement, the limit is 100 km/h and the threshold for a fine about 107 km/h. A driver is fined only when the measurement shows, with 99.9 % confidence, that the limit was exceeded. The inward band of a production test protects the other party, the person who later relies on the monitor.

One company's rule, with its numbers

A guard band can depend on the test uncertainty ratio of Chapter 12, as it does in the rule that Fluke Corporation publishes for stating conformity on its calibration certificates. Fluke applies no guard band when the ratio is at least four to one. Below that ratio Fluke moves the acceptance limit inward, by one of four methods that it names, two of them from ILAC's guidelines. With the first, Fluke subtracts U from the specification, the limit that the instrument must meet. With the second, a root-difference-square form, Fluke takes the square root of the specification squared minus U squared. Fluke bases its statements on an estimated false-accept risk of 2 %, the limit that ANSI/NCSL Z540.3 set (Chapter 12). Fluke issues a "conditional pass" when an error lies within the specification but the false-accept risk could exceed 2 %.

Fluke does not mention blood-pressure monitors in its policy, but the engineer can apply the policy to one. Since 3 divided by 1.4 is 2.14, the ratio of the 3 mmHg limit to the test's 1.4 mmHg is 2.1 to one, below four to one, so the policy calls for a guard band. With the first form the engineer subtracts U and reaches an acceptance limit of 1.6 mmHg, the same as ILAC's w = U. The root-difference-square form gives an acceptance limit of 2.65 mmHg: 3 squared minus 1.4 squared is 9 minus 1.96, or 7.04, its square root is 2.65, and 3 minus 2.65 leaves a guard band of only 0.35 mmHg. Under that form the monitor at +3.0 mmHg is a conditional pass in Fluke's sense, within the specification but with a false-accept risk that may exceed 2 %. The two forms differ by 2.65 minus 1.6, or 1.05 mmHg of acceptance limit, and on a production line that difference decides how many monitors are scrapped.

What each rule costs

Every decision rule trades the user's risk against the maker's yield, the share of its output that passes the test. The engineer can see that trade only by counting the whole stream of items tested. The JCGM calls the risk counted that way a global risk: the probability, judged before any item is measured, that a non-conforming item will be accepted or a conforming one rejected. In the JCGM's example, precision resistors of nominal 1500 Ω must lie between 1499.8 and 1500.2 Ω, and about 90 % of the process's output conforms. The measuring system has a standard uncertainty of 0.04 Ω, so U is 0.08 Ω, and the guard band of 0.02 Ω is a quarter of U. An inspector applying that guard band accepts 84 resistors in every 100 and rejects 16.

34 — What a rule costs, counted per hundred

UncertaintyLimits and decisionsFocal detail

Of the 84 accepted resistors, 83 conform and 1 does not, a global consumer's risk of 1 in 100, or 1 %, carried by whoever receives the parts. Of the 16 rejected, 9 are truly out of tolerance and 7 conform, a global producer's risk of 7 in 100, or 7 %, carried by the maker. Seven good parts are therefore scrapped for every bad part shipped. Moving the acceptance limits inward would ship fewer bad parts and scrap more good ones, and moving them outward would do the reverse. On the monitor's production line the same count tells the engineer what each guard band costs in good monitors scrapped.

Counting the uncertainty changes the result for real sphygmomanometers as well, and by a large factor. In 2008 Silva Junior tested new and used aneroid gauges against a pressure standard for a master's dissertation in metrology at PUC-Rio, a university in Rio de Janeiro, supervised by Costa Monteiro. Of the gauges, 60 % passed when only their measured errors were counted, and 12 %, a fifth of 60 %, once the uncertainty of the measurement was counted, as the dissertation's abstract reports. The abstract gives neither the number of gauges nor the exact rule. Silva Junior proposed a lower limit that takes the uncertainty into account.

No guard band written for sphygmomanometers by OIML, a national metrology institute or an accreditation body has been found in open sources as of October 2026. Under the rules in force, a ratio rule governs the reference and simple acceptance governs the decision. The nearest is a proposal by Ramírez-Barrera and colleagues, in the 2021 bench study of aneroid gauges that Chapter 10 described. Citing the JCGM, they propose a safety margin of no more than 30 % of the tolerance interval. They put that margin at 2.7 mmHg, taking 30 % of the range of diastolic pressures associated with prehypertension, a band of slightly raised blood pressure. Applied to the 6 mmHg between the monitor's limits of −3 and +3 mmHg, the same 30 % would give 1.8 mmHg. They do not say whether the margin applies to the error alone or to the error with its uncertainty, and the margin is a proposal, not a rule in force. An engineer who adopts it must therefore still decide how to apply it.

A maker that tests its own monitors chooses its own rule, and the duties that ISO/IEC 17025 places on laboratories show what that choice involves. The standard's 2017 edition gives a laboratory three such duties, as ILAC and the accreditation bodies describe them: the laboratory agrees the decision rule with its customer, documents it with regard to the risk it carries, and identifies it in any statement of conformity. In UKAS's words, the rule "shall be described in the certificate or report". By the same reasoning, the engineer's rule should be fixed before testing, documented with its risk and named on each test record.

The engineer makes that choice at every pressure the test checks, not only at 150 mmHg. Under OIML's test procedure the engineer takes the pressure from 0 mmHg to the top of the scale in steps of no more than 50 mmHg, and India's rules use the same steps. At each step the engineer applies the limit that the named document sets there, with a guard band from the test's uncertainty at that step.

35 — The limit at each test step, by document

Limits and decisionsFocal detail

+ Part IV · The chain of references

From the bench upward.

To calibrate each Alcotest breath-test machine in New Jersey, an officer warmed solutions of known alcohol content to about 34 °C and confirmed their temperature to within 0.2 °C with a thermometer traceable to NIST, the US national metrology institute. One coordinator was charged with skipping that check, and the machines he had calibrated had taken evidential breath samples from 20,667 people. A retired judge who heard the evidence for the state's Supreme Court accepted testimony that a solution one degree off could make a sample of 0.075 % alcohol read as 0.082 %. On 13 November 2018 the court ruled that breath-test results from machines calibrated without a NIST-traceable thermometer could not be used as evidence. This part follows such checks upward: what a calibration hands back, what makes a chain of calibrations traceable, why a stranger's certificate is believed, and how long a calibration lasts.

+ The questionWhen a laboratory calibrates an instrument, what exactly does it return?

Two steps, and neither adjusts

Calibration is an operation in two steps, as the VIM, the vocabulary of metrology of Chapter 1, defines it, and neither step adjusts the instrument. In the first step a laboratory relates the values that its measurement standards provide to the indications of the instrument, each with its uncertainty. In the second step it uses that relation to obtain a measurement result from an indication. The first step therefore produces a record of pairs: at each test point, what the standard said and what the instrument showed. The second step turns that record into a rule for reading the instrument afterward.

A laboratory may express the relation as a statement, a calibration function, a diagram, a curve or a table, the forms the VIM lists. In some cases the relation is a correction of the indication with its uncertainty, either added to each indication or multiplying it. The first step alone is often taken for the whole calibration, according to a note in the VIM. A laboratory that returns only a table of errors has done only the first step and left the second to the user. In the monitor of the earlier chapters the firmware performs the second step. The coefficients of Chapter 9, which turn the converter's counts into millimeters of mercury, are the monitor's rule for obtaining a result from an indication.

Two other operations are often called calibration, and the VIM defines each of them separately. Adjustment of a measuring system is a set of operations that makes the system give prescribed indications for given values of the quantity, and its kinds include zero, offset and span adjustment, by the VIM's list. Verification is the provision of objective evidence that an item fulfills specified requirements, such as a maker's specification. Calibration measures the error, adjustment changes it, and verification judges it against a limit.

Calibration is "a prerequisite for adjustment", in the VIM's words, and after an adjustment the system "must usually be recalibrated". A calibration made before an adjustment and one made after it therefore describe two different instruments, and a record that keeps only the second has lost the evidence of how far the instrument had drifted before it was adjusted.

The monitor on the bench

For the monitor, the first step takes place on a bench. The tester replaces the cuff with a rigid metal vessel of 500 ml, within 25 ml, as OIML's test procedure for automated sphygmomanometers requires. The vessel holds a steady pressure because its volume cannot change, while a cuff wrapped round an arm moves with every pulse (Chapter 4). T-shaped connectors, called T-pieces, join the vessel to the monitor's pressure port, a hand pump and a reference manometer. The tester raises the pressure in steps of at most 50 mmHg, from zero to the top of the monitor's scale, and then lowers it through the same steps. By OIML's procedure, the result at each step is the monitor's reading minus the reference's.

An automated monitor does not normally let anyone else set its pressure. In use it pumps the cuff up by itself and lets the air out through a valve, reading the pressure all the while (Chapter 7). For the test the monitor enters a service mode, which OIML's rules allow only service personnel to use. In that mode the monitor closes its vent valve, so that the air from the hand pump stays in the vessel, as Fluke Biomedical, a maker of test equipment, describes it. Rossmax, a monitor maker, states how its own monitors enter the mode: the power is drained, the power button is pressed three times, and the display shows "00". In that state the monitor no longer controls the pressure, and its display shows only what its sensor reads.

The same set-up also tests for leaks, because a pressure that falls while the two instruments are read gives a pair of readings that describes no single pressure. Fluke advises waiting at least 60 seconds at each step before reading, and measuring the loss of pressure over five minutes. Fluke adds that most monitor makers recommend a leak of less than 8 mmHg per minute, while OIML allows an automated monitor at most 6 mmHg per minute. A leak between the two figures meets the makers' usual recommendation and fails OIML's limit.

36 — The monitor on the calibration bench

The quantity being measuredReferences and standardsReadingFocal detail

The reference manometer

The reference manometer is the pressure gauge whose reading serves as the reference value at each step, and the whole calibration rests on it. A reference manometer is one whose own error is known from its own calibration and is small beside the error being measured. OIML allows the reference a maximum permissible error of ±0.8 mmHg, or 0.1 kPa, and India sets the same limit in its rules for automated sphygmomanometers. Mindray, a maker of patient monitors, checks the pressure channel of its VS-900 against ±3 mmHg and asks in its service manual for a manometer "calibrated with accuracy equal to or better than 0.75 mmHg". That figure is a quarter of the ±3 mmHg, since 0.75 divided by 3 is 0.25. A reference must be several times better than the limit it serves, because its own error raises the risk of a wrong pass or fail (Chapter 12).

A reference used in practice can be far better than these limits. In a 2021 bench study, Ramírez-Barrera and colleagues calibrated four non-automated sphygmomanometers from the General Hospital of Medellín in the metrology laboratory of the city's Instituto Tecnológico Metropolitano, which funded the work. Their steps followed the pattern of OIML's procedure: each test point lay at most 50 mmHg from the next, from zero to the top of each scale, and the authors ran two rising and two falling series on every instrument. Their reference was a digital manometer with a resolution of 0.01 mmHg, an accuracy of ±0.025 % of the reading and, by its own certificate, an expanded uncertainty of ±0.062 mmHg.

A reference stays a reference only while something better checks it in turn. Rossmax sells a calibration system for its own monitors, the CalPro, and states its accuracy as ±0.8 mmHg. Rossmax asks in the manual that the CalPro be compared with a reference at a metrology center every two years, and that it differ from that reference by no more than ±0.2 mmHg. The reference manometer is checked in its turn by a better standard, and that standard by a better one still (Chapter 15). Perkin-Elmer, in the opening story, relied on a reference that no one had measured independently. It did not verify its null corrector's dimensions after assembly, and a lens about 1.3 mm out of place guided the polishing of the whole mirror.

Laboratories also keep their best references out of daily use. In a procedure revised in 2019, FDA's own testing laboratories use their reference masses and thermometers "for calibration verification only and not as working standards", store them in a protected area and have the masses calibrated every five years.

Adjustment, and the record before and after it

Adjustment follows only after the first step has shown an error worth removing. Rossmax's CalPro runs the sequence in order. Over a data link it first reads the monitor at 11 pressures, in four falling groups that each start from zero: 295, 270 and 240 mmHg; 210, 180 and 150; 120, 90 and 60; and 30 mmHg. The monitor passes if it reads within ±3 mmHg at every point. If it fails, the CalPro programs it at 0, 300, 200 and 100 mmHg, which is the adjustment, and then reads the 11 points again. The display shows PASS or FAIL, and Rossmax tells its partners to return a monitor that still fails to the maker. Rossmax presents the CalPro as a system for its partners' service work in the field, not as its production station.

A shorter sequence adjusts at two points, because two pressures far apart fix a straight line, and therefore both the offset and the span of Chapter 11. Welch Allyn, a maker of patient monitors, describes one in its service manual for the Ambulo 2400, the ambulatory monitor of Chapter 9. The technician sets the main processor's pressure channel at two reference points, 250 and 15 mmHg, zeroes it with all pressure drained, and then tests the result against ±3 mmHg.

37 — Calibration, adjustment, calibration again, verification

The signal in the chainLimits and decisionsReadingFocal detail

A laboratory that adjusts an instrument calibrates it first and, usually, again afterward, and the two calibrations are known in the trade as as found and as left. ISO/IEC 17025 is the standard for the competence of testing and calibration laboratories (Chapter 16). A calibration certificate under that standard adds four things to an ordinary test report, as NIST and two bodies that accredit laboratories, UKAS in the United Kingdom and SADCAS in southern Africa, describe the standard. The certificate gives the uncertainty of each result, the conditions that influence the results and a statement of how the results are traceable, and, where available, the results before and after any adjustment or repair. The as-found values show whether the monitor had been outside its limit while in use, and the maker must then decide what to do about the readings it gave (Chapter 26). The as-left values describe the monitor that leaves the bench.

As of October 2026, open sources have yielded no monitor maker's account of its own production calibration station, with the pressures it applies and the coefficients it writes, and the makers' patents describe designs instead. Health and Life, a Taiwanese maker, patented a factory tool with which "more than one electronic sphygmomanometer can be set and calibrated at the same time". The tool works from two states, atmospheric pressure and a maximum, with a straight-line proportion between them. Shenzhen CHK Technology, a Chinese monitor maker, states in its 2010 patent application that "each sensor must be calibrated", and in its method a program sets the gain and offset of the monitor's amplifier (Chapter 9). Each inventor described a proposal rather than a factory's present practice, so a production test rests on the published test methods rather than on any one maker's practice (Chapters 22 and 23).

Verification asks whether a limit is met

Verification needs a limit, and the limit belongs to whoever sets the requirement. Under OIML's rules, verifying an automated monitor, new or in service, covers at least the cuff-pressure limit, the repeatability and the leak, and needs no climatic chamber (Chapter 30). OIML sets the cuff-pressure limit at ±3 mmHg or 2 % of the reading, whichever is greater. Because 2 % of 150 mmHg is 3 mmHg, OIML allows more than 3 mmHg above 150 mmHg: 2 % of 200 mmHg is 4.0 mmHg, and 2 % of 295 mmHg is 5.9 mmHg.

A maker may set a limit of its own. Mindray verifies the VS-900's pressure channel at 0, 50 and 200 mmHg against ±3 mmHg, and Rossmax allows ±3 mmHg at every point of its check. At five of Rossmax's 11 points, from 180 to 295 mmHg, the maker's limit is tighter than OIML's, and at 295 mmHg it is about half, since 3 divided by 5.9 is 0.51. A monitor that passes Rossmax's check therefore meets OIML's limit at every point, and a monitor that meets OIML's limit may still fail Rossmax's.

A calibration hands back an error with an uncertainty, and a verification has to decide what to do with both. Ramírez-Barrera and colleagues reported errors and uncertainties but did not state whether any instrument passed at any point. Their figures leave the decision to whoever applies a limit, and at one point the decision is not obvious.

38 — What one calibration point hands back

References and standardsNoise and errorUncertaintyLimits and decisionsReadingFocal detail

The reading, not the estimate

Calibration, adjustment and verification all concern the cuff-pressure reading, and none of them reaches the blood-pressure estimate. The reference manometer and the vessel hold a steady pressure, and a steady pressure carries no oscillations, so the algorithm that derives systolic and diastolic values from the oscillations (Chapter 9) never runs.

The estimate can be adjusted in the field, but only against another estimate. In a patent granted in 2004, Microlife, a monitor maker, describes a calibrating device that recalibrates a wrist monitor's estimate in the field. The device writes new constants into the monitor's memory after three paired readings against an upper-arm monitor, and accepts ±20 mmHg for the systolic value and ±12 mmHg for the diastolic. The procedure adjusts one estimate against another, so it is not a calibration of the cuff pressure in the VIM's sense. A clinical study validates the estimate instead, comparing it with a reference measured on patients (Chapter 24).

+ The questionWhat makes a number traceable, and what breaks the chain?

A property of a result

A sticker on an instrument says "NIST traceable", and NIST itself says it does not certify such claims: it "does not define, specify, assure, or certify metrological traceability of measurement results other than those that NIST itself provides", under a directive in force since 31 May 2019. The sticker also attaches the claim to the wrong object. Metrological traceability is a property of a measurement result: the result "can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty", in the VIM's definition (Chapter 14), which NIST adopts. An instrument can be calibrated and a laboratory can be competent, but only a result is traceable, and only through the chain behind it.

Calibrating an instrument is not enough to make its results traceable, because every result has a history after the calibration. The monitor's comparison with a reference manometer (Chapter 14) may lie a year behind a reading it takes today, and that reading rests on the comparison, on the coefficients written then, on how far the sensor has drifted since and on the zero the monitor took that morning (Chapter 17). Having an instrument calibrated, even by NIST, is "not enough to make the measurement result obtained using that instrument traceable", in NIST's answers to common questions. NIST divides the responsibility for a claim of traceability: whoever provides a result must support any claim that it is traceable, and whoever uses the result must judge whether the claim holds.

Traceability also runs to a reference, such as a measurement standard, and not to the institution that holds the reference. ILAC calls the phrase "traceable to a specific National Metrology Institute" a common misconception, because traceability belongs to the values of measurement standards and to measurement results, not to "the organization providing them". The word has other senses as well: it is sometimes used for the traceability of a sample, a document, an instrument or a material, according to a note to the VIM's definition. A device maker also uses the word for the link from each design requirement to the evidence that the design meets it (Chapter 25). Only the metrological sense concerns the chain of calibrations behind the monitor's reading.

Each link adds uncertainty

Traceability needs a calibration hierarchy, a "sequence of calibrations from a reference to the final measuring system" in the VIM's definition. Along that sequence "measurement uncertainty necessarily increases", in the VIM's words, and the reason follows from Chapter 11's method. Each calibration compares an instrument with a standard, so the instrument's budget carries the standard's uncertainty as one row, beside the instrument's own repeatability, resolution and hysteresis at that comparison. A combined uncertainty is the square root of the sum of the rows' squares, so it can never be smaller than the standard's row. Every link down the chain therefore has at least the uncertainty of the link above it, and usually more.

The monitor's own hierarchy runs upward through four levels, and the figures given for them here come from different published sources, not from the documented chain of any one monitor. At the bottom the monitor itself must read the cuff pressure within ±3 mmHg, or 2 % of the reading above 150 mmHg (Chapter 14). Above it stands the maker's reference manometer, for which OIML sets a maximum permissible error of ±0.8 mmHg. Above that stands a reference manometer of the kind Ramírez-Barrera and colleagues used in their 2021 bench study (Chapter 10). They report the expanded uncertainty on its certificate, ±0.062 mmHg with a coverage factor of 1.99, but not the pressure at which that figure applies. At the top of the pressure chain stands a pressure balance, calibrated in its turn at a national metrology institute. NPL, the UK's national metrology institute, calibrates its customers' gas-operated pressure balances from 16 to 700 kPa at 0.0021 %, a figure it publishes without a coverage factor. At 150 mmHg, which is 20.0 kPa, 0.0021 % is 150 × 0.000021 = 0.00315 mmHg, about 0.003 mmHg.

Read down the chain, the four figures grow from about 0.003 mmHg to 0.062, 0.8 and 3 mmHg, and 3 divided by 0.00315 is about 950, nearly a thousandfold over three steps. The four are not all the same kind of number. The upper two are uncertainties, which a laboratory states for its own result. The lower two are maximum permissible errors, limits that a rule sets for every instrument of the kind. Because each reference must be several times better than the instrument it calibrates (Chapter 12), the chain needs a wide margin at its top to end inside the monitor's limit after three such steps.

39 — The monitor's chain, from a pressure balance down to the cuff

References and standardsUncertaintyLimits and decisionsReadingFocal detail

The top of the pressure chain

A pressure balance makes a known pressure from masses, an area and gravity, and it is called a balance because a gas pressure balances a weight, not because it weighs anything. A vertical piston fits closely in a cylinder. The gas pushes up on the piston's base while masses stacked on the piston push down, and when the piston floats, the gas pressure balances the weight of the piston and its masses. That weight is their mass times the local acceleration of gravity, slightly reduced by the buoyancy of the air around them. Dividing it by the piston's effective area, the area on which the pressure acts, gives the pressure, "the ratio of the downward force to the area" in the words of NIST's 1994 account of its pressure calibration service. NIST corrects the result for temperature and for the piston's slight distortion under pressure, and names the effective area as the main limit on accuracy.

Each of the three inputs needs a chain of its own, so the hierarchy behind a pressure balance branches. When a result has several inputs, "each of the input quantity values should itself be metrologically traceable", in the VIM's words. In NIST's laboratory in 1994, the masses were traceable to its mass standards laboratory, and its dimensional metrology group measured the pistons' diameters. Gravity cannot be sent away for calibration, so it is measured where the balance stands: 9.801011 m/s² in one room of NIST's metrology building at Gaithersburg, by NIST's figure.

The masses are the link that ties pressure to the kilogram. Weights pass down a chain of classes, each used to check the class below it: in OIML's recommendation for weights, class E2 weights, for example, are "intended for use in the verification or calibration of class F1 weights". Since OIML amended that recommendation in 2025, the top class has been defined as derived from "internationally recognised realisations of the definition of the kilogram in the SI" instead of from the old prototype (Chapter 18). Through its masses, the top of the monitor's chain therefore rests on the Planck constant, whose fixed value has defined the kilogram since 2019 (Chapter 19).

India's primary standard of pressure works the same way. It is an air piston gauge at CSIR-NPL, India's national metrology institute: a pressure balance operated with air, established as the primary standard from 6.5 to 360 kPa, about 49 to 2,700 mmHg. In a 2020 paper, Thakur and two colleagues at the institute found the gauge's effective area, about 3.357 cm², from dimensional and mass measurements "traceable to the SI units of meter and kilogram". They stated the area's expanded uncertainty as nearly 11 parts per million at k = 2 (Chapter 12), and checked the gauge against another of the institute's standards, an ultrasonic interferometer manometer. Below 6.5 kPa the cuff's range needs another standard, and CSIR-NPL describes one in a report to the consultative committee that advises the CIPM on mass: a force-balanced piston gauge for 0 to 14 kPa, which is 0 to about 105 mmHg.

40 — A pressure balance: weight over area

The quantity being measuredReferences and standardsFocal detail

What breaks the chain

A chain breaks wherever one of its links cannot be shown. In New Jersey the breath-test results depended on the temperature of the reference solutions as well as on their alcohol, and the temperature branch lacked its traceable thermometer (the opening of this part). Nor does a number on a certificate show a link: by NIST's account, its test report numbers "are intended to be used solely for administrative purposes" and should not be used as "the sole proof of traceability". A link is also tied to a date. A reference drifts, while the values on its certificate describe it on the day it was calibrated, so a calibration holds for a limited time (Chapter 17), and the specification of a reference "must include the time at which this reference was used", in the VIM's words.

A chain can also be complete and still fail its purpose, because traceability "does not ensure that the measurement uncertainty is adequate for a given purpose or that there is an absence of mistakes", in the VIM's words, and NIST takes the same view of fitness for purpose in its policy. A monitor calibrated against a traceable reference whose uncertainty came close to the monitor's ±3 mmHg limit would be traceable and of little use, because the reference's uncertainty alone would fill most of that limit.

Accreditation bodies decide which links they accept. In its policy on traceability, issued in July 2020, ILAC prefers two routes. The first is a calibration by a national metrology institute whose service is covered by the CIPM's mutual recognition arrangement (Chapter 21). The second is a calibration by an accredited calibration laboratory whose scope covers that calibration (Chapter 16). ILAC allows other routes where those two are not possible. Where the SI is the reference, every route ends in a realization of the SI unit, and the result then has traceability to a measurement unit, in the VIM's term.

Chains for things that are not pressure

Chemistry and laboratory medicine build the same chains from different links. A blood test cannot be calibrated with masses on a piston, so its chain runs through certified reference materials, materials whose value a competent producer certifies together with its uncertainty, and through reference measurement procedures. An in vitro diagnostic test, made on a sample taken from the body, is calibrated against calibrators, materials with assigned values. The requirements for tracing those values are set out in ISO 17511, confirmed in 2026.

The upper links of these chains are listed in the database of the Joint Committee for Traceability in Laboratory Medicine, or JCTLM, which the BIPM set up with ILAC and the International Federation of Clinical Chemistry and Laboratory Medicine. ILAC accepts a certified value as traceable when, among other routes, an accredited producer issued it under its scope or the JCTLM database lists it. A test maker can therefore rest a calibrator's chain on a listed material. The companion guides on immunoassays, A few molecules in a drop, and on PCR, Copy and count, follow these chains through calibrators and standard curves.

+ The questionWhy should anyone trust a calibration certificate from a laboratory they have never visited?

A register of laboratories

A monitor maker's reference manometer goes out for calibration and comes back with a certificate from a laboratory that the maker's staff have never visited. The maker cannot audit that laboratory itself, so it relies on an accreditation body that has audited the laboratory against a published standard. Accreditation is an independent body's assessment of a laboratory against such a standard, followed by its formal recognition that the laboratory is competent for a stated list of tasks.

In India that body is NABL, the National Accreditation Board for Testing and Calibration Laboratories, a constituent board of the Quality Council of India. NABL accredits testing and calibration laboratories against ISO/IEC 17025, the international standard for their competence. It also accredits the providers of proficiency tests, in which laboratories' results are compared, and producers of reference materials.

NABL's register holds far more laboratories than any customer could visit. In early September 2026 it held 1,305 calibration laboratories, by the count that Germany Trade & Invest, or GTAI, a German federal agency that reports on foreign markets, gave on 30 September 2026 in a market report on laboratory technology in India. The report calls the laboratories certified, but certification is the word for quality systems, and NABL accredits laboratories.

What the laboratory must show

A laboratory accredited under ISO/IEC 17025 must control its own instruments, because it calibrates its customers' instruments with them. It verifies each instrument before putting it into service, and calibrates it where its accuracy affects the validity of results or where traceability needs it, as SADCAS, which accredits laboratories in southern Africa, and PJLA, a US accreditation body, describe the standard's clause on equipment. It keeps a calibration program, labels what needs calibration, and takes doubtful equipment out of service and examines the effect. Its records for each instrument include the software and firmware version, the calibration dates and results, and the due date. ISO published the standard's third edition in November 2017, confirmed it in 2023 and sells it rather than publishing it openly. UKAS in the United Kingdom and NIST, in its checklist for certificates, also describe its requirements.

A certificate shows the numbers a laboratory reports, but not whether the laboratory reached and reported them as the standard requires. As accreditation bodies describe the standard, the laboratory traces each result to the SI through a documented unbroken chain: by calibration at a competent laboratory, by certified reference materials from a competent producer, or by realizing the SI unit directly (Chapter 15). Its certificates carry the four items that Chapter 14 listed, from the uncertainty of each result to the results before and after any adjustment, where those results are available. Where it states that an instrument conforms to a specification, it documents the decision rule it applied, and the measurement uncertainty "shall be taken into account", in UKAS's words (Chapter 13). Accreditation is the customer's evidence that a qualified body has checked this work.

The scope and its CMC

An accreditation covers only the calibrations that its scope lists, and each row of the scope gives a range, a method and a calibration and measurement capability, or CMC. The CMC is the capability "available to customers under normal conditions": the smallest uncertainty that the laboratory may state for that calibration, given as an expanded uncertainty with a coverage probability of about 95 % (Chapter 12). A national institute's CMCs are the ones that the BIPM's database publishes (Chapter 21). On a certificate the laboratory states both the coverage factor and the coverage probability, and gives the expanded uncertainty to at most two significant digits. The definition and these rules are those of ILAC, the International Laboratory Accreditation Cooperation, through which accreditation bodies cooperated until the end of 2025, in its policy on uncertainty in calibration, issued in September 2020.

A certificate's uncertainty can be larger than the CMC but never smaller: a laboratory "shall not report a smaller measurement uncertainty than the uncertainty described by the CMC", in ILAC's words. The laboratory works out its CMC from an uncertainty budget (Chapter 11) for the best existing device, ILAC's name for the best instrument of the kind that the laboratory calibrates. On a certificate it replaces that device's rows with the rows of the customer's own instrument, such as its resolution, repeatability and hysteresis, and no customer's instrument is better than the best of its kind. Reported uncertainties therefore "tend to be larger" than the CMC, as ILAC puts it, and the CMC is the best that a customer's reference manometer can receive from that laboratory.

Accreditation alone does not tell the maker whether a laboratory can support the cuff-pressure check, because accredited capabilities at the cuff's pressures lie far apart. S M Gauge Company, a UK laboratory accredited by UKAS, lists dead-weight testers, pressure balances of the kind in Chapter 15, only above 2.5 MPa, so at the cuff's pressures its accreditation covers calibration of gas gauge pressure by comparison with a reference instrument. Its CMC rises with the pressure: 2.9 Pa from −15 to 15 kPa, 4.4 Pa from 15 to 25 kPa, 11 Pa from 25 to 50 kPa and 18 Pa from 50 to 100 kPa, each at a coverage probability of about 95 %. Even the largest, 18 Pa, is about 0.14 mmHg, since 1 mmHg is 133.322 Pa (Chapter 3), so every row is a small fraction of the 1 mmHg step of the monitor's display.

PSG CIRD, the industrial research and development center of PSG College of Technology in Coimbatore, offers a much coarser capability, 5.8 mmHg at k = 2. Its NABL scope, valid from 30 January 2026 to 29 January 2030, gives that CMC to its rows for sphygmomanometers from 50 to 200 mmHg and for the blood-pressure channels of patient monitors from 50 to 400 mmHg, measured "Using Vital Sign Simulator by Direct Method". PSG CIRD does not say whether those rows check the cuff pressure or the values that a simulator presents to the monitor's algorithm.

41 — Two accredited scopes at 150 mmHg

UncertaintyLimits and decisionsReadingFocal detail

Laboratories tested against each other

Accreditation also tests a laboratory's results, not only its procedures, through proficiency testing: a provider sends the same item, or items of known value, to several laboratories and compares what each reports. Before granting accreditation, the accreditation body asks each laboratory for a participation plan and confirms "representative and satisfactory participation" for its scope, under ILAC's policy on proficiency testing, issued in January 2024. Where a laboratory's performance is not satisfactory, the body looks for evidence of "prompt and appropriate corrective actions". A laboratory's stated capability is therefore checked against measurements of shared items, not only against its own records.

How often a laboratory takes part is its own decision, made according to risk. Participation is "considered mandatory when available, appropriate and deemed necessary", in ILAC's words, but ILAC sets no fixed frequency, and each laboratory sets a minimum for every area of its competence. Where no formal proficiency test is available for a calibration, a laboratory in India can still set its results against other laboratories' results, because NABL has a separate document for such comparisons between calibration laboratories.

Trust across borders

A certificate from Coimbatore or from the United Kingdom is believed in another country because accreditation bodies assess each other and sign an arrangement to recognize one another's accreditations. That arrangement was ILAC's, and on 1 December 2025 it had 121 signatories representing 122 economies. On 1 January 2026 Global Accreditation Cooperation Incorporated, known as Global ACI, began full operations. It replaced two bodies, ILAC and the International Accreditation Forum, known as IAF, and on that day their two arrangements passed into one, the Global ACI MRA, or Multilateral Recognition Arrangement. Existing accreditations "will continue to be recognised", as ILAC and IAF stated in their joint announcement.

During the change to Global ACI, a certificate and the rules it was issued under both stay valid. UKAS told its customers on 15 May 2026 that the new Global ACI MRA mark could not be used until a registration process was complete, and UKAS expected the old marks to end in three to five years. Documents with the old marks stay valid until they are renewed, reissued, updated or otherwise replaced, by UKAS's account, so a certificate with ILAC's mark keeps its standing in the meantime. ILAC's rules also stand: as of October 2026, ILAC still lists its policies on traceability, uncertainty and proficiency testing as current on its site. NABL states that it is a signatory to the Global ACI arrangement and to APAC, the regional cooperation for Asia and the Pacific, so the accreditations it grants in India carry into the new arrangement (Chapter 30).

The device maker's own laboratory

A device maker may calibrate its own references instead of sending them out. Under ISO 13485, the quality-system standard for device makers, the maker calibrates or verifies its measuring equipment against traceable standards (Chapter 17), but none of the open descriptions of that clause, FDA's training for auditors among them, settles whether it requires accreditation. Micro Precision, a calibration company with an interest in selling accredited calibration, writes that the clause "doesn't explicitly require" an accredited provider. ILAC wrote its traceability policy for accredited organizations, not for a maker's factory laboratory. For a maker that calibrates in-house, its own records are therefore the only evidence of the chain, the uncertainty and the competence, because no accreditation body has checked them.

42 — Why a stranger's certificate is believed

References and standardsReadingFocal detail

+ The questionHow long does a calibration stay true, and who decides?

A date the owner writes

The due date on a calibration label is the owner's prediction, not a result of the calibration. The laboratory measures the instrument on one day, and its results describe the instrument on that day only. The laboratory cannot know how the instrument will be used, stored or carried afterward, so the owner, who does know, chooses the interval. Choosing it means predicting how long the instrument will stay within its limits, or, in OIML and ILAC's words, determining "the maximum period that should be permitted between successive calibrations".

An accredited laboratory accordingly leaves the interval to its customer. Under a clause of ISO/IEC 17025, as NIST, SADCAS and UKAS each describe it, a certificate or label carries no recommendation on the calibration interval unless the customer agreed it or a legal regulation requires one. UKAS asks a laboratory that does print a due date to show whose date it is, with a phrase such as "Customer requested calibration due date."

A US device maker sets its own calibration intervals, now under ISO 13485, and until 2026 it also had to show each due date by law. FDA's former rule on inspection, measuring and test equipment required records that included "the next calibration date", displayed on or near each piece of equipment or readily available. FDA replaced that rule with its Quality Management System Regulation, the QMSR, which took effect on 2 February 2026, brings in ISO 13485:2016 by reference and so makes the standard's requirements part of the regulation.

What changes between calibrations

A calibration stays true only as long as the instrument does not change, and every part of the monitor's chain can change. Semiconductor pressure sensors drift strongly with temperature, as Omron's engineers wrote in a patent filed in 1980, so the monitor in that patent zeroes its sensor before each measurement. The span can drift too, and so can the tightness of the valves and tubes, and the reference manometer itself.

Drift also continues with time, and use wears the monitor. The zero of a pressure sensor "may initially change 0.1% annually and can become progressively worse over time", as engineers at Baker Hughes wrote in a 2022 patent on industrial sensors, not blood-pressure monitors. OIML asks that an automated monitor's cuff-pressure reading change by no more than 3 mmHg after 10,000 simulated measurement cycles, a test of wear rather than of time.

Four makers recommend intervals for their own instruments, and none of them states how it chose its interval. Microlife recommends that its BP B3 Basic home monitor "is tested for accuracy every 2 years or after mechanical impact", through its own service. Welch Allyn recommends calibrating its Ambulo 2400 at least once a year, Mindray recommends checking the VS-900's blood-pressure channel at least once a year, and Rossmax asks for its CalPro to be recalibrated every two years (Chapter 14). The owner therefore cannot tell what evidence each figure rests on. For some instruments, India's rules fix the interval by law (Chapter 30).

How an interval is chosen

In the international guidance, the owner chooses an interval by judging risk, not by applying a fixed rule. OIML and ILAC publish that guidance jointly as OIML D 10 and ILAC G24, in an edition of 2022. Staff with the technical competence for it make the initial decision, which "is based mainly on a risk assessment analysis". The factors the staff weigh, as OIML and ILAC list them, include the "risk of the measuring equipment exceeding the predetermined limits", the uncertainty needed, the maker's recommendation, wear and drift, how heavily and where the equipment is used, and the results of checks between calibrations. The staff also weigh cost against uncertainty, because frequent recalibration costs more, and "these costs need to be balanced against increased measurement uncertainties". Fixed intervals, in OIML and ILAC's words, "are not recommended unless the interval has been specified in a normative document", such as a standard or a regulation.

Once results accumulate, the laboratory reviews the interval by one of five methods that OIML and ILAC describe. In the staircase method, the laboratory extends or keeps the next interval when the deviation found at calibration lies within a defined share of the maximum permissible error, and shortens it otherwise. A control chart, a plot of each calibration's result against the date, follows the results over calendar time, and that method suits only equipment that drifts. In the other methods, the laboratory counts hours of use, checks critical parameters often, "once a day" in one example, or applies other statistics. OIML and ILAC give no step sizes and no percentages, and they leave each laboratory free to use any of the methods or none.

NIST does give numbers, for mass standards, in GMP 11, its good-practice procedure for US legal-metrology laboratories, which check instruments that the law regulates. A laboratory's working standards that it calibrates itself, and its balances, start at 12 months, and pairs of reference kilograms calibrated at NIST start at 48 months. No interval may exceed 10 years without exceptional analysis of the laboratory's data. The laboratory's technical manager changes an interval on documented evidence, and an initial interval ends early when a proficiency test fails, or when results on a control chart fall outside its warning limits, the lines drawn on either side of the expected value, with no correctable cause. In NIST's scheme as in OIML's, the interval is a hypothesis that each calibration tests.

The monitor's own zero

Between calibrations, the monitor corrects the largest part of its sensor's error every time it starts. Before measuring, the firmware reads the sensor with the cuff at the pressure of the open air and takes that reading as its zero, a step called auto-zero. In the method of Omron's patent filed in 1980, the monitor leaves its sensor "exposed to the atmosphere", stores the reading as a correction value and subtracts it from every later reading. The capture ends "After a certain period of time has elapsed", and no duration is stated. The same method follows slow drift during use. The monitor sets a second value about 1 mmHg above the stored zero, and if the reading rests between the two for a set time, 10 seconds in the patent's example, the higher value becomes the new zero. Because the second value lies above the zero, the method corrects only upward drift.

In Omron's later patents the monitor zeroes its sensor at power-on, and India now requires the step by law. In an Omron patent granted in 2015, pressing the power switch starts "the 0 mmHg correction of the pressure sensors", and in one of 2005 the monitor completes "zero setting, which is to say initial reset" at the third step of its flowchart. In Shenzhen CHK's 2010 patent application, the monitor likewise performs "the zero point offset correction" when the sensor is turned on. Under India's rules for automated sphygmomanometers, notified on 28 July 2025, as under OIML's recommendation, the monitor "shall be capable of automatic zero adjustment", at least when it is powered on. It must zero again or switch itself off when the transducer's output drifts by one scale interval, 1 mmHg, or more. None of these documents states how long the zero takes to settle, or how large an offset the firmware accepts before it reports a fault.

Auto-zero is an adjustment in the VIM's sense (Chapter 14), and its strength and its limit come from the same fact: it compares the sensor with one pressure only, that of the open air. An offset is the same at every pressure, so one reading at zero measures it completely. An error of span grows with the reading and vanishes at zero, so the zero cannot see it at all.

43 — What the monitor's zero can and cannot see

The quantity being measuredThe signal in the chainNoise and errorReadingFocal detail

Checks between calibrations

Between full calibrations, a laboratory or a factory checks that nothing has moved. Intermediate checks are comparisons made between two calibrations to confirm that an instrument still works and keeps its calibration status. A laboratory "should have an appropriate system of intermediate checks", in OIML and ILAC's words, and the results of those checks should fall within predetermined limits before the equipment is approved for further use. Under ISO/IEC 17025, as SADCAS describes it, such checks follow a procedure where they are needed. A reference manometer can be compared with a second gauge at one pressure. For the monitor, a check at zero and at one pressure tests both the offset and the span, and in India's test procedure for automated sphygmomanometers, a reading at 50 mmHg taken after switch-on is checked for drift.

A failed check calls into question every result since the last good one. An air-quality laboratory at the University of California, Davis, applies that rule with numbers, although it checks balances rather than pressure. Under its procedure of July 2022, the laboratory weighs reference weights at the start of work and every four hours, with an acceptance limit of ±0.003 mg, and processes no samples until the check passes. When a check fails, the laboratory weighs again every filter it weighed since the last check that passed.

44 — Between two calibrations

References and standardsNoise and errorLimits and decisionsReadingFocal detail

What the quality system asks

Under ISO 13485, the quality-system standard for device makers, a maker calibrates or verifies its monitoring and measuring equipment at specified intervals, or before use, against standards traceable to international or national measurement standards, as FDA's training for auditors and other open sources describe the standard's clause. Where no such standard exists, the maker records the basis it used. Japan's quality-system rule for device makers, Ministerial Ordinance 169, set out the same two points in its Article 53: equipment is "calibrated or verified at the specified intervals", and "in case where no such standards exist, the basis used for the calibration or verification shall be recorded". That English text, quoted in a trade article in 2012, is of the version that matched the standard's 2003 edition. Japan revised the ordinance's second chapter, which holds Article 53, in March 2021 to align it with ISO 13485:2016.

Software used for monitoring and measurement is also validated for its intended use, according to FDA's training. When equipment is found not to conform, the maker assesses and records the validity of the earlier results and acts on the equipment and on any product affected (Chapter 26).

+ Part V · The top of the chain

From an object to a constant.

For 130 years the kilogram was a cylinder of platinum and iridium, about 39 millimeters high and 39 across, kept in a safe at the International Bureau of Weights and Measures near Paris. Every calibrated mass in the world led back to that one object, and so did every cuff pressure calibrated through the masses of a pressure balance. Chapter 28 shows that the links at the top of the chain add almost nothing to a monitor's uncertainty budget, but a maker's claim that its cuff pressures are traceable depends in part on them. An error at this level, such as the one the BIPM found in 2014, has to be traced through every certificate that rests on it. This part follows the top of the chain through its change in 2019. Chapter 18 shows what the cylinder could and could not tell the people who kept it, and Chapter 19 how a fixed value of the Planck constant, a constant of quantum physics, came to define the kilogram. Chapter 20 describes the instruments that measure a mass from that constant, and Chapter 21 follows the kilogram they realize down to the balances of every country, India's among them.

+ The questionWhat goes wrong when a unit is defined by a single object?

One cylinder, right by definition

Until 2019 the kilogram was the mass of one metal cylinder, which Johnson Matthey, in England, had made from an alloy of 90 % platinum and 10 % iridium. Its height and its diameter were each about 39 mm, according to a 2004 review by Schwitz and colleagues at METAS, Switzerland's national metrology institute. The BIPM, the International Bureau of Weights and Measures, kept the cylinder in a safe at Sèvres near Paris. In 1889 the first General Conference on Weights and Measures, the CGPM of Chapter 3, sanctioned it as the international prototype of the kilogram and declared that the prototype "shall henceforth be considered as the unit of mass".

A unit defined by an object has a property that no other standard shares: its value cannot be wrong. Every other kilogram was a copy whose mass someone had measured, and every such measurement carried an uncertainty. The international prototype was 1 kg by declaration, exactly, and no measurement could give it an uncertainty, because nothing stood above it to compare it with. For the same reason, no measurement could reveal a change in it. If the cylinder lost a microgram, a millionth of a gram, the kilogram lost a microgram with it, and every copy measured against the cylinder would seem to have gained one. Until 2019 the chain of Chapter 15, from the monitor's reference manometer through a pressure balance and its masses, ended at this cylinder.

Copies, compared again and again

The prototype came out of its safe only on rare occasions, so laboratories around the world measured mass against copies of it. Johnson Matthey delivered 40 copies in 1884, and in 1889, 34 of them went to the states that had signed the Metre Convention of 1875 and asked for one, by the account of a 2001 review by Jabbour and Yaniv of NIST. These copies became the states' national prototypes. The BIPM kept official copies beside the prototype, two at first and six after one was replaced and four were added. In its declaration of 1889 the CGPM recorded that the national kilograms differed from the international one by no more than 1 mg, and only a comparison with the prototype could show whether a copy still agreed that closely.

A copy is checked against the prototype on a balance, and a balance used this way reports only the difference between two masses. The differences that mattered were small: a kilogram holds a billion micrograms, so a difference of one microgram between two kilograms is a difference of one part per billion. The BIPM compared the national prototypes with the international one in three periodic verifications, from 1899 to 1911, from 1947 to 1954 and from 1988 to 1992, the dates that Schwitz and colleagues give. Georges Girard, the head of the BIPM's mass section, led the third. In that verification each national prototype was measured against the international one with a standard uncertainty of 2.3 µg, or 2.3 parts per billion.

What the verifications found

The verifications found that the copies and the prototype were drifting apart, and that the copies tended to grow heavier relative to the prototype. In the first, two of the 25 prototypes verified had changed by as much as 50 µg. The seventeen national prototypes that Schwitz and colleagues plot across the verifications drifted by an average of 50 µg in 100 years, which is 50 parts per billion a century. In the second and third verifications many of the BIPM's official copies had also increased in mass with respect to the prototype, as Stock and colleagues at the BIPM report in their 2015 account of a later calibration campaign.

The surface of every cylinder, the prototype's included, gathers contamination between cleanings, and the contamination adds mass. During the third verification the BIPM found that the official copies gained between 0.6 and 1.3 µg a year, and the international prototype itself 1.5 µg a year. The typical rate that the BIPM observed for national prototypes is 1 µg a year. The long-term instability is attributed to surface effects "that are not yet fully understood", in the words of Jabbour and Yaniv. A cause that no one could model was also a cause that no one could correct, because a correction needs a rate that holds for each object, and the rates differed from one cylinder to the next.

45 — The copies drift apart from the prototype

References and standardsNoise and errorUncertaintyFocal detail

Cleaning before weighing

Because contamination adds mass between cleanings, the BIPM cleaned every prototype by hand before comparing it. In the method that Girard described in a BIPM monograph of 1990, a metrologist rubbed the whole surface of the cylinder fairly vigorously with chamois leather that had soaked for 48 hours in equal parts of alcohol and ether. A jet of steam from a flask of double-distilled water then washed each surface for fifteen to twenty minutes, about fifty minutes in all. The method "relies on the human touch and therefore can be highly irreproducible", in Jabbour and Yaniv's words, so two careful metrologists could leave the same cylinder at slightly different masses.

A cleaned prototype starts to gain mass again at once. Girard followed prototypes 7, 67 and 73 after cleaning and washing, as the same monograph reports, and each gained about 1 µg a month during the first three to four months. The mass of a prototype therefore depended on how long ago it had been cleaned, and on the hands that had cleaned it. At about 1 µg a month, a prototype gained about 3 µg in the three months after a cleaning, more than the 2.3 µg standard uncertainty with which the third verification compared it.

Nobody could say which had moved

The verifications showed a growing difference between the prototype and its copies, and a difference cannot show which of two masses changed. If the copies gained 50 µg, the difference grows by 50 µg; if the prototype lost 50 µg, the difference grows by exactly the same amount, and the balance reads the same numbers in both cases. A third object would not settle the question, because it too could be compared only with the prototype, whose mass was fixed by declaration rather than measured. The prototype's own mass "is subject to small and not easily predictable changes", in the words of Schwitz and colleagues, and no comparison could say how large those changes were.

The CIPM, the International Committee for Weights and Measures of Chapter 3, drew that conclusion in 1993. In a recommendation after the third verification, it noted the significant drifts found in national prototypes and "the fundamental impossibility of drawing definite conclusions from these results". It recommended work toward "a new definition of the unit of mass based upon fundamental or atomic constants". The experiments that followed led to the definition of 2019 (Chapters 19 and 20).

The weighing of December 2013

To prepare a new definition of the kilogram, based on a fixed value of the Planck constant (Chapter 19), the BIPM began the calibration campaign by weighing the international prototype between 11 and 27 December 2013. It was the prototype's first weighing since the third verification, and in the meantime the prototype and its six official copies had stood in a safe, unused. In 2013 the CCM, the consultative committee that advises the CIPM on mass, had set conditions for the new definition. Among them, it asked that the BIPM's standards and the mass standards used in the experiments that measured the Planck constant be compared "as directly as possible with the international prototype".

The BIPM then cleaned and washed the prototype and its copies between 23 December 2013 and 17 February 2014. Weighed before and after, the official copies lost an average of 15 µg in the cleaning, with a standard deviation of 2 µg, as Stock of the BIPM reported to the CCM in February 2015. The BIPM followed the mass that the objects regained for about ten months, until November 2014. At first they gained 0.01 to 0.03 µg a day, which over 30 days is 0.3 to 0.9 µg a month, close to Girard's figure of about 1 µg a month for prototypes 7, 67 and 73.

The prototype and its copies still stood in the same relation to one another as in the third verification, within the uncertainty of the comparisons. The differences between the prototype and the official copies had changed by an average of 1 µg since then, against an uncertainty of 3 µg for each comparison, so the set had "behaved as a consistent set", in the words of Stock and colleagues. A copy kept away from the BIPM gave a further check. Prototype No. 34, which belongs to the French Academy of Sciences and had stayed unused in Paris since the third verification, came to the BIPM in September 2014. Cleaning removed 19.6 µg from it after 22 years, which is 19.6 ÷ 22, about 0.9 µg a year, close to the typical 1 µg a year. Its mass relative to the international prototype came out 1 µg lower than in the third verification, a change of the same size as the official copies' average.

The BIPM did find an error, but one level below the prototype, in the masses it used every day. Its working standards, the kilograms against which it calibrated other countries' standards, had all lost between 18 and 88 µg against the prototype since 1992, and the BIPM later attributed the loss to wear. The BIPM's unit was still traceable to the prototype through the values those standards had been given in the third verification. A standard that has lost mass but keeps its old value gives every kilogram compared with it a value that is too high. The as-maintained mass unit, the kilogram as the BIPM actually kept it in those standards, was therefore found in 2014 to be "offset by 35 µg with respect to the IPK", the international prototype of the kilogram. The CCM put the change at 35 µg over 22 years.

46 — The weighing of 2013–14 finds the fault one step down

References and standardsNoise and errorFocal detail

The offset passed into the results that rested on the BIPM's calibrations of those years. By NIST's account the maintained unit was 35 µg larger than the prototype, so NIST had to lower by about 35 µg the value that the BIPM had given NIST's own kilogram K85 in 2012. The BIPM updated the certificates for calibrations of 1 kg standards that it had issued between 1 January 2003 and 31 December 2013. The experiments on the Planck constant that used masses calibrated by the BIPM carried the same offset, and these were the experiments that the campaign was meant to support. In 2015 the CIPM recommended that the determinations of the Planck constant, which "will provide the basis for the future definition of the kilogram", be updated with the corrections that the BIPM gave the institutes concerned. NIST lowered its own result for the Planck constant by 35 parts per billion, the same fraction of its value as 35 µg is of a kilogram. NRC, Canada's national metrology institute, applied the same correction, and both did so before the value of the Planck constant was fixed (Chapter 20).

+ The questionHow can a number fixed by vote define a kilogram?

A value chosen, not measured

The number 6.626 070 15, divided by 10³⁴, has been exact since 20 May 2019: it is the value of the Planck constant in joule seconds. Written out in full, it has 33 zeros after the decimal point before its first digit. Until that day laboratories measured the constant, and its value carried an uncertainty like any other measured value. Since then it carries none, because the General Conference on Weights and Measures, the CGPM of Chapter 3, decided in November 2018 that the constant has exactly this value, and that decision defines the kilogram.

The Planck constant, written h, comes from quantum physics, where it links the energy carried by light to the light's frequency. Its unit, the joule second, equals a kilogram multiplied by a square meter and divided by a second, as the SI Brochure states. The CGPM had already defined the second through the frequency of a caesium atom and the meter through the speed of light. The kilogram was therefore the one part of that unit not yet defined, so fixing the number for h fixed the kilogram. The definition in the SI Brochure says exactly this: the kilogram is defined by taking the numerical value of h as fixed at that number when h is expressed in joule seconds. An experiment that measured h in joule seconds against a known kilogram can therefore be run the other way: given h, it measures a mass (Chapter 20).

The second and the meter had each been defined by fixing a number. In 1967 the 13th CGPM defined the second as the duration of 9 192 631 770 periods of the radiation from a transition between two energy levels of the caesium-133 atom. In 1983 the 17th CGPM defined the meter as the length of the path that light travels in vacuum in 1/299 792 458 of a second. The CGPM thereby made the speed of light exactly 299 792 458 meters per second, because a meter became whatever length light covers in that fraction of a second. In 2018 the CGPM kept those two numbers unchanged, restating them as fixed values of two constants, the caesium frequency and the speed of light. Until 20 May 2019 the kilogram was the last unit still defined by an object, the cylinder of Chapter 18.

Seven constants, one system

Since 20 May 2019 the whole SI rests on seven constants whose values are fixed, listed below as the first table of the SI Brochure gives them. Each of the seven base units is defined through one or more of them: the second, meter, kilogram, ampere, kelvin, mole and candela. Fixing the values did not make them more accurate: laboratories no longer measure them at all, and the experiments that used to determine them now determine the units instead.

The CGPM chose the values so that every unit kept its size on the day the new definitions took effect: the values "have been chosen to be consistent with the earlier definitions in so far as advances in science and knowledge allow", in the words of the SI Brochure. For the kilogram, the CGPM needed a value of h for which the international prototype still had a mass of 1 kg on 20 May 2019, within the uncertainty with which h was then known. Before any vote, the CCM, the committee that advises the CIPM of Chapter 3 on mass, set the conditions that the measurements of h had to meet, and a task group of CODATA calculated the value and its uncertainty. In 2017 CODATA was the Committee on Data for Science and Technology of the International Council for Science.

47 — On 20 May 2019 the uncertainty moves; no mass changes

References and standardsUncertaintyReadingFocal detail

Conditions set before the vote

Before the CIPM asked CODATA for values to fix, the measurements of h had to meet four conditions, which the CCM set in 2013. At least three independent experiments had to give consistent values of h, so that the value would not rest on one method alone. They had to include work with watt balances, the instruments now called Kibble balances, which weigh a mass against an electrical force, and with silicon spheres, whose atoms are counted (Chapter 20). Each needed a relative standard uncertainty, the standard uncertainty of Chapter 11 expressed as a fraction of the value, no larger than 5 parts in 100 million, which is 50 parts per billion. At least one of them had to reach 2 parts in 100 million, or 20 parts per billion.

On a kilogram, the uncertainties that the CCM allowed amount to small masses, since each part per billion of a kilogram is 1 µg (Chapter 18). A relative standard uncertainty of 50 parts per billion is therefore 50 µg, and 20 parts per billion is 20 µg, less than the 35 µg offset that the BIPM's as-maintained mass unit had built up against the prototype by 2014.

The third condition concerned the masses rather than h: the BIPM's prototypes and reference masses, and the masses used in the experiments, had to be compared as directly as possible with the international prototype. Meeting it took the prototype out of its safe in December 2013, and the comparisons that followed found the 35 µg offset (Chapter 18). The fourth required the procedures for realizing the new kilogram, and for disseminating it to other masses, to be validated in accordance with the principles of the CIPM's arrangement for mutual recognition (Chapter 21). Under that arrangement, national institutes accept one another's results.

The CCM declared the conditions met in 2017, but it warned that the best results did not fully agree. The most recent results with relative standard uncertainties below 50 parts per billion "do not pass the standard chi-squared test of consistency", in the CCM's words. That test shows whether a set of results scatters around its common value by more than the results' stated uncertainties allow. The results each met the conditions on uncertainty, but together they spread a little more widely than those uncertainties predicted, which suggested that at least one budget missed or understated an effect. The CCM still recommended that the CIPM proceed with the planned redefinition at the next CGPM, and the task group that calculated h had to account for the disagreement.

One calculation, and a wider uncertainty

The value of h came from one calculation over all the data, made by CODATA's Task Group on Fundamental Constants, which David Newell of NIST chaired. The group combined every relevant result available by 1 July 2017 in a special least-squares adjustment, a calculation that finds the one set of values for the constants that best fits all the measurements together. It was to supply values of h, the elementary charge, the Boltzmann constant and the Avogadro constant for the CGPM of November 2018.

Three results from Kibble balances entered the calculation for h, and two of them met the CCM's tighter condition of 20 parts per billion. NIST-4, NIST's fourth balance, had a relative standard uncertainty of 13 parts per billion, and the balance at NRC, Canada's national metrology institute, had 9.1 parts per billion. The balance at LNE, France's national metrology institute, had 57 parts per billion, just above the CCM's wider condition of 50. The group left out a fourth result, from NIM, China's national metrology institute, which had measured h with a related instrument, a joule balance. At 240 parts per billion that result failed the task group's self-sensitivity criterion, a test that removes results too uncertain to change the adjusted value.

Silicon spheres, the second method that the first condition required, supplied results inside 50 parts per billion. Fujii and colleagues, at the national metrology institutes of Japan, Italy and Germany, put the relative standard uncertainty of the latest sphere result, of 2017, at about 12 parts per billion (Chapter 20). NRC's balance, NIST-4 and the spheres therefore met the first condition, while LNE's result entered the calculation without counting toward it.

48 — The Kibble-balance results against the CCM's conditions

UncertaintyLimits and decisionsFocal detail

The task group found the data for h "somewhat inconsistent", and it widened the uncertainty to cover the spread among the results that the CCM's test had flagged. The adjustment alone would have given h a relative standard uncertainty of 6 parts per billion, and the task group expanded it to 10 parts per billion. It then chose the exact digits so that, at the moment of the change, the international prototype still had a mass of exactly 1 kg on the new scale. Widening the uncertainty did not change the digits chosen for h, but it set the relative standard uncertainty of the prototype's mass after the change at 10 parts per billion.

The CGPM turned that measured value of h into a definition by a vote, without measuring anything. At its 26th meeting, in Versailles, it voted unanimously for the revision on 16 November 2018. In a resolution of that meeting, the CGPM repealed the definition based on the mass of the international prototype, in force since 1889, and fixed the seven constants with effect from 20 May 2019. From then on, the experiments that had measured h in terms of the prototype measure masses in terms of h.

What changed on 20 May 2019

On 20 May 2019 no mass in any laboratory changed. What changed was which quantity carried the uncertainty: before that day the international prototype was exact and h carried a relative standard uncertainty of 10 parts per billion, and after it h is exact. At the change the prototype's mass was 1 kg with a relative standard uncertainty of 1 part in 100 million, which is 10 parts per billion, or 10 µg. The uncertainty of h had passed to the prototype: the SI Brochure gives that figure as the standard uncertainty of the combined best estimates of h at that time. From that day the prototype's mass is a quantity to be determined by experiment, whose latest value Chapter 21 gives, and the cylinder that defined the kilogram for 130 years is a mass like any other, measured and stated with an uncertainty.

For everyday measurement the change was far too small to see, because an uncertainty of 10 parts per billion at the top of the chain is tiny beside the uncertainties added further down. A pressure balance generates a pressure equal to a downward force divided by the area of its piston, and its masses under gravity supply that force, as NIST describes it (Chapter 15). A relative change in those masses therefore changes the pressure by the same fraction. At a cuff pressure of 150 mmHg, 10 parts per billion is 0.0000015 mmHg. The channel's combined standard uncertainty at that pressure is 0.70 mmHg (Chapter 11), about 470,000 times as large. Electrical laboratories, by contrast, had a shift to apply on that day, in the conventional values of the electrical units, for reasons that Chapter 20 explains.

As of October 2026, the seven constants and the kilogram's definition stand as the 26th CGPM fixed them. The 28th CGPM met in Versailles from 13 to 15 October 2026 and adopted seven resolutions, none of which changes the SI or the kilogram.

+ The questionHow does a Kibble balance turn the Planck constant into a mass, and is there another way?

A balance built for the ampere

A Kibble balance sets the weight of a mass against an electrical force, and it was first built to measure electric current, not mass. Bryan Kibble invented it in 1975 at Britain's National Physical Laboratory, NPL, as Schlamminger and Haddad of NIST date it in a 2019 review of the instrument. By NPL's account the first such balance improved the accuracy with which the ampere, the unit of electric current, could be measured. In that first use the mass on the pan was the known quantity and the electrical unit was the unknown. Since the redefinition of Chapter 19 the roles have reversed: the Planck constant, h, is fixed, and the mass is what the balance measures.

Two measurements with one coil

The electrical force acts on a coil of wire that carries a current in the field of a strong magnet, and the balance compares that force with the weight in two separate measurements. In the weighing mode, which NIST also calls the force mode, the balance holds the coil at a fixed position. A mass is placed on the balance or taken off, and the current through the coil changes until the electromagnetic force exactly balances the change in weight. That weight is the mass multiplied by the local acceleration of gravity, and the force is the current multiplied by a factor set by the magnet's field and the length of wire inside it. The balance never needs the value of that factor, because a second measurement with the same coil cancels it.

In the moving mode, also called the velocity mode, the balance sweeps the same coil through the same field at a known speed and measures the speed and the voltage together. A coil moving through a magnetic field generates a voltage, and that voltage is the speed multiplied by the same factor of field and wire. The weight multiplied by the speed is therefore the factor times the speed times the current, which is the voltage multiplied by the current, and the factor cancels. Weight times speed is a mechanical power and voltage times current an electrical one, which is why the instrument was first called the watt balance. A mass then follows from a voltage, a current, a speed and the local gravity, and every one of those is a measurement of time, length or an electrical quantity.

NIST-4, NIST's fourth balance, shows what the two modes demand in practice. It used test masses of 0.5 kg and 1 kg in stainless steel and two platinum-iridium kilograms, loaded from 0.5 kg up to 2 kg. In the moving mode the coil travels slowly, at a nominal 0.975 mm a second over a sweep of 78 mm, so one sweep takes 78 divided by 0.975, about 80 seconds, and with a 1 kg mass the coil generates about 0.68 V. Because the weight depends on the local acceleration of gravity, an absolute gravimeter measures that acceleration at the balance itself. A single value of h took many repetitions. From 22 December 2015 to 30 April 2017 Haddad and colleagues, all NIST staff, made 1,174 sets of measurements, more than 10,000 weighings, and in 2017 they reported h with a relative standard uncertainty of 13 parts per billion.

49 — One coil, two measurements

The quantity being measuredReferences and standardsThe signal in the chainFocal detail

Voltage and current from two quantum effects

Two effects of quantum physics serve as the standards for the voltage and the current, and they bring the Planck constant into the balance. In the Josephson effect, microwaves of a known frequency drive a junction between two superconductors, materials that carry a current without resistance when cooled far enough. The junction then holds a voltage set only by that frequency and by the Josephson constant. That constant equals twice the elementary charge divided by h, where the elementary charge is the size of the charge that one electron carries. In the quantum Hall effect, a conducting layer held in a strong magnetic field at low temperature shows a resistance set by the von Klitzing constant, and that constant equals h divided by the square of the elementary charge. The quantum computing guide in this series, The price of a right answer, explains the Josephson junction itself.

A balance measures its voltage against a Josephson standard and its current as a voltage across a resistor calibrated against a quantum Hall standard. A voltage measured this way is a frequency divided by the Josephson constant, which makes it proportional to h divided by the elementary charge. The current is such a voltage divided by a resistance proportional to h divided by the square of the elementary charge, so it is proportional to the elementary charge alone. Their product is therefore proportional to h, with the elementary charge cancelled, so the weight that the current balances is tied to h, the meter and the second alone.

Because h and the elementary charge have both been exact since 2019, so have the two constants. The Josephson constant is 483 597.848 416 984 GHz per volt and the von Klitzing constant is 25 812.807 459 3045 Ω, as the CCEM, the CIPM's consultative committee on electrical units, gives them. From 1 January 1990 electrical laboratories had used conventional values of the two constants, adopted by the CIPM: 483 597.9 GHz per volt and 25 812.807 Ω. On 20 May 2019 the Josephson constant became smaller than that conventional value by about 107 parts per billion, and the von Klitzing constant larger by about 18 parts per billion.

The changes apply to voltages and resistances measured with the 1990 values, as the CCEM notes, so laboratories changed the values they assign to them. The voltmeters that test a voltage reference like the one in Chapter 6 trace, through their own calibrations, to Josephson standards, so the Josephson change applies to the monitor's converter reference too. At the reference's 2.5 V a step of 107 parts per billion, 107 nV on each volt, is 2.5 times 107 nV, about 0.27 µV. One count of the converter is 0.61 mV (Chapter 11), some 2,300 times as large, so the change is far too small for the monitor to register.

Counting the atoms in a sphere

The second way to realize the kilogram, called X-ray crystal density or XRCD, counts atoms instead of weighing against a current, as Bettin and colleagues of PTB and of NMIJ, Japan's national metrology institute, describe it in a 2019 review. A sphere of almost pure silicon-28, a single crystal of about 1 kg, holds its atoms in a regular lattice built of cubic cells that each hold eight atoms on average, and X-rays measure the lattice, which gives the method its name. The sphere's volume divided by the volume of one cell, the cube of its edge, gives the number of cells, and eight times that number gives the number of atoms. The count multiplied by the mean mass of one silicon atom gives the sphere's mass. That mean mass follows from the fractions of the isotopes in the crystal, and atomic physics ties it to h through further constants, among them the mass of the electron and the Rydberg constant.

A count that precise needs a sphere that is nearly perfect in its shape and nearly pure in its silicon, because the mass follows from the sphere's volume and from the mean mass of its atoms. The large spheres are about 94 mm across, and PTB's depart from a perfect sphere by less than 50 nm, with a surface roughness below 0.2 nm. The silicon is enriched so that 99.9958 % to 99.9993 % of its atoms, depending on the crystal, are silicon-28.

Several institutes share the measurements in the International Avogadro Coordination, each taking one part of the count. PTB measures the spheres' volumes and their molar mass, the mass of a mole of their atoms. Since 2019 the number of atoms in a mole has been fixed: it is the Avogadro constant in Chapter 19's table, so the molar mass divided by that number gives the mean mass of one atom. NMIJ, with Japan's accelerator research organization KEK, measures the lattice strain and the surface. INRIM, Italy's national metrology institute, measures the lattice spacing, and NIST the molar masses.

Before 2019 the sphere, like the Kibble balance, measured a constant rather than a mass. The spheres' masses were known from the prototype, through the mass standards that the BIPM calibrated for the project in its extraordinary campaign of 2014 (Chapter 18), so the count gave the value of the Avogadro constant. In a paper published in December 2017, Fujii and colleagues from NMIJ, INRIM and PTB reported four such results, the latest with a relative standard uncertainty of about 12 parts per billion, close to NIST-4's 13.

50 — Counting the atoms in a silicon sphere

References and standardsFocal detail

Each method carries its own budget, and the two budgets have different shapes. NIST-4's largest rows are of similar size: the electrical measurements, the calibration of the test masses, the fitting of the field profile, the mechanics of the balance, its alignment and the local gravity each supply between 4 and 7 parts per billion. The sphere's budget is led by one row, the volume of the sphere, at 15 parts per billion, followed by the thin layer on its surface at 10. The rows of each budget add by the root-sum-of-squares of Chapter 11, which squares each row, so the largest rows count most and the shape of a budget decides which better measurement would lower its total most.

51 — Two budgets at the top of the chain, drawn as squares

Noise and errorUncertaintyFocal detail

Who realizes the kilogram today

Ten laboratories realized the kilogram in the key comparison of 2024, the third of its kind. In a key comparison, institutes set their results for one quantity side by side against a common reference value (Chapter 21). The BIPM published the final report of the 2024 comparison on 20 February 2026. Six laboratories operated Kibble balances: the BIPM itself and five national institutes, LNE in France, METAS in Switzerland, NIST in the United States, NRC in Canada and UME in Türkiye. NIM in China used a joule balance, a related design. Three institutes, CMS/ITRI in Chinese Taipei, NMIJ in Japan and PTB in Germany, used silicon-28 spheres whose masses were determined by XRCD. India is not among the ten.

NRC's balance shows how a realization depends on the rest of the chain. NRC's masses had been calibrated by the BIPM, so when the BIPM corrected its mass unit in 2014 (Chapter 18), NRC's determination of h shifted by 35 parts per billion. The same correction cut NRC's uncertainty for the traceability of its masses from 7.2 to 3 parts per billion, as Wood and Sanchez of NRC reported at a conference in 2015. At the time NRC measured the balance's voltage against a programmable Josephson array that PTB had supplied, so a realization in Canada rested in part on a voltage standard from Germany. The balance's 2017 result reached 9.1 parts per billion, the smallest uncertainty among the Kibble balances in the adjustment of Chapter 19.

Smaller balances are being built for calibration laboratories. In 2024 NIST delivered a prototype tabletop Kibble balance to the US Army, by NIST's account the first such delivery in the United States, and NIST aims for laboratories to measure masses from 1 mg to 1 kg this way. A design by Li and colleagues at Tsinghua University, published as a preprint in January 2026, targets class E2 calibrations from 1 g to 1 kg, the second most accurate class in OIML's rules for weights.

The first international comparison of such balances tested them against conventional calibrations. In that blind comparison, published in July 2026, tabletop balances at TU Ilmenau, PTB and NIST measured two sets of weights of OIML class E1, the most accurate class, from 1 mg to 10 g. The balances showed generally good agreement, in the authors' words, with conventional calibrations of the same weights by the makers' accredited laboratories, at uncertainties of the E1 and E2 levels. In June 2025, a year before that comparison was published, NIST noted that manufacturers still sent their weights to NIST for calibration.

+ The questionHow does a unit realized in a few laboratories reach every country's balances?

A copy kept in New Delhi

In a laboratory in New Delhi, India keeps its own platinum-iridium copy of the old kilogram. It is copy No. 57, known as NPK-57, and CSIR-NPL, India's national metrology institute, holds it in its mass metrology section. The BIPM calibrated it in 1955, handed it over in 1958, and recalibrated it in 1985, 1992, 2002, 2012 and 2022.

The copy's mass changes between calibrations, so its value holds only as of its last calibration. Mandal and colleagues, all of CSIR-NPL, gave the changes in a 2012 conference paper: 218 µg from 1955 to 1985, about 7.3 µg a year; 36 µg from 1985 to 1992; and 24 µg from 1992 to 2002, about 2.4 µg a year. Each change runs from a value taken after one cleaning to a value taken before the next, so it spans the years between two visits to Sèvres, over which contamination gathers on a cylinder's surface (Chapter 18). In that paper the authors gave the interval between calibrations as at most ten years.

India does not realize the kilogram. CSIR-NPL took no part in the 2024 comparison of realizations (Chapter 20), and it says that it is working toward the new definition and the infrastructure that goes with it. India therefore still receives its kilogram as a calibrated cylinder, as it did in 1958, but the value on the cylinder's certificate now has a different origin. The BIPM continues to calibrate platinum-iridium prototypes and stainless-steel standards for its Member States, but since 1 February 2021 it has taken the traceability of those calibrations from a value agreed among the institutes that do realize the kilogram. The 2022 calibration of NPK-57 falls after that date, so by the BIPM's own rule its value rests on the agreed value and, through it, on the Planck constant.

Realizing a unit and disseminating it

Realizing a unit and disseminating it are different jobs, and since 2019 the two need not happen in the same laboratory. To realize the kilogram is to produce a mass whose value follows from the definition, with an instrument such as a Kibble balance or a silicon sphere (Chapter 20). To disseminate it is to pass that value down to other masses by comparison: from a realization to national standards, from national standards to the working standards of accredited laboratories, and from those to the weights used in factories.

The realizations do not yet agree with one another closely enough for each to serve alone. In 2017 the CCM therefore asked the institutes with a realization to use a consensus value, a value for the kilogram that the CCM computes from the key comparisons of the realizations. The institutes are to use it "until the dispersion in values becomes compatible with the individual realization uncertainties", that is, until the uncertainties that the realizations each state account for the spread among them. Member States without a realization receive traceability to the same value through the BIPM's calibrations.

Each consensus value states what the old prototype weighs on the scale of the realizations, and the CCM has set three so far. The first, of 2021, was 1 kg − 2 µg with a standard uncertainty of 20 µg. It was the mean of three sets of results: the CCM's pilot comparison of 2016, the first key comparison of realizations in 2019 and the BIPM's extraordinary campaign of 2014 against the prototype (Chapter 18). Because it agreed with 1 kg within its uncertainty, the BIPM made no change to the international mass scale. The second, of 2023, was 1 kg − 7 µg. The third has applied since 1 March 2026: it puts the mass of the international prototype at 1 kg − 12 µg, with the standard uncertainty unchanged at 20 µg. A mass value carried from the prototype, taken as exactly 1 kg, therefore came out too high. In its notice of February 2026 the BIPM asked for values traceable to the prototype-based unit to be reduced by 12 µg, and values traceable to the second consensus value by 5 µg, the step from 1 kg − 7 µg to 1 kg − 12 µg.

52 — Three comparisons, three consensus values

References and standardsUncertaintyFocal detail

Individual realizations may take over only when they agree well and repeatedly, and the CCM's working group on mass listed four criteria for that in its report of June 2025. At least five consistent realizations must reach relative standard uncertainties of 40 parts per billion or better and agree with the comparison's reference value in two consecutive key comparisons. At least three of them must reach 20 parts per billion or better, the level that the CCM required of the best measurement of h before the change (Chapter 19). The consistent set must include two independent methods, Kibble balances and silicon spheres, so that the unit does not rest on one method alone. The consensus value must lie within 5 parts per billion of the final reference value. The CCM still adopted a third consensus value in 2026, a sign that individual realizations have not yet taken over. The next comparison of realizations is planned for 2027, and the CCM repeats such comparisons every three to four years.

Key comparisons, for the kilogram and for the cuff

A key comparison is the test in which national institutes show whether their results for one quantity agree. Several institutes measure the same quantity, usually on one transfer standard that travels between them, and a pilot laboratory organizes the work and analyzes the results. The comparison yields a key comparison reference value, and for each institute a degree of equivalence, the difference between its result and that reference value, stated with the uncertainty of the difference.

Institutes have compared their realizations of the kilogram in three key comparisons, in 2019, 2021 and 2024, with seven, nine and ten participants. Each reference value is the difference between the mass that the realizations gave a 1 kg standard and the mass that the BIPM's as-maintained mass unit gave it (Chapter 18). That unit represents the mass of the international prototype, as Stock of the BIPM and Davidson of NPL write in their report on the calculation of the 2026 consensus value. The values were −18.8, −15.2 and −10.7 µg, so on the realizations' scale the prototype came out lighter than 1 kg by about those amounts. Their standard uncertainties were 9.0, 8.9 and 6.4 µg, the first two including 5 µg for the stability of the BIPM's unit up to 2025. The reference value moved by 8.1 µg in five years, from −18.8 to −10.7 µg, about as much as its own uncertainty, and the CCM now bases the consensus value on the mean of all three rather than on the latest.

The cuff's own quantity has key comparisons too, and India's institute piloted one of them. From October 1998 to 2001 CSIR-NPL led a comparison in gas gauge pressure, the cuff's kind of pressure (Chapter 4), from 20 to 105 kPa for APMP, the regional metrology organization for Asia and the Pacific, under the code APMP.M.P-K6. In millimeters of mercury that range runs from about 150 to 788 mmHg, but the laboratories measured at nominal points from 21.4 to 101.2 kPa. The two lowest points, 21.4 and 41.3 kPa, are about 161 and 310 mmHg, inside the 50 kPa full scale of the sensor in Chapter 11. Because the lowest lies above the cuff pressure of 150 mmHg used in Chapter 11's budget, the comparison gives no direct evidence at that pressure or below it.

53 — A key comparison for the cuff's own quantity

The quantity being measuredReferences and standardsUncertaintyFocal detail

The laboratories measured one transfer standard in turn: a piston and cylinder of nominal effective area 335.7 mm² on a pressure balance base, which NMIJ in Japan supplied. A pressure balance generates its pressure as a force divided by the piston's effective area (Chapter 15), so what each laboratory measured was that area at each pressure. Ten laboratories took part, CSIR-NPL among them. PTB in Germany, one of the ten, joined as an invited laboratory. It was the one laboratory that also took part in CCM.P-K6, the comparison in the same quantity at the level of the CCM, whose work covers pressure as well as mass. PTB's results therefore tie the regional comparison to the worldwide one.

CSIR-NPL's result differed from the reference value by far less than its uncertainty. At 21.4 kPa CSIR-NPL's relative standard uncertainty was 15.8 parts per million, and PTB's 6.4 parts per million. CSIR-NPL's degree of equivalence was −0.77 parts per million, with an expanded uncertainty at k = 2 (Chapter 12) of about 33 parts per million, so the difference was about 2 % of its own uncertainty, 0.77 divided by 33. The other laboratories agreed as well: in their final report, Bandyopadhyay of CSIR-NPL and nine colleagues found "an excellent agreement of all participating laboratories within the estimated expanded uncertainties".

A mechanism for trusting another country's number

National institutes recognize one another's results under an arrangement that rests on key comparisons. The CIPM MRA is that mutual recognition arrangement, "the framework through which National Metrology Institutes (NMIs) demonstrate the international equivalence" of their measurement standards and of the certificates they issue, in the BIPM's description. The arrangement produces a set of calibration and measurement capabilities, or CMCs (Chapter 16). Each is an institute's statement of what it can calibrate and with what uncertainty, peer-reviewed and approved before it is published in the BIPM's key comparison database, the KCDB. Accredited laboratories state CMCs of their own, and their chains of calibration end at a national institute's CMC in the KCDB.

A CMC rests on two kinds of evidence: the institute's comparisons, such as the pressure comparison that CSIR-NPL led, and reviews of the institute itself. In November 2020, APMP reviewers visited CSIR-NPL and assessed all its work for the CCM's quantities against ISO/IEC 17025:2017, and CSIR-NPL reported no nonconformities, that is, no departures from the standard's requirements. Worldwide, the KCDB listed about 26,000 peer-reviewed CMCs and about 2,000 comparisons, about 1,200 of them key comparisons, in the report that Milton, the BIPM's director, gave in June 2025. CSIR-NPL had 54 CMCs registered in the quantities that the CCM covers, with another 20 planned, by its own report to the CCM of about 2021, and a certificate issued in India in those quantities can end its chain at one of them.

From a consensus value to a factory's weights

Inside a national institute and below it, the kilogram passes from weight to weight by comparison. In a 2010 conference paper, Mandal and Gopan of CSIR-NPL described how the institute re-established its working standards, from 1 mg to 20 kg, from NPK-57 through four 1 kg transfer standards. From NPK-57, CSIR-NPL carries the unit to weights from 1 mg to 2,000 kg, using among other instruments a vacuum mass comparator that reads to 0.1 µg. Accredited laboratories and factories use weights calibrated down from such standards.

OIML's Recommendation R 111 sorts those weights into classes, with class E1 as the link between national mass standards and the classes below it. A class E1 kilogram may differ from its nominal value by no more than 0.5 mg, and the expanded uncertainty of its calibration must not exceed a third of that limit. The 0.5 mg limit is 500 µg, about 42 times the 2026 reduction of 12 µg, so the reduction is small even against the limit of class E1. In a 2025 amendment, OIML changed the reference for class E1 from the international prototype of Chapter 18 to "internationally recognised realisations of the definition of the kilogram in the SI", the realizations of Chapter 20.

The masses of a pressure balance are calibrated along the same path. NIST's pressure laboratory, for one, used masses traceable to NIST's own mass laboratory, as Bean of NIST described in 1994. The balance's pressure comes from the weight of those masses (Chapter 15), so a change in their calibrated values passes to every reference manometer calibrated against the balance. Through the production station of Chapter 14, the change passes on to every monitor calibrated there.

A change at the top of the chain reaches all of these at once, and the 2026 consensus value shows how far. Mass values traceable to the prototype-based unit fell by 12 µg for each kilogram, which is 12 parts per billion, and a pressure balance's pressure changes by the same fraction as its masses, far less than the uncertainty of its piston's area. Because the standard uncertainty stayed at 20 µg, institutes' published capabilities needed no further adjustment, by the BIPM's account. The first consensus value, in 2021, had required more. Institutes traceable to it then had to include its standard uncertainty of 20 µg in their budgets, so the BIPM asked those whose CMC for 1 kg lay at or near 20 µg to increase their calibration uncertainty.

+ Part VI · Proving the measurement

In a product.

Design verification asks whether a product meets its requirements, and every answer it gives is a measurement. A device maker measures its products to verify them, and when the product is itself a measuring instrument, such as the blood-pressure monitor, the maker's test station measures how well the product measures. The station's numbers then need proof of their own before they can decide anything. In Chapter 22 the engineer tests the production pressure test itself and separates the scatter that comes from the monitors from the scatter that the station and its technicians add. In Chapter 23 the engineer sets out the evidence that makes the test method valid, and in Chapter 24 follows the monitor's accuracy claims to its label, including the claim that no calibration can prove, the one for the blood-pressure estimate.

+ The questionBefore trusting a measuring system's numbers, how do engineers test the system itself?

Three sources of scatter

Three technicians test the same ten monitors three times each, which gives 90 results, and the engineer who plans the study wants to know how much of their spread comes from the test itself. At the end of the line each monitor enters its service mode, a technician connects it to a rigid vessel and a reference manometer, and the station holds a series of steady pressures (Chapter 14). At each pressure the technician records the monitor's error, its reading minus the reference's, and the decision rule of Chapter 13 turns that error into a pass or a fail. Each recorded error is itself a measurement made by the station, so it carries the station's own scatter as well as the monitor's error, and the engineer must know the station's share before the station sorts any monitor.

Part of the spread of the 90 results is real, because the ten monitors truly differ from one another: each sensor keeps some hysteresis and some residual error after calibration (Chapter 11). That part-to-part variation is what the test exists to see. When one technician tests one monitor three times, the three results still differ a little, through small changes in how the pressure settles, in the reference's last digit and in the monitor's rounding. That spread is the station's repeatability, measured under the repeatability conditions of Chapter 2. When three technicians test the same monitor, their averages differ as well, because each connects, waits and reads in a slightly different way, and that spread is the station's reproducibility.

Engineers in manufacturing call any measuring instrument or test system a gauge. They call repeatability and reproducibility together the gauge R&R, the variation that the measuring system adds to what it measures, and the study that measures it a gauge study. The Automotive Industry Action Group, AIAG, publishes the method that separates the three sources in its Measurement Systems Analysis reference manual, and engineers call the whole discipline by those words, measurement-system analysis, or MSA. The manual's fourth edition, of June 2010, is the most recent that the American National Standards Institute, ANSI, lists in its store as of October 2026. A pressure test fits the manual's primary focus, which ANSI describes as "systems where readings can be replicated on each part": at a pressure station a technician can test the same monitor again at the same pressure.

54 — The crossed study: ten monitors, three technicians, three trials

The quantity being measuredReferences and standardsNoise and errorReadingFocal detail

Bias, linearity and stability come first

Before measuring the scatter, the engineer asks whether the station is right on average, because a station that repeats well can still repeat the same error. Engineers who follow MSA estimate the systematic error of Chapter 2 as the station's bias: the average difference between the station's results on a part and that part's known value. That bias belongs to the station, not to the monitor. Linearity is the way the bias changes across the range, and stability is the way it changes over time.

The bias can differ from one point of the range to another. In a worked example of a linearity and bias study by Minitab, which makes statistical software, five parts span the range, and a separate inspection gives each a known value, its master value. The bias is present at three of the five master values and absent at the other two, so a station can be right at one point of its range and wrong at another, and the engineer checks the bias across the whole range.

For the pressure station, a known pressure serves as the part with a known value. A calibration laboratory compares the station's reference manometer with a better reference and finds the station's bias at each test point, from the lowest test pressure to the highest (Chapter 14). Its certificate reports the bias point by point, and so shows the linearity as well. The engineer then follows the stability of the bias between calibrations with the intermediate checks of Chapter 17. No laboratory reports what the technicians add, so the engineer measures that share with a gauge study.

The crossed study

Engineers call a gauge study crossed when every technician tests every monitor, as in the design that opens this chapter: three technicians each test the same ten monitors three times, in random order. The engineer judges the station against the spread of the monitors in the study, so the ten monitors must resemble those that the line produces. Ten monitors chosen to be nearly identical would make any station look poor, and ten chosen to differ widely would make any station look good.

The engineer can analyze the 90 results by the simplest method, the average-and-range method, which needs nothing beyond differences, products and square roots. For each technician and each monitor, the engineer takes the range of the three results, the highest minus the lowest, so 3 technicians and 10 monitors give 30 ranges. A factor from a table turns an average range into a standard deviation. The factor depends on how many results each range covers, because the range of more results tends to be wider for the same scatter. The engineer multiplies the average of the 30 ranges by the factor for three trials and obtains the repeatability as a standard deviation, which MSA calls the equipment variation, EV.

The engineer then multiplies the largest difference between the technicians' averages by the factor for three technicians, squares the result, subtracts a small correction for the repeat scatter that each average already holds, and takes the root. The result is the appraiser variation, AV, appraiser being MSA's word for the person who measures. From the range of the ten monitors' averages and the factor for ten parts, the engineer obtains the part variation, PV, in the same way. The three are standard deviations of independent sources, so the engineer combines them by the root-sum-of-squares of Chapter 11: EV and AV into the gauge's R&R, written GRR, and GRR and PV into the study's total variation, TV. The engineer's main result is %GRR, the gauge's R&R divided by the total variation and expressed as a percentage.

Engineers who follow AIAG's manual judge %GRR by three bands, as McNeese of BPI Consulting, a company that sells a statistics add-in for spreadsheets, reproduces them in a 2015 tutorial. Under 10 % the tutorial's verdict is "Generally considered to be an acceptable measurements system", from 10 to 30 % it is "May be acceptable for some applications", and over 30 % it is "Considered to be unacceptable". Minitab gives the same bands in its help pages and makes the middle one depend on the application, on the cost of the measuring device and on the cost of repair. The manual itself is sold rather than published openly, and both companies cite its fourth edition.

A variance is the square of a standard deviation, and Minitab also states the rule in variances, as the percent contribution to the study's total variance: under 1 % acceptable, 1 to 9 % depending on the application and costs, and over 9 % not acceptable. The two scales are one rule: a ratio of 10 % or 30 % between standard deviations is a ratio of 1 % or 9 % between their squares, since 0.1 squared is 0.01 and 0.3 squared is 0.09. A station that takes a quarter of the spread as a standard deviation therefore takes only a quarter squared, a sixteenth, as a variance. An engineer who reports a share must say which of the two it is.

The number of distinct categories, or ndc, measures how finely the station can sort monitors: it estimates how many groups of parts the station can tell apart within the spread of the parts. Minitab computes it from the ratio of the part variation to the gauge's R&R: it multiplies that ratio by a fixed factor, 1.41, the square root of 2, and cuts the result down to a whole number. Minitab writes that AIAG recommends five or more categories, and that fewer than two are "of no value for controlling the process". A station with one category can only report that every monitor looks the same, because its own scatter covers the real differences between monitors.

55 — The study's spread, added as squares

The quantity being measuredNoise and errorLimits and decisionsFocal detail

Statistics software usually analyzes the same results by the analysis of variance, which splits the sum of the squared deviations directly into its sources. BPI ran that analysis on the same 90 results and found the gauge at 7.76 % of the total variance, in the same middle band as the average-and-range method's 7 %. Because the two methods give slightly different numbers, the engineer reports which one produced each figure and never mixes them in one table.

A monitor that shows whole millimeters of mercury can hide the station's repeatability, as Chapter 10 showed for repeated readings: three trials that all display 150 give a range of zero, although the pressure behind them scattered. The study then reports a repeatability that belongs to the display step, not to the station. The engineer therefore records the monitor's value before rounding, from a service mode or a data link where the maker provides one, and otherwise reports the display step beside the result.

A verdict needs its own study

Some stations record a verdict instead of a number. Rossmax's CalPro, the field system of Chapter 14, shows PASS or FAIL, and a production station that applies the decision rule of Chapter 13 may keep only that result. A verdict cannot be averaged, so the engineer judges it by attribute agreement: how often one technician gives the same verdict on the same monitor when repeating, how often different technicians agree, and how often the verdicts match the standard, the verdict known to be right for each monitor. Minitab reports consistency apart from correctness, because agreement alone does not show that a verdict is right: "Consistent ratings aren't necessarily correct ratings." Two technicians who pass the same faulty monitor every time agree perfectly and are wrong every time.

Minitab measures agreement with a statistic called kappa, which corrects the share of agreeing verdicts for the share that chance alone would produce. Minitab writes that AIAG suggests a kappa of at least 0.75 for good agreement and that larger values, such as 0.90, are preferred. For a pressure station, the hard cases are monitors whose true errors lie close to the limit. Technicians shown only clearly good monitors would agree almost every time and prove nothing, because every verdict would be easy.

Where the rules come from

A maker with several identical stations need not repeat the whole study on each one, and the rule that allows this comes from the car industry, as the method does. IATF, the International Automotive Task Force, owns the automotive quality standard IATF 16949, and in its list of frequently asked questions it answers that a complete study of each single instrument is not required. Instruments with the same characteristics "can be grouped", and "a sample instrument (representative of the gauge family) can be used", so one station can serve as the sample for the stations identical to it. IATF 16949:2016 is the edition in force as of October 2026, and IATF plans a revision for mid-2027, after which the answer may change.

Device makers encounter the gauge study in process validation, in which a maker shows with evidence that a manufacturing process consistently gives products that meet their requirements. The Global Harmonization Task Force, GHTF, an international body, published guidance on process validation in 2004. In an annex, GHTF states that "When studying variation, good measurements are required", and that "Many times an evaluation of the measurement system should be performed using a gauge R&R or similar study". GHTF describes the gauge study as a means of "evaluating the precision and accuracy of a measurement device". GHTF closed in 2012, and the guidance remains available in the archive of GHTF's documents that its successor, the International Medical Device Regulators Forum, IMDRF, keeps. In Chapter 23 the engineer follows the same guidance from the gauge to the whole test method.

The engineer can also judge a measuring process by a second route, set out in ISO 22514-7, on the capability of measurement processes. On that route the engineer builds an uncertainty budget for the process and judges the resulting uncertainty with a capability ratio, which sets it against the tolerance the process must check. ISO describes the standard as following the approach of the GUM, the method of Chapter 11, and as "primarily developed to be used for simple one-dimensional measurement processes", a class that includes a pressure reading. ISO 22514-7 is in force in its 2021 edition with an amendment of 2024, and its third edition is in the approval stage as of October 2026. A gauge study instead measures the scatter that actually appears, operators included, and the two answers check each other.

+ The questionWhat evidence shows that a test method gives the right answer every time it is run?

A test can agree with a wrong reference

The mirror of the opening story agreed perfectly with the one instrument that tested it, and that agreement was all the evidence there was. A production pressure test can fail in the same way, because each of its results is the monitor's reading minus the reference's. If the station's reference manometer read too high, a monitor that read too high by the same amount would show no error, and the station would pass it and record it as right. In Chapter 22 the engineer measured how much the station scatters when technicians repeat a test. The engineer now needs a wider answer: whether the whole method, from the fixture to the decision, gives the right answer each time a technician runs it, and what evidence can show that it does.

A test method is the complete procedure by which a maker decides whether a product meets a requirement: the equipment and its settings, the steps and their conditions, the number of samples, the calculation and the acceptance criteria. For the monitor's pressure test it covers the vessel and its connections, the reference manometer, the service mode and the test points. It also covers the time the technician waits at each point, the order of the two readings and the decision rule of Chapter 13. Test-method validation is the evidence that this procedure, run as written, gives results that are right and that repeat. A test method is a process whose product is a result, so the definition of process validation applies to it: establishing, by objective evidence, that a process consistently produces a result that meets its predetermined requirements, as the Global Harmonization Task Force, GHTF, defines it in its guidance of 2004 (Chapter 22).

Whether a process needs validation depends on whether its output can be checked afterward. GHTF sets validation beside verification, which it defines as "confirmation by examination and provision of objective evidence that the specified requirements have been fulfilled". Here verification has its design-and-process sense and applies to a product, not, as in Chapter 14, to a measuring instrument. Where a product can be checked after it is made, GHTF asks makers to consider "whether or not verification alone is sufficient to eliminate unacceptable risk and is a cost effective solution". A test's result cannot be checked in this way. The maker could confirm a pass only by testing the monitor again on a second, better station, and a maker who did that for every monitor would not need the first station. The maker therefore proves the method once, in advance, and then trusts each result that the proven method produces.

What FDA asks of a bench test

FDA asks a maker that submits bench tests to show how each test was planned as well as what it found, in its guidance of 20 December 2019 on non-clinical bench performance testing in premarket submissions. FDA writes that the test report should describe "the acceptance criteria that you prospectively identified", with "a clinical/scientific/engineering justification for these criteria, when applicable". FDA recommends "a scientific rationale to support the number of samples tested", and asks for "the data collected for all test samples (including outlying and anomalous results)". Where a test follows a standard, FDA asks for "a full citation of the standard, including the version", and for any departure from it. The guidance does not require test-method validation under that name, but each of these requests assumes a method fixed before the data and shown to work.

ISO 13485:2016, the quality-system standard for device makers, requires the method itself to be written down, and FDA's QMSR has incorporated the standard by reference since 2 February 2026 (Chapter 17). For the standard's clause on design verification, Tartal of FDA gives this summary in FDA's training slides on design and development: "The verification plans, including methods, acceptance criteria, and statistical techniques must be documented". The engineer therefore writes the method into the plan, with its acceptance criteria, before any monitor is tested.

FDA has cited the absence of such evidence in enforcement. On 27 June 2025 FDA sent a warning letter to an Italian maker of radio-frequency, laser and infrared heating devices. FDA wrote that the firm had "not established process validation and/or test method validation procedures" for the system that calibrated its devices' output. The firm's acceptance records listed results "without identifying the test equipment used (e.g., laser power meter)", and "quantitative acceptance points were only recorded as two check marks on a separate uncontrolled document". FDA issued the letter under the older Quality System Regulation, before the QMSR took effect, and a warning letter states FDA's allegations rather than a court's finding. Each of the three faults leaves a reviewer unable to tell whether the test could have found an error. Without validation nothing shows that the method works, an unnamed instrument cannot be linked to its calibration, and a check mark keeps no value to compare with the criterion.

56 — The pressure test as a method, element by element

The quantity being measuredReferences and standardsNoise and errorLimits and decisionsReadingFocal detail

What a validated test must show

A clear published list of what a validated test must show comes from medicines rather than devices. ICH, the international council that harmonizes technical requirements for medicines, set out the list in its guideline Q2(R2), which FDA issued as guidance in March 2024. Q2(R2) covers the analytical procedures used to test medicines, and the objective of their validation is "to demonstrate that the analytical procedure is fit for the intended purpose". ICH names the characteristics: specificity, range, accuracy and precision, with precision split into repeatability and intermediate precision. It defines accuracy as the "closeness of agreement" with a reference value and robustness as the "capacity to meet the expected performance criteria during normal use", and it places the study of robustness in the development phase.

ICH also states how many results each characteristic typically needs. For repeatability it asks for nine determinations over the range, or "a minimum of six determinations at 100 percent of the test concentration". For accuracy it gives, as one design, three concentrations with three replicates each. An engineer who reads the guideline for a pressure station puts test points where a drug laboratory puts concentrations. Six repeats at 150 mmHg, or three repeats at each of three pressures, would then be the minimum for the station's repeatability, read across from a text that ICH wrote for medicines.

Each characteristic has a counterpart in the pressure test. Range is the span of the test points. Accuracy is the agreement of the station's result with the monitor's true error, and it rests on the reference manometer's calibration, the subject of Chapter 14, and on the test uncertainty ratio of Chapter 12. Precision, in the sense of Chapter 2, is the station's repeatability and its reproducibility across days and technicians, which the gauge study of Chapter 22 measures. Operator independence, the property that the result does not change with who runs the test, matters because a monitor's verdict must not depend on the technician. ICH covers it under intermediate precision, whose typical variations include "different days, environmental conditions, analysts, and equipment", and a gauge R&R study, which GHTF's guidance names, measures it as reproducibility (Chapter 22).

Specificity is the method's response to the monitor's error alone, and not to a leak, a moving pressure or a change of temperature. Robustness is the method's capacity to keep meeting its criteria despite the small changes that daily use brings, such as a slightly different vessel, a longer wait or a warmer room.

The pressure test, element by element

A maker can validate its own cuff-pressure test against the procedure that OIML publishes for that test in its recommendation R 149-2 of 2020. In that procedure the tester replaces the cuff with a rigid metal vessel of 500 ml ± 25 ml and connects the monitor and a reference manometer through T-pieces and hoses no longer than 600 mm. The reference manometer's maximum permissible error is ±0.8 mmHg. The tester then raises the pressure from zero to the top of the scale in steps no larger than 50 mmHg, which sets the method's range, and takes the monitor's reading minus the reference's as the result. A maker's validation shows that its own station meets or improves on each of those elements, and that nothing else in the station moves the result.

The vessel must hold its air, because a leak lets the pressure fall while the technician reads. OIML limits an automated monitor's air leakage to 6 mmHg a minute in R 149-1. In its test procedure, R 149-2, the tester measures the leak at no fewer than three pressures, waits at least 60 s, and then measures the fall over 5 minutes. Even within OIML's limit the pressure moves during a reading. If the monitor and the reference are read at different moments, they see different pressures, and the difference enters the result as an error that belongs to neither instrument.

57 — What a gap between two readings costs

The quantity being measuredReferences and standardsUncertaintyFocal detail

The pressure must also hold still, because the monitor itself moves it quickly. During a measurement a monitor deflates the cuff at about 2 to 3 mmHg a second, the published rates of Chapter 7. In OIML's static test the station holds each pressure steady, so the only movement left during a reading is the leak. If a station compared the two instruments during a deflation at 3 mmHg a second, each second of gap between the readings would add 3 mmHg of error, thirty times the 0.1 mmHg a second of a leak at OIML's limit. The test's specificity therefore depends on the hold and on the order and timing of the two readings.

A method proves only what it tests

A test method proves only what it exercises, and a simulator test shows that limit plainly. A simulator replays the same oscillations to the monitor each time, so a monitor that returns the same values shows that its algorithm repeats. The simulator's oscillations do not come from a person's artery, however, so a repeatable answer on the simulator does not show that the answer is right, and Chapter 24 describes the study on people that does.

The simulator must itself repeat. Under the technical specification ISO TS 81060-5, which FDA recognized in July 2020, the simulators used to test automated monitors must meet requirements for repeatability and reproducibility, for the oscillometric method only. Fluke Biomedical's ProSim 8 simulator "generates a very repeatable signal within ± 2 mmHg", in its maker's words, a figure for the simulated oscillations rather than for static pressure.

Automating the reading moves part of the validation into software. Kumar and four colleagues at CSIR-NPL, India's national metrology institute, describe a rig whose software "calibrates 20 BP measuring instruments together", in a dataset they published in 2023. A camera reads each monitor's display by image processing, so code, not a technician, reads each number. Whoever runs such a rig must therefore show that the code reads every digit correctly under the rig's own conditions, the validation of software for its intended use that Chapter 17 described.

+ The questionWhen a device's label states its accuracy, how was that number proven, and what does it promise?

Two numbers on one label

A blood-pressure monitor's label carries two accuracy figures, each proven in a different place by a different kind of evidence. Under ISO 81060-2, the standard for the clinical investigation of automated monitors, the estimate's mean difference from reference measurements must be no more than 5 mmHg, with a standard deviation of no more than 8 mmHg. That is the standard's criterion 1, and a collaboration of three bodies set the protocol behind it: AAMI, the Association for the Advancement of Medical Instrumentation, ESH, the European Society of Hypertension, and ISO. For the reading, Microlife and A&D, two monitor makers, each state ±3 mmHg for the cuff pressure (Chapter 11).

The ±3 mmHg is a bench claim about the reading, and the limits it meets are set in a device standard and in OIML's rules (Chapter 13). The maker proves that bench claim with the evidence of the earlier chapters. A laboratory calibrates the monitor against a reference manometer at steady pressures (Chapter 14), and a decision rule turns each measured error into a pass or a fail (Chapter 13). A gauge study and a validated test method then show that the test station can be trusted to make those decisions (Chapters 22 and 23). None of that evidence reaches the systolic and diastolic values on the same display.

58 — One label, two claims, two kinds of proof

The quantity being measuredReferences and standardsLimits and decisionsThe algorithm's estimateReadingFocal detail

The estimate needs people

Calibration cannot reach the estimate, because the estimate is the output of the maker's own rules. The firmware derives systolic and diastolic pressure from the envelope of the oscillations, using ratios that the maker chooses (Chapter 9). No manometer holds a systolic pressure for the monitor to be compared with, because that pressure exists only in a person's artery while the heart beats. The maker therefore compares the estimate with a reference method, an independent way of finding blood pressure in the same people at the same visit. Under ISO 81060-2 the reference method is measurement by two observers at the same time.

The word reference thus has two senses, and they differ in what stands behind them. A reference standard, such as the manometer of Chapter 14, carries a value that a chain of calibrations ties to the SI, and the reference measurement procedures of Chapter 15 are links in such chains. A reference method carries no such value and is trusted because a protocol fixes who measures, how and when. The proof of the estimate is clinical validation: a study in people that compares the device's estimates with a reference method under a protocol fixed before the first subject is measured. Validation in this sense differs from the validation of a test method in Chapter 23, which proves a procedure on the bench.

The protocol fixes in advance whom a study must measure, and the collaboration, chaired by Stergiou, described it openly in a statement published in 2018, while ISO sells the standard itself. A study needs at least 85 subjects, and in the general population they must be older than 12, with at least 30 % men and at least 30 % women. Set shares of them must have low or high reference systolic and diastolic values, so that the monitor is tested across the range it claims. Each cuff the maker supplies "shall be tested on at least 1/(2×n) of the subjects", where n is the number of cuffs: with two cuffs, each is tested on at least a quarter of them. ISO 81060-2 is in force in its 2018 edition with amendments of 2020 and 2024, and as of October 2026 a revision is in draft (Chapter 31). FDA recognizes the 2018 edition with both amendments, in part, so the edition and amendments that a validation followed are part of its claim.

The collaboration prefers the same-arm sequential method, in which the observers' measurements and the monitor's are taken one after another on the same arm. For criterion 1 the investigators compare every pair of measurements, three for each subject, so 255 in a study of 85. The mean of the differences must not exceed 5 mmHg, and their standard deviation must not exceed 8 mmHg. OIML sets the same two limits for the estimate in R 149-1, and the maker meets them through its own clinical investigation. For criterion 2 the investigators first average each subject's differences, and the criterion limits the standard deviation of those 85 averages. That limit depends on the mean difference: it is 6.95 mmHg when the mean difference is zero and falls to 4.79 mmHg when it is 5 mmHg, as Noh and colleagues tabulate it in a 2024 review of the history of blood-pressure measurement.

Why criterion 2 slides with the mean

Criterion 2's limit slides because it comes from one rule in the collaboration's statement: "A device is considered acceptable if its estimated probability of a tolerable error (≤10 mm Hg) is at least 85%." On a bell curve, 85 % of values lie within about 1.44 standard deviations of the center, the same property that Chapter 12 used at 95 % and 2 standard deviations. A monitor whose mean difference is zero may therefore scatter by up to about 10 divided by 1.44, or 6.94 mmHg, the 6.95 mmHg of Noh's table to rounding, before more than 15 % of its subjects' errors exceed 10 mmHg. A monitor whose mean difference is 5 mmHg has already used half of the 10 mmHg on one side, so it may scatter less. At 4.79 mmHg, about 85 % of a bell curve centered 5 mmHg from zero still lies within ±10 mmHg. Both end values of Noh's table fit that rule to within a few hundredths of a millimeter of mercury.

59 — Criterion 2's sliding limit and a published pass

UncertaintyLimits and decisionsThe algorithm's estimateFocal detail

Accuracy claims use a small set of statistics, and the two criteria contain most of them. An estimate's bias, the systematic error of Chapter 2, is the mean of its differences from the reference, criterion 1's first figure. Its scatter is the standard deviation of those differences. The limits of agreement are the bias plus and minus about twice that standard deviation, the band that holds about 95 % of single differences when they follow a bell curve. A percent within states the share of results inside a fixed band, as the tolerable-error rule does with 85 % within ±10 mmHg. Only the limits of agreement and the percent within say how far a single measurement may lie from the reference.

What the estimate depends on that the reading does not

Everything between the cuff and the artery lies outside the bench test, and the cuff's size shows how much that matters. In a trial published in 2023, Ishigami and colleagues at Johns Hopkins measured the blood pressure of 195 adults with an automated device. Each adult was measured with an appropriately sized cuff and with cuffs too small or too large, in an order set at random, a design called a randomized crossover trial. The adults had a mean age of 54, 68 % of them were Black and 51 % had hypertension. With a regular adult cuff, the systolic estimate was 3.6 mmHg lower than with an appropriately sized cuff in people with small arms, 4.8 mmHg higher in people with large arms and 19.5 mmHg higher in people with extra-large arms, as the authors' institution summarizes the results.

The largest of these errors is 6.5 times the whole ±3 mmHg limit on the reading, since 19.5 divided by 3 is 6.5. Each figure comes with a 95 % confidence interval, the range that the authors' analysis gives for the true effect at that level of confidence. The intervals run from 1.7 to 5.6 mmHg lower for small arms, from 3.0 to 6.6 higher for large arms and from 16.1 to 22.9 higher for extra-large arms. A monitor whose cuff-pressure reading is perfect still makes these errors. Its sensor reads the cuff's pressure correctly, and the error arises between the cuff and the artery, where no bench test looks.

60 — A wrong cuff against the reading's whole limit

The quantity being measuredUncertaintyLimits and decisionsThe algorithm's estimateFocal detail

A monitor's accuracy claim covers its cuffs and the way each measurement is taken, not the monitor alone. Microlife offers its BP B3 Basic with five cuffs, from S for arms of 17 to 22 cm to L-XL for arms of 32 to 52 cm, and under ISO 81060-2 each cuff is tested on its share of the subjects. In the monitor's manual, Microlife also attaches conditions to every measurement. The cuff sits at heart height with its lower edge 2 to 3 cm above the elbow, and the person sits with the back supported and the legs uncrossed, after 5 minutes of rest. For about 30 minutes before, the person does not eat, smoke or take caffeine, and during the measurement keeps the arm still and does not talk. A validation's figures hold for measurements taken as its protocol took them, and the maker passes those conditions to the user in its instructions.

Other claims, other statistics

Makers of other measuring devices state accuracy with the same statistics in different combinations, and each combination answers its own question. Makers of blood-glucose meters for self-testing state a percent within, under the criteria of ISO 15197:2013, which is under revision as of October 2026. Glucose is stated in mg/dL, milligrams in each deciliter of blood, and a reagent lot is one batch of test strips. At least 95 % of each lot's results must lie within ±15 mg/dL of the comparison method below 100 mg/dL, and within ±15 % at or above it. At least 99 % of all results must also fall in the zones of a consensus error grid that the criterion calls clinically acceptable.

A percent within means little until it names its band, its share and the unit it counts. Hwang and colleagues, who state those criteria, tested a meter made by SD Biosensor against them in a 2022 accuracy study carried out in Ulm, Germany, and SD Biosensor funded the study and employed the first author at the time. They measured 100 samples in duplicate with three reagent lots, which gave 600 results against a laboratory analyzer. Of the 186 results below 100 mg/dL, 185 lay within ±15 mg/dL, and of the 414 at or above it, 405 lay within ±15 %, so 185 plus 405, or 590 of 600 results, met the band, 98.3 %. These figures pool the three lots, while the criterion applies to each lot. FDA would count the same results against different bands. In its guidance for over-the-counter glucose meters, issued on 29 September 2020, it asks for 95 % of results within ±15 % and 99 % within ±20 % across the whole claimed range, with no band in mg/dL at low glucose.

Makers of clinical thermometers state a bias and limits of agreement. For a thermometer that FDA cleared on 10 November 2025, its maker, Withings, gives a clinical bias of −0.074 °F, limits of agreement of ±1.023 °F and a repeatability of 0.29 °F in its summary for the clearance. The figures were measured at the forehead in 105 subjects in four age groups, from infants under 3 months to people over 5 years. A difference of one degree Fahrenheit is 5/9 of a degree Celsius, so the limits of agreement are 1.023 times 5/9, about ±0.57 °C. Withings states its figures "relative to the predicate device, the Withings Thermo (SCT01)", an earlier thermometer to which a 510(k) claims substantial equivalence (Chapter 31), not to a reference temperature taken at a site inside the body. On the maker's account, the thermometer standard, ISO 80601-2-56, sets no pass or fail limit for these figures, since in Withings' words it "does not establish specific acceptance criteria". ISO published a new standard on the clinical performance evaluation of thermometers, ISO 12487, on 21 May 2026, after that clearance.

Makers of pulse oximeters state accuracy as Arms, the square root of the average squared difference from oxygen saturation measured in arterial blood, a figure that counts bias and scatter together. One Arms is about one standard deviation, so a measurement has a probability of 68 % of lying within 1 Arms of the arterial value, as FDA staff explained to an advisory panel in 2024. A claim of 3 % therefore allows about one measurement in three, the share outside that 68 %, to differ from the arterial value by more than 3 percentage points of saturation.

None of these statistics is a sensitivity in the sense that medicine gives the word, the share of people with a condition whom a test detects. That diagnostic sensitivity belongs to a decision made from the estimate, such as a diagnosis of hypertension, and it differs from the instrument's sensitivity of Chapter 4, the change in output for each unit of input. A reader of an accuracy claim asks four questions: which population was measured, against which reference, with which statistic, and what that statistic says about one measurement.

+ Part VII · The measuring system

As a system.

The sensor in TI's blood-pressure design can meet every figure on Omron's data sheet with an offset 4.0 mV from the typical value, about 36 mmHg at the cuff, and the monitor built around it can still read within ±3 mmHg, because its firmware measures that offset and subtracts it (Chapter 11). The reverse also happens: parts that each meet their own data sheets can make a monitor that fails, because no data sheet says how its errors add to those of the next part. This part treats the cuff-pressure channel as one engineered system. Chapter 25 shares one accuracy requirement among the people who own the parts, and Chapter 26 follows what a maker must do when a reference or a part turns out to have been wrong. Chapter 27 asks how the monitor stays accurate in use, and Chapter 28 walks the whole chain from the Planck constant to the cuff, which answers the central question.

+ The questionHow is one accuracy requirement shared among the sensor, the electronics, the code and the calibration, and who owns each share?

One line becomes seven numbers

One line in a monitor's requirements states that the cuff pressure shall read within ±3 mmHg or 2 % of the reading, whichever is greater. A design team divides that line into seven smaller numbers, and different people own them. The maker cannot loosen the limit, because bodies outside the firm set it. OIML sets the limit in its 2020 recommendation for automated sphygmomanometers, at any point of the range, with the pressure rising or falling, from 10 to 40 °C. India's Department of Consumer Affairs set the same figures for the same devices in a rule of July 2025 (Chapter 30). The limit's two branches meet at 150 mmHg, where 2 % of the reading is 3 mmHg. The shares are therefore worked out at that pressure.

The seven numbers are the rows of the uncertainty budget that the engineer drew up at 150 mmHg in Chapter 11. Five rows carry a number there: the reference manometer used at calibration, the sensor's hysteresis, the display step, the converter step and the front end's noise. Two more rows carry only a name: the residuals that the firmware leaves after it corrects the sensor's nonlinearity and its drift with temperature. Chapter 11's budget asked whether a finished design would meet the limit. Before anyone chooses the parts, a design team uses the same rows as limits that each part must stay within.

Engineers call a budget used as a requirement an error budget: a set of shares for one measured quantity whose combination stays within the instrument's limit, each with its size, its owner and its proof. Before the design exists, the team decides how large each row may be, names the person or the firm who will deliver it, and states how each share will be shown to be met. Dividing a requirement among the parts of a design is a step of systems engineering, "Allocate system requirements to functions and to next lower level" in the words of NASA's systems engineering handbook.

61 — One requirement, seven shares, each with an owner

References and standardsThe signal in the chainLimits and decisionsReadingFocal detail

Worst case or root-sum-of-squares

The team first decides how the shares are to add, because the method decides how large each share may be. The worst case adds every share at its limit, as if every error sat at its edge in the same direction at once. Eicke and colleagues of NASA's metrology and calibration working group compared three methods in the agency's 1995 guidelines for measurement assurance. They wrote that the linear method, the worst case, "assumes that all errors are additive in one direction". The quadrature method, the root-sum-of-squares, "yields the smallest uncertainty of the three", by their account, and the estimates "can differ significantly (sometimes as much as a factor of 2)". For the monitor, that difference decides how much of the 3 mmHg is left for the firmware's corrections.

An engineer may use the root-sum-of-squares where the errors are independent, because independent errors seldom all push the reading the same way at the same moment (Chapter 11). None of the monitor's five rows shares a cause with another. The hysteresis belongs to the sensor, the display and converter steps come from rounding, the noise is random, and the reference manometer is a separate instrument with errors of its own. The worst case still has a use beside the root-sum-of-squares, because it describes a single bad unit in which every part sits at its limit, and so gives a bound that no unit built from parts within their limits can exceed.

62 — Worst case against root-sum-of-squares, at 150 mmHg

UncertaintyLimits and decisionsFocal detail

A standard that writes the shares down

OIML has written such a division into its rule for weighing instruments, because firms often build a commercial scale from modules that other firms make. In R 76-1, its 2006 recommendation for non-automatic weighing instruments, OIML lets three modules each take a fraction of the instrument's maximum permissible error. They are the load cell, which senses the load, the electronic indicator, which shows the result, and the connecting elements between them. OIML requires the fractions to satisfy an equation, which appears to limit the sum of their squares to 1. Its default fractions are 0.7 for load cells, 0.5 for electronic indicators and 0.5 for connecting elements. Squared, they are 0.49, 0.25 and 0.25, which add to 0.99 and meet the rule, while the fractions themselves add to 1.7.

Three modules may therefore claim 170 % of the instrument's limit between them, added directly, because OIML expects their errors to combine as squares, as independent errors do. OIML also bounds each share. Where more than one module contributes, a fraction may not exceed 0.8 or fall below 0.3, a purely digital device may take 0, and a module that is already a complete weighing module may take 1. The firm that assembles the scale then checks that the modules fit each other. Detecto, a scale maker, records such checks on its worksheet for one of its platform scales: the sum of the fractions, the number of scale intervals, or display steps, that each module allows, and the load cell's signal for each interval at the indicator's input.

For a blood-pressure monitor the maker writes the shares itself, because OIML wrote this allocation for weighing instruments only. OIML and India set one limit for a whole sphygmomanometer and divide none of it among its parts. A maker can still take two things from the weighing rule that any allocation needs: a stated method by which the shares add, and one agreed number that both firms check wherever one firm's module meets another's.

63 — OIML R 76-1: three modules share one limit

The signal in the chainUncertaintyLimits and decisionsReadingFocal detail

Each share has an owner

Someone owns each of the monitor's seven rows. Engineers call the boundary between two owners an interface, the place where one part's output becomes another's input. The sensor's maker answers for its hysteresis and its nonlinearity before correction, as Omron's data sheet states them. The electronics team answers for the converter step and the front end's noise, which TI's design sets. The interface between these two owners is the bridge's output of about 112 µV for each millimeter of mercury, a number that the sensor must deliver and the amplifier must accept. The firmware team answers for the display's rounding and the two residuals, because the coefficients and the correction tables are its work (Chapter 9). A separate team owns the algorithm that computes systolic and diastolic pressure, since its error belongs to the estimate, which no row of this budget covers (Chapter 24).

Three more owners stand outside the monitor: the calibration chain, the production test and the user's surroundings. The maker's calibration engineers answer for the reference manometer's row, which OIML caps at ±0.8 mmHg, and the laboratory that calibrates the manometer answers for the uncertainty on the manometer's certificate. How small that uncertainty must be follows from the four-to-one ratio of Chapter 12. Eicke and colleagues stated in the same 1995 guidelines that a calibration's uncertainty "must be no greater than 1/4 of the tolerance of the instrument or standard being calibrated". For a manometer with a tolerance of ±0.8 mmHg, that is 0.8 ÷ 4 = 0.2 mmHg at most.

The production test team answers for the uncertainty of the check that each monitor meets the limit, which Chapters 22 and 23 examine. The user's surroundings set the conditions: OIML's limit holds from 10 to 40 °C, and Omron states its temperature figures from 0 to 85 °C, so the sensor's figures cover the whole band. No single published source names all these owners. The maker therefore draws up the list from its own chain.

The design team keeps each interface under control by writing its number, with its unit and its limit, into both owners' documents, so that a change by one owner shows up as a broken requirement for the other. That practice is "establishing and using formal interface management to maintain internal and external interface definition", in the words of NASA's systems engineering handbook. On the monitor, the budget assumes that the firmware's auto-zero step removes the sensor's offset (Chapter 11). A firmware engineer who changes that step therefore changes how much of the offset reaches the reading, and the team records the change in the budget before it reaches the code.

From requirement to evidence

A team that allocates shares must also prove that each one was met. The record of that proof gives the word "traceability" a second meaning. In metrology the word names the chain of calibrations from a result to the SI, metrological traceability (Chapter 15). Device makers use it for a different link, design traceability: the documented path from each requirement to the design output that answers it and to the verification that shows the output meets it. An engineer who keeps the two apart in the design file avoids a confusion, because the two meanings share the word and nothing else.

In the United States the duty to keep that record rests on FDA's quality management system regulation, the QMSR, in force since 2 February 2026. The duty itself is older, because the Quality System Regulation that the QMSR replaced had required design controls, its rules for design and development, since 1997. For the devices that the QMSR's design provision covers, FDA brings design and development under clause 7.3 of ISO 13485, the standard's clause on design.

For the budget, the record must hold each share's owner, the way its trace is kept, and a documented test with an acceptance limit (Chapter 23). In FDA's training slides on clause 7.3, Tartal of FDA's device center asks that design planning "Note roles and responsibilities, traceability methods, and resources needed", which covers the owner and the trace. Verification, Tartal states, must be "performed per documented plans and procedures to ensure outputs meet inputs".

For the monitor, the team writes each share as one line of that record. The maker traces the hysteresis row to Omron's data sheet and to its own incoming check of sample sensors. It traces the converter step to TI's design analysis, and the two residuals to a test at several pressures and temperatures, with an acceptance limit set by the method of the solved example. It traces the reference row to the manometer's certificate, and the firmware team's results from verifying its code under IEC 62304 (Chapter 9) enter the same record. Read downward, the record leads from each requirement to its evidence. Read upward, it tells the team which requirement a failed test threatens and which owner must act. A trace kept both ways is the "bidirectional traceability" that NASA's systems engineering handbook asks of a systems engineer.

+ The questionWhat happens to every result measured with an instrument later found out of tolerance?

A wrong reference reaches backward

A fault found at one link of a measurement chain reaches backward, to every result that the link produced since it was last known to be good. In 2014 the BIPM found that its working standards had moved the mass unit it maintained 35 µg away from the international prototype. The BIPM had issued each certificate for its calibrations of 1 kg standards with the uncertainty it could state on the day, but the reference behind the certificates had moved, and every value that rested on the reference had moved with it. The BIPM therefore updated the certificates it had issued from 1 January 2003 to 31 December 2013 (Chapter 18). Eicke and colleagues set down the rule in NASA's 1995 guidelines for its laboratories: when a laboratory's unit is adjusted, "Everything assigned using the local standards must be recalculated to reflect the adjustment."

For the monitor's maker, the link most exposed to this risk is the reference manometer at the calibration station. The station compares every monitor it passes with that manometer, and the manometer goes back to its own laboratory at intervals (Chapter 17). The laboratory may report that the manometer, as it arrived, read outside OIML's maximum permissible error for a reference, ±0.8 mmHg (Chapter 12). If it does, every monitor that the station passed since the manometer's last good calibration was judged against a reference that may already have been wrong, and the maker has to find those monitors. The search backward from a faulty reference to every result and every product that rested on it is reverse traceability, the chain of Chapter 15 read from the top down.

The search ends in a judgment. For each result found, the maker decides whether the reference's error could have made the result wrong by enough to matter, and what to do about the products involved. That judgment is an out-of-tolerance impact assessment. Without the search, an error can stay hidden until the product is in use, as the Hubble mirror's did in the opening story. A court can also demand the search. At the far end of the chain, the Supreme Court of New Jersey ordered the State to notify all affected defendants once it ruled on the breath-test calibrations (the opening of Part IV).

64 — A reference found wrong reaches backward

References and standardsUncertaintyLimits and decisionsReadingFocal detail

What the rules ask a device maker

In the United States the assessment is a legal duty, and since 2026 its wording has come from a standard. On 2 February 2026 FDA replaced its Quality System Regulation with its Quality Management System Regulation, the QMSR, which incorporates ISO 13485:2016 by reference and has no section of its own on the duty. ISO 13485 places the duty in its clause on monitoring and measuring equipment. As an FDA warning letter and a joint audit program of several regulators describe the duty, the maker assesses the validity of earlier results when equipment is found out of specification (Chapter 17).

FDA enforces the duty in warning letters that state the failure in FDA's own words. In July 2026 FDA sent one to Nipro Renal Solutions USA, a maker of concentrates for dialysis solutions, and cited ISO 13485's clause 7.6 without quoting it. FDA's inspectors found that the firm's sole instrument for endotoxin testing had been in use since 18 December 2023, for monitoring and for the final release of product. FDA wrote that "this instrument has never been calibrated, and a calibration schedule has never been established". FDA then named the missing step: "Your firm has not provided a plan to assess the validity of previous test results." That plan is the impact assessment, a search back through every release that rested on the instrument and a judgment on each. The letter gives FDA's findings, not the firm's reply, so it shows what FDA expects rather than how the firm answered.

Auditors check the assessment as a task of its own. Under the Medical Device Single Audit Program, MDSAP, one audit of a maker serves several regulators, and the program's auditors follow the tasks that its audit approach sets out. Right after the task on the "Control of monitoring and measuring device", an MDSAP auditor works through one titled "Impact analysis of monitoring and measuring device found out of specifications". A maker that has not recorded such an analysis for each reference found out of tolerance has nothing to show the auditor for that task.

Working out which monitors are affected

How wide the search must be depends on what the station recorded. The station may have kept each monitor's serial number, its recorded error at each test point and the identity of the reference used, as Chapter 14 recommends. The maker can then correct each recorded error by the reference's error and see which monitors are suspect. If the records hold only "pass", every monitor tested since the reference's last good calibration is suspect, and the maker can narrow the list only by testing again the units it can still reach.

The monitors that the assessment flags count as nonconforming product, the quality-system term for product that does not meet its requirements, until the maker shows otherwise. The maker then decides what to do with each group, from correcting the records to recalling units from the field. The choice depends on the risk to patients, the same measure by which FDA classifies a device recall as Class I, II or III (Chapter 9).

For a blood-pressure monitor the decision must also weigh the estimates. The algorithm takes systolic and diastolic pressure as the cuff pressures at chosen points of the oscillations (Chapter 9), so a monitor whose cuff-pressure reading is high would report high estimates too. "A consistent 5 mmHg error can more than double or halve the number of patients diagnosed with diastolic hypertension", PTB, Germany's national metrology institute, warns in a 2021 proposal to OIML, citing earlier work.

Faults inside the monitor

A reference is not the only link that can fail, because the monitor itself can develop a fault. An instrument that then stops or warns is safer than one that reports a wrong number. A fault, in OIML's recommendation for weighing instruments, is the "Difference between the error of indication and the intrinsic error of an instrument": the error the instrument shows in use minus the error it had when sound. A significant fault is one "greater than e", where e, the verification scale interval, is the step used to class and check the instrument. In the 1992 edition of the same recommendation, since superseded, OIML required that on a significant fault "the instrument shall either be made inoperative automatically" or give a warning until the user acts. The monitor's own checks follow that pattern of stopping or warning.

Each likely fault in the monitor has a check of its own, and the makers' manuals show several. The sensor's offset drifts, and India and OIML require the monitor to zero itself again, or switch off, when the drift reaches 1 mmHg (Chapter 17). A leak in the cuff or the tube lowers the pressure the pump can reach, and Microlife's BP B3 Basic then shows "Err 3": "An adequate pressure cannot be generated in the cuff. A leak may have occurred." A valve that fails to open can leave the cuff too tight, so the monitors also watch for over-pressure. Microlife's monitors show "HI" when the cuff pressure passes 299 mmHg, and Welch Allyn's Ambulo 2400 lets the cuff pressure fall to zero within 3 seconds when it exceeds the monitor's maximum of 285 mmHg.

The firmware can fail too, and it can check itself with a checksum, a number computed from stored data, so that a changed bit gives a different number. A program can run that check at start-up: in an example from OIML's 2023 document on software-controlled measuring instruments, the program "calculates a checksum of the program code and legally relevant parameters" and stops when the values do not match. Welch Allyn's monitors likewise show an error code when their calibration is missing or corrupted (Chapter 9). OIML also states that "If the software is modified in any way, a new software identification is required", so a firmware update appears in the records as a change.

One fault, a drift of the span, has no self-check. A span that drifts makes every reading wrong in proportion to the pressure, while the zero stays correct, so auto-zero cannot detect it (Chapter 17). Only a comparison at a known pressure finds a span drift, which is why the calibration interval and the service check of Chapter 27 exist.

65 — Single faults in the monitor and what catches each

The quantity being measuredThe signal in the chainNoise and errorReadingFocal detail

A fault at the edge of the range

A fault in code can lie at the edge of a measuring range: LifeScan's OneTouch Verio IQ blood-glucose meter had one, and LifeScan began recalling the meters in the United States in March 2013. By FDA's record, the meter "will shut off and revert to set up mode at glucose values above 1023" instead of displaying "EXTREME HI". FDA recorded the root cause as "Software design", a fault present in every meter that runs the code, so its record lists 710,413 meters in the US. FDA classified the recall as Class I on 12 April 2013 and has since terminated it. The figure 1023 is one less than 1,024, a boundary in binary counting (Chapter 8), but the record does not say what the code did wrong.

The Verio IQ failed in the opposite way to the InsuLinx meter of Chapter 9. The InsuLinx showed a wrong number at very high glucose, while the Verio IQ showed none and switched itself off at the values where a warning mattered most. FDA asks for that warning in its 2020 guidance for home glucose meters: a meter "should identify and provide an error code in situations where the measured glucose value falls outside" its measuring range. For critical values, FDA adds, the device "should give a message such as "high" or "low."" Both faults appeared only at rare, extremely high glucose values, above 1,000 mg/dL, so a calibration at ordinary glucose levels would not have exercised the code that failed. A single fault at the edge of a range shows itself only when a test reaches the edge.

A fault becomes harm through a sequence of events. ISO 14971, the standard for risk management of medical devices, names each step, and FDA reproduces its definitions in its guidance on human factors of August 2026. A hazard is a "Potential source of harm", and a hazardous situation a "Circumstance in which people, property or the environment is/are exposed to one or more hazards". Harm is "Injury or damage to the health of people, or damage to property or the environment". In this guide's reading of those terms, the Verio IQ's hazard was its behavior above 1023 mg/dL, and the hazardous situation was a person with an extremely high glucose who received neither a number nor a warning. For the monitor, by the same reading, the hazard is a monitor that reads high, and the sequence of events runs from a reference manometer out of tolerance through a station that passes such monitors. The hazardous situation is then a patient whose estimates are too high, and the harm is any injury to health that follows from a diagnosis or a treatment decided on them.

+ The questionHow does a measuring device stay accurate for years after it leaves the factory?

A check the user can make

A blood-glucose meter can be tested at home, because its reference comes in a bottle. Control solution is a liquid of known value that tests the meter, not the patient. MicroTech Medical makes two levels of it for its GoChek meter and sells them separately from the meter. The user is told "to compare the control results with the expected control ranges printed on the strip vial", according to FDA's review of the meter. The meter, by the review's account, "automatically detects that a control solution is being used." With the bottle, anyone who owns the meter can test the meter and its strips together, at any time, without sending them back to the maker.

Two levels of control solution test the meter at two points of its range, so they can find an error that grows with the glucose value, a span error, as well as an offset, which shifts every result alike (Chapter 11). FDA asks for that check in its 2020 guidance for glucose meters sold for home use: "The use of external control solutions by the user should be promoted," and "At least two levels of control material should be specified in the labeling as available to the user." FDA also asks for labeling that gives "instructions for what to do if the control material values are not within the manufacturer's allowable range", but it sets no frequency for the test.

The blood-pressure monitor has no such bottle, because its reference is a pressure, not a liquid. To set a known pressure, a technician needs a reference manometer, a pump and a rigid vessel, and must put the monitor into the service mode that OIML and India reserve for service personnel (Chapter 14). In the manuals for two of its monitors, Microlife gives the user no calibration procedure and recommends instead a test of accuracy every 2 years or after a mechanical impact, through its own service. The monitor checks itself against a known value only through auto-zero against the open air, which tests the zero and not the span (Chapter 17). Between one service test and the next, the user has no way to tell whether the monitor's span has moved.

An instrument can also carry its span reference inside it. Sartorius builds one, an internal weight, into its Entris II analytical balance, model BCE64I-1S, and the balance adjusts itself with that weight, a feature Sartorius lists as "Internal automatic (isoCAL)". The adjustment "accounts for environmental or temporal changes that can impact the accuracy of your weighing results", in Sartorius's words, and runs when predefined time intervals or temperature values are exceeded, according to Imlab, a distributor of Sartorius balances. The internal weight is a reference like any other and needs a calibration of its own, which neither Sartorius nor Imlab describes. A monitor would need a known pressure inside it to do the same, and none of the published monitor designs in the earlier chapters carries one.

66 — Who checks what after the factory

The quantity being measuredReferences and standardsThe algorithm's estimateReadingFocal detail

What use does to a monitor

A monitor in use is pumped up and let down thousands of times, carried, dropped and kept in rooms that are hot or cold. Before a model goes on sale, a laboratory tests samples of it, not every unit sold, against some of those stresses. OIML's recommendation for automated sphygmomanometers, R 149-1, asks that after 10,000 simulated measurement cycles the cuff-pressure reading change by no more than 3 mmHg, and India's rule sets the same figures. Microlife gives its BP B3 Basic an expected service life of 5 years or 10,000 measurements, so the durability test puts about a lifetime of cycles on a sample. R 149-1 also requires storage tests at −5 °C and at 50 °C, and requires the limit still to be met after vibration and shock.

A monitor in service must still meet the limit it met at the factory, because R 149-1 sets no wider limit for use, and its verification in service checks the same ±3 mmHg. OIML treats weighing instruments differently, and states in R 76-1 that "The maximum permissible errors in service shall be twice the maximum permissible errors on initial verification." A scale may therefore drift to twice its limit as new before it fails in law. A sphygmomanometer has no such allowance: the drift it may develop in use is limited to what remains of the ±3 mmHg after its own error and its test's uncertainty at the factory (Chapter 25).

Surveys of devices already in use show how many of them stay within that limit. A'Court and colleagues at the University of Oxford tested the blood-pressure devices of 38 general practices in England in a cross-sectional study published in 2011 (Chapter 2). They inflated each device to 280 mmHg, compared it with a reference pressure meter at 250, 200, 150, 100 and 50 mmHg, and passed it if every reading lay within 3 mmHg of the reference. The UK's National Institute for Health Research funded the work, and the authors declared no competing interests.

A second survey applied the same rule to monitors that patients use at home. In 2020 Hodgkinson and colleagues reported ACCU-RATE, a cross-sectional study of 327 home monitors owned by patients with high blood pressure. They tested each from 0 to 300 mmHg at intervals of 50 mmHg against a reference tester, an Omron PA350, and failed any monitor beyond ±3 mmHg at any interval. The National Institute for Health Research funded the study, and no monitor maker funded it. One author, Richard McManus of the University of Oxford, declared that he had received research support in the form of blood-pressure monitors from Omron, the tester's maker, and from Lloyds Pharmacies.

67 — Two field surveys of devices in use

Noise and errorUncertaintyReadingFocal detail

Service checks and re-verification after a repair

In a service check a technician repeats the factory's comparison in the field: the monitor in its service mode, a rigid vessel in place of the cuff, and a reference manometer reading the same pressure (Chapter 14). India's rule and the makers keep that work for trained people. India's rule also requires seals against opening the case or tampering with the measuring parts. Welch Allyn's Ambulo 2400 has a second, independent safety processor that reads the pressure alongside the main processor, and Welch Allyn allows only its authorized service personnel to calibrate that processor. Mindray states that the tests in its VS-900 manual "should be performed by qualified service personnel only".

A repair is a different event from a routine check, because it can change the instrument that the last calibration described. A technician may replace the sensor, the pump, a valve or a length of tube. A new sensor brings an offset and a span of its own, which may differ from the old sensor's by as much as Omron's tolerances allow (Chapter 11), so the coefficients stored for the old sensor no longer fit. A new tube or valve can leak. In either case the certificate on file describes a monitor that no longer exists. The repaired monitor needs re-verification after a repair: a check against the same limits as when new, before it goes back into use.

OIML and India each name a repair as a reason to verify an instrument again. OIML asks in R 148-1 that a non-automated sphygmomanometer be verified "before use and during the instrument's lifetime, and after repair". For automated monitors, OIML states in R 149-1 that verification covers at least the cuff-pressure limit, the repeatability and the air leakage, the three properties that a repair is most likely to disturb. India's general rules for weights and measures require re-verification before use after any repair, dismantling or reinstallation, as the law firm S.S. Rana describes them (Chapter 30 maps the jurisdictions). For software, OIML notes in its software document that when a legally relevant parameter changes, a re-verification "might be required depending on national legislation". New firmware changes the monitor as a repair does, and it carries a new software identification (Chapter 26).

What field evidence can and cannot show

A maker learns about its monitors in use from three kinds of record: the as-found values of service checks, the complaints of users and clinics, and its own testing of returned units. Of the three, the as-found values tell the maker most, because each records a calibration made after a known time in use. A maker that collects them by model, age and serial number can see drift before a survey does. Complaints arrive without a reference, so they show where to look rather than how large an error is.

A field record can also point to a fault that a check of the cuff pressure would not find. In August 2026 Midmark began recalling four models of its IQvitals Zone vital-signs monitors across the United States, and FDA classified the recall as Class II on 18 September 2026. Class II is the middle of the three classes that FDA assigns to recalls by risk. These monitors offer more than one deflation method, the way a monitor lets air out of the cuff while its algorithm reads the oscillations. FDA gives the reason as "A performance issue may result in inaccurate blood pressure readings when the Linear Deflation Method is used." Midmark told its users to "use only the Step Deflation Method". FDA's record does not say that the cuff-pressure reading itself was wrong. Because the remedy changes only the deflation method, the evidence points to a fault in the method behind the estimate rather than in the reading.

A technician who checks the cuff pressure in service cannot find a fault of that kind. The technician holds the pressure steady in a rigid vessel, so the monitor never runs a deflation method at all. A check of the pressure alone leaves untested the algorithm's step from the oscillations to the systolic and diastolic values (Chapters 1 and 9). In the field, therefore, a technician tests only the reading against its limit. A test on a simulator, which produces in the cuff the oscillations of an arm, shows whether the algorithm still repeats its answers (Chapter 23), and only a clinical validation against people shows that the estimate is right (Chapter 24).

+ The questionPut together, what makes the cuff pressure one blood-pressure monitor reports mean what it says?

Two ends of one chain

The two ends of the monitor's chain can be compared directly, because both are standard uncertainties and both can be stated as a fraction of the value they describe. At the top stands the kilogram's consensus value, from which mass calibrations have taken their traceability since 1 March 2026 (Chapter 21). The CCM, the consultative committee that advises the CIPM on mass, gives that value a standard uncertainty of 20 parts per billion. At the bottom, the engineer of Chapter 11 found the monitor's combined standard uncertainty at 150 mmHg to be 0.70 mmHg, and 0.70 divided by 150 is about 4.7 parts per thousand. The relative uncertainty at the bottom is therefore about 230,000 times as large as at the top. Chapter 19 found about 470,000 with the 10 µg, or 10 parts per billion, that the BIPM gave the prototype at the redefinition of 2019; the consensus value's uncertainty is twice that, so the 230,000 is about half.

Every link between the two ends is a comparison, and each comparison carries the uncertainty of the link above it and adds its own (Chapter 15). Uncertainties therefore "grow progressively through the chain of measurements", as Eicke and colleagues wrote in NASA's measurement assurance guidelines of 1995. They drew the consequence for the top of the chain: "as the length of the chain increases, requirements at the higher echelons become more stringent". Each added link adds its own uncertainty before the chain reaches the limit at its bottom, so a longer chain needs a smaller uncertainty at its top. The monitor's chain runs from the defining constant down to the cuff, and Chapter 15 followed its lower links at 150 mmHg, from a national pressure balance to the monitor's limit, through uncertainties and maximum permissible errors. At each link an institute, a laboratory or a maker states the figure and answers for it.

68 — From the Planck constant to the cuff, link by link

References and standardsUncertaintyLimits and decisionsReadingFocal detail

From a constant to a pressure

The chain starts with a number that has no uncertainty at all. In 2018 the General Conference on Weights and Measures, the CGPM, fixed the Planck constant, h, at exactly 6.626 070 15 ÷ 10³⁴ joule seconds, with effect from 20 May 2019 (Chapter 19). The meter and the second were already fixed through other constants, so that number defines the kilogram. A definition is not yet a mass, however, and a national metrology institute must realize the kilogram with an instrument. NIST's Kibble balance, NIST-4, measured h in 2017 with a relative standard uncertainty of 13 parts per billion, and NRC's balance in Canada reached 9.1 parts per billion. Now that h is fixed, the same measurement realizes a kilogram, so each figure is also the relative standard uncertainty of a kilogram realized on that balance (Chapter 20).

No single balance sets the world's mass scale. Several institutes realize the kilogram, their realizations are compared in key comparisons, and the CCM computes one consensus value from the results. The current consensus value carries a standard uncertainty of 20 µg (Chapter 21), and in a kilogram 20 µg is the 20 parts per billion at the top of the chain. National institutes that do not realize the kilogram themselves take the unit from the same value through the BIPM's calibrations, so their masses start from the same 20 parts per billion. India does so through its platinum-iridium copy No. 57, which CSIR-NPL keeps (Chapter 21).

On a pressure balance, masses under measured gravity press down on a piston, and the gas pressure that balances them equals their weight divided by the piston's effective area (Chapter 15). The pressure is therefore in proportion to the mass on the piston, so a fractional uncertainty in the masses becomes the same fractional uncertainty in the pressure. At 150 mmHg, 20 parts per billion is three millionths of a millimeter of mercury.

The piston's own area adds far more. NIST's gas pressure scale rests on two primary piston gauges, which cover 20 kPa to 1 MPa, as Olson and colleagues of NIST described it in 2010. Each gauge's effective area carries a relative standard uncertainty of 3.0 to 3.2 parts per million, and the other contributions, among them mass, gravity and temperature, about 2.5 parts per million. Combined by the root-sum-of-squares (Chapter 11), 3.2 and 2.5 parts per million give about 4.1 parts per million, about 200 times the kilogram's 20 parts per billion, so at this link the piston's area, not the kilogram, sets the uncertainty. The cuff's 150 mmHg is 20.0 kPa, the lowest pressure of the gauges' range, so these gauges reach down to the monitor's test pressure. There their 4.1 parts per million is 0.0006 mmHg.

Each national institute answers for its own link. NPL's figure of Chapter 15, about 0.003 mmHg at this pressure, is larger than NIST's because it belongs one link lower: NPL, the UK's national metrology institute, states it for calibrating a customer's pressure balance, and gives no coverage factor for it. India's primary standard is an air piston gauge kept by CSIR-NPL, which gives the gauge's effective area an expanded uncertainty of nearly 11 parts per million at k = 2 (Chapter 15). The institutes show in key comparisons that their links agree. The national institutes thus hand the laboratories below them a pressure known to parts per million.

From the laboratory to the bench

Below the national institutes, accredited laboratories calibrate reference instruments for industry, and at this link the uncertainty grows again. A laboratory of this kind compares the instrument with a reference instrument instead of generating a pressure from masses, and each comparison adds the repeatability and the resolution of the instrument being calibrated. UKAS accredits S M Gauge Company, a UK laboratory, to calibrate gas gauge pressure from 15 to 25 kPa with an expanded uncertainty of 4.4 Pa at about 95 %, by its schedule of June 2026 (Chapter 16). That figure is the laboratory's calibration and measurement capability, the smallest uncertainty it may state for such a calibration. At 150 mmHg, 4.4 Pa is 0.033 mmHg, and 4.4 Pa in 20.0 kPa is 220 parts per million. A reference manometer that this laboratory calibrates therefore reaches the maker's bench with an uncertainty no smaller than about 0.033 mmHg.

The maker owns the next link, and its budget counts the reference manometer at OIML's limit, not at the manometer's own calibration. At its calibration station the maker compares each monitor with a reference manometer (Chapter 14), and OIML allows that manometer a maximum permissible error of ±0.8 mmHg. In a 2021 bench study, Ramírez-Barrera and colleagues checked four sphygmomanometers against a reference manometer whose certificate gave an expanded uncertainty of ±0.062 mmHg, with a coverage factor of 1.99 (Chapter 15). That certificate figure is larger than the accredited laboratory's best capability above and far smaller than OIML's limit. The engineer of Chapter 11 counted the reference as 0.8 mmHg divided by the square root of 3, about 0.46 mmHg, because the limit is what the maker's procedure guarantees for every reference the station may use.

At the bench the monitor adds the largest uncertainties of the whole chain. The sensor's hysteresis and the display's 1 mmHg step join the reference's row, and together the three give most of the combined standard uncertainty of 0.70 mmHg, which becomes an expanded uncertainty of ±1.4 mmHg at k = 2 (Chapter 12). The production test then decides whether each monitor passes. With a guard band equal to the 1.4 mmHg, the maker passes a monitor only if its measured error at 150 mmHg lies within 1.6 mmHg of zero, the ±3 mmHg that OIML and India set less 1.4 mmHg (Chapter 13). Within the maker, the design team answers for the budget (Chapter 25), the test engineers for the decision (Chapters 22 and 23) and the service for keeping the monitor within its limit in use (Chapter 27).

What the chain answers, and where it stops

What makes the reading mean what it says has two parts, because the links above the bench and the bench itself do different work. The national institutes and the accredited laboratories decide whether the cuff pressure is tied to the SI at all, and they add almost nothing to its uncertainty. The maker's bench decides how large that uncertainty is. A maker who wants a smaller uncertainty must therefore work on the sensor, the firmware and the reference used at calibration. A maker who skips a link above the bench gains no accuracy and loses the tie to the unit.

For the cuff pressure that one monitor reports to mean what it says, the three conditions set out at the start of this guide must hold, and the chain names an owner for each part. First, both chains must be known and unbroken. Laboratories whose competence others have checked must have done, dated and recorded every calibration in the chain above the monitor (Chapters 15 and 16). The design team must give the monitor's own chain, its six stages from sense to decide, a budget that fits within its limit, with every share owned and verified (Chapters 11 and 25).

Second, the uncertainty must be stated and small enough for the decision. Each laboratory must state its uncertainty, small beside the limit of the link below (Chapter 12), and the maker must count the test's uncertainty when it decides whether a monitor passes (Chapter 13). Third, tests must show that the monitor stays within its stated uncertainty between calibrations, and the maker must find any fault or wrong reference and trace each back to the results it affected (Chapters 17, 26 and 27).

A chain in which every link is checked against the next guards against the failure of the opening story. In a checked chain the next comparison can catch a wrong reference long before a telescope reaches orbit.

The chain stops at the reading. The monitor also shows systolic and diastolic values, and its algorithm derives these estimates from the oscillations that the heartbeat makes in the cuff pressure (Chapter 9). A calibration of the cuff pressure never tests the rules that turn those oscillations into the estimate. Only a clinical validation against a reference method on people can prove the estimate (Chapter 24). A monitor whose cuff pressure traces to the Planck constant can still report a blood pressure that its algorithm gets wrong, so the two claims need two kinds of proof.

69 — What the chain above the bench adds, and where the chain stops

References and standardsNoise and errorUncertaintyThe algorithm's estimateReadingFocal detail

The platinum-iridium cylinder that defined the kilogram from 1889 to 2019 is now measured like any other mass. Until 2019 its mass was exactly 1 kg by declaration, so no one could state an uncertainty for it (Chapter 18). The BIPM still keeps the cylinder at Sèvres, and since 1 March 2026 the CCM has put its mass at 1 kg − 12 µg in the consensus value, with a standard uncertainty of 20 µg.

+ Part VIII · The industry in 2026

The makers at each link.

More than four fifths of the monitor's uncertainty budget at 150 mmHg, counted in squares, rests on two figures that organizations outside the monitor maker state: OIML's limit for the reference manometer and Omron's hysteresis for the sensor (Chapter 29). The companies behind such figures change, and one company can hold several links of the chain at once, as maker, seller and tester. A&D Company held all three roles for scales until 14 July 2026, when Japan's Ministry of Economy, Trade and Industry, METI, revoked its designation as a body that verifies weighing instruments on the state's behalf. A&D makes balances, scales, load cells and blood-pressure monitors, and METI had designated it to verify non-automatic scales other than vehicle scales, and automatic catchweighers. In September 2025 A&D disclosed that it had repaired scales without removing their verification marks, which Japan's Measurement Act requires a repairer to remove. A&D's own site still lists verified scales among its products, but A&D may no longer verify scales itself. Part VIII names who holds each link of the monitor's chain, with every company's status dated to November 2026 and every company figure labeled as the company's own.

+ The questionWho makes the references, instruments, sensors, converters and calibration services the chain depends on, India included?

The sensor's maker changed owners

On 1 October 2026 Omron transferred the shares of Aratas Corporation to a company established by The Carlyle Group, and Aratas left the Omron Group. Aratas makes the 2SMPP-03, the pressure sensor at the start of the monitor's chain (Chapter 1). The sensor's maker had been part of Omron itself, as its Device & Module Solutions business, until 1 July 2026, when that business passed by a company split to a subsidiary and took the name Aratas. Omron kept a minority interest after the sale: it invested in the parent of Carlyle's company for 5 % of the voting rights, as Aratas states it.

For the engineer who designs the monitor, the sale changed a company's name and nothing in the part. The 2SMPP-03 is a small part of the business that was sold: Omron's notice of the sale gives the value of the business transferred as 81,000 million yen and states no price, and Aratas describes itself as a maker of relays, switches, connectors and sensors with about 6,000 employees. Aratas lists the 2SMPP-03 as in production, and the data sheet on Aratas's site still carries Omron's name and catalog number. Every sensor figure in Chapter 11's budget, from the span tolerance to the hysteresis, is therefore Omron's statement about a part that Aratas now makes and sells. A design file that names the source of each figure needs two names and a date: Omron as the author of the data sheet, and Aratas as the maker since 1 July 2026.

Other companies make such sensors, and several chip makers supply the links that follow. TDK Electronics makes the C32/2, a bare sensor die, and NXP the MPXx2050 family, and both state that their sensors' outputs are ratiometric, the property that lets a design do without a separate voltage reference (Chapters 4 and 6). Texas Instruments, TI, supplies two chips of the reference design in Chapter 1: the INA350 instrumentation amplifier, and the MSPM0L1306 microcontroller, whose 12-bit converter digitizes the bridge's output. Analog Devices makes the bridge converters and voltage references that Part II cites. Microchip Technology demonstrates its 24-bit MCP3564 converter in a weigh scale, and Renesas offers a blood-pressure evaluation kit built on its RL78/H1D microcontroller.

Two of these chip makers agreed in 2026 to buy other companies, and neither purchase includes a converter business. TI agreed on 4 February 2026 to buy Silicon Labs, a maker of wireless processors, with closing expected in the first half of 2027. Analog Devices agreed on 9 September 2026 to buy Alif Semiconductor, a maker of low-power microcontrollers, with closing expected in the last quarter of 2026.

Monitors, and the names on them

The monitor makers cited earlier state their own accuracy figures. A&D Company states ±3 mmHg for the cuff pressure of its UA-651, and Microlife AG states the same accuracy and a 1 mmHg display step for two of its monitors (Chapter 8). A&D also holds three layers of the chain at once, because its own range runs from load cells and balances to blood-pressure monitors. It is a subsidiary of A&D HOLON Holdings. When METI revoked A&D's verification designation in July 2026, the decision concerned its scales, not its monitors (Part VIII).

The brand on a monitor's box does not always name the company that made it. Under the EU's device regulation the manufacturer issues the device's EU declaration of conformity, its statement that the device meets the regulation's requirements (Chapter 31). The declaration therefore names the company that the regulation treats as the manufacturer, even where the box carries another brand. Joytech Healthcare of Hangzhou issues that declaration for several of Beurer's arm and wrist monitors, among them the BM 92, and Ya Horng Electronic of Taiwan makes Garmin's Index BPM. An engineer who buys a monitor as a reference device, or audits a supplier, therefore reads the declaration and the certificate behind it.

Monitors are tested with instruments of their own. A simulator reproduces the oscillations that a cuff picks up from an arm, so it tests the monitor's estimate of blood pressure as well as its pressure reading, and FDA recognizes a technical specification for the repeatability of such simulators (Chapter 31). Fluke Biomedical of Everett, Washington, makes the BP Pump 2, a simulator and tester for non-invasive blood-pressure monitors, and the ProSim 8, another simulator. Fluke Biomedical belongs to Fortive. Rigel Medical makes another such instrument, the Uni-SiM, whose calibration certificate the engineer reads in Chapter 12.

The reference layer changed owners too

Above the monitor's calibration station stands the reference manometer, and one maker of such references also changed owners in 2026. On 1 January 2026 Crane Company completed its purchase of Baker Hughes's precision sensors and instrumentation business, which included Druck, Panametrics and Reuter-Stokes. Druck, which now calls itself "A Crane Company brand" on its site, makes instruments that generate, control and measure pressure for calibration. Druck also sells 4Sight2, software for managing calibrations, which places it in the software layer as well.

India's national institute uses a Druck gauge as the reference of a rig that calibrates 20 monitors together. Kumar and four colleagues at CSIR-NPL described the rig in a 2023 dataset (Chapter 23): a Proportion-Air regulator driven by a National Instruments card sets the pressure, and a Druck DPI-104 digital gauge reads it as the reference. The authors cite OIML's Recommendations R 148 and R 149 (Chapter 30), but the public description of their dataset gives neither the test points, nor the limits, nor the DPI-104's accuracy. The rig belongs to a national institute, not to a factory.

70 — One reference gauge for twenty monitors

The quantity being measuredReferences and standardsNoise and errorReadingFocal detail

A rig that shares one reference among twenty monitors cannot find that reference's error by itself. The reference's error enters every monitor's result at the same moment and in the same direction, so it is one shared cause, not twenty independent errors (Chapter 11). If the DPI-104 read 0.5 mmHg high, all twenty monitors would appear 0.5 mmHg low, and comparing their results with each other would never show it. Only a comparison of the gauge with a better reference, at the link above the rig, can find that error. The gauge's own certificate therefore carries more weight than any number of monitors that agree with it.

Other makers supply the same reference layer, with instruments, calibration software and the masses for dead-weight testers. Beamex of Finland makes the MC6 family of field calibrators, a bench calibrator and the POC8 pressure controller, with calibration-management software of its own, CMX and LOGiCAL. Fluke, a Fortive business, makes calibrators and offers CalStudio, a cloud platform for calibration procedures. Nagman Instruments and Electronics of Chennai makes temperature, pressure and signal calibrators, hand pumps and dead-weight testers. A dead-weight tester generates a pressure the way Chapter 15's pressure balance does, with masses on a piston. Such masses come from makers of reference weights, among them Troemner of Thorofare, New Jersey, a unit of Mettler-Toledo since 2016. Troemner's calibration laboratories are accredited to ISO/IEC 17025, by its own statement (Chapter 16).

Institutes and laboratories

At the top of the chain stand the BIPM and the national institutes, which are public bodies: among them NIST in the United States, PTB in Germany, NPL in the United Kingdom and CSIR-NPL in India. The institutes realize and disseminate units, and they take part in the CIPM's arrangement for mutual recognition rather than holding accreditation as a laboratory does (Chapter 21). CSIR-NPL states that it keeps a quality system to ISO/IEC 17025:2017 and to ISO 17034:2016, the standard for producers of reference materials. CSIR-NPL also calibrates for customers directly: its calibration and testing service, by its own count, serves nearly 4,200 of them from industry, laboratories and government.

Between the institutes and the factories stand the calibration laboratories, and two groups among them grew by purchase around 2026. Trescal, headquartered in Paris, has been a portfolio company of EQT Infrastructure V since 2023. In January 2026 Trescal announced 14 acquisitions. A trade publication reported that one of them took Trescal into India, through a domestic laboratory in Bengaluru and Hyderabad offering NABL-accredited services, but did not name the laboratory. Transcat, a US company listed on Nasdaq, reports 33 calibration service centers with ISO/IEC 17025:2017 scopes of accreditation at the end of its fiscal year on 28 March 2026. It bought SCM Metrology and Laboratories of Costa Rica with effect from 9 April 2026.

Whose figures the reading rests on

The owners in that table matter to the monitor's maker because its reading's uncertainty is built from their figures. In Chapter 11 the engineer's budget gave a combined standard uncertainty of 0.70 mmHg for the corrected reading at 150 mmHg, and each of its rows rests on a figure that some organization states. With each row set beside its owner, the maker can see how much of that uncertainty it controls in its own design and how much it obtains from suppliers and laboratories.

71 — The corrected budget, by whose figure each row is

References and standardsNoise and errorUncertaintyFocal detail

The maker sets the display step itself, but it can change the two largest rows only through its choice of supplier and of laboratory. A reference whose certificate states an expanded uncertainty well below OIML's limit would shrink the largest row, as the patient simulator's 0.09 mmHg in Chapter 12 shows, while a sensor with less hysteresis would shrink the second. The owner changes of 2026, at Aratas and at Druck, altered none of these figures. They altered the name that the design file must record beside two of them, and the date from which each name holds.

India, as the records show

India's chain for the reading runs through Indian institutions. CSIR-NPL keeps the country's primary standard of pressure, an air piston gauge, and piloted a key comparison in gas pressure (Chapters 15 and 21). NABL accredits the calibration laboratories below the national institute, and its register held 1,305 of them in early September 2026 (Chapter 16). Five Regional Reference Standard Laboratories link the national institute to the States' legal-metrology laboratories (Chapter 30).

Indian makers build instruments and sensors of their own. Besides Nagman, ADI ARTECH Transducers of Vadodara makes strain-gauge load cells and force, torque and pressure sensors, Essae-Teraoka of Bengaluru makes weighing scales and balances, and Tempsens of Udaipur makes temperature sensors and calibrators. The pages of all four state neither their owners nor an accreditation body for a laboratory of their own.

For the monitor itself, India has an announced factory but no confirmed production. Omron Healthcare established a company in India on 14 July 2022 to run a factory of about 24,000 m² in Chennai. In June 2023 Omron Healthcare stated that the factory would begin making blood-pressure monitors in March 2025, with the date still to be confirmed. In July 2025 a trade publication quoted the managing director of Omron Healthcare India, Hiroshi Ogawa: "Currently we are sourcing BPMs from Vietnam," BPMs being blood-pressure monitors. No known record confirms that production has started, and the factory belongs to a Japanese company.

Indian companies sell monitors, but no known record shows one of them making home automated monitors in India. Morepen Laboratories stated in a 2021 filing to the stock exchanges that it led the domestic market for blood-pressure monitors, and it reported revenue of Rs 26 crore, about 260 million rupees, from them in the quarter from April to June 2024. Neither document says where its monitors are made. BPL Medical Technologies sells a fully automatic monitor whose product page names no maker or country of origin. Skanray Technologies of Mysuru holds an ISO 9001 certificate whose scope includes the contract manufacture of multi-parameter patient monitors. Such a monitor can carry a blood-pressure channel, but neither the certificate nor Skanray's About page names one, and a hospital patient monitor is a different device from the home monitor this book follows.

72 — India's part of the chain, as the records show

References and standardsThe signal in the chainReadingFocal detail

+ Part IX · Quality and regulation, as of November 2026

What the law asks.

The BIPM's Member States agree on the units together, but each state writes its own rules for the instruments its people buy and the devices its doctors use. The units are agreed in the General Conference on Weights and Measures, whose 28th meeting, at Versailles from 13 to 15 October 2026, adopted seven resolutions, none of which changed the SI (Chapter 19). Two of the resolutions concern how measurements cross borders. One gives States that take no part in the BIPM's work a status as Observers, and the CIPM's President expects that up to 85 States could take it. The other encourages the CIPM to extend the SI's reference point into a digital framework and invites national institutes to advance digital certificates. Part IX maps those rules for the monitor in the United States, the European Union and India as of November 2026. For each, it explains how the system works before it cites the clauses that apply to the monitor, and it says which texts are still drafts.

+ The questionWho governs the chain across borders, and how does a measurement made in one country count in another?

A state enforces some measurements

A state can make a measurement a matter of law, and that use of its power is called legal metrology. OIML, the intergovernmental body that writes model rules for measuring instruments, defines it in its 2022 vocabulary as the "practice and process of applying statutory and regulatory structure and enforcement to metrology", and a note to the definition adds that legal metrology's scope "may be different from country to country". The state names in law the instruments that must meet a limit, and an official, or a body that the state designates, checks each instrument and marks it. Institutes and laboratories build the chain of Parts IV and V from comparisons that they agree to recognize, and the state adds its power to that agreement. The state can also take back a task it has delegated: in July 2026 Japan withdrew A&D's designation as a body that verifies scales on the state's behalf (Part VIII).

A state checks an instrument's design before the instrument is sold: an authority tests samples of it, a step that OIML calls type evaluation and India's law calls approval of the model. After that, an official or a designated body checks each instrument of the approved type, and OIML calls that check verification, a "conformity assessment procedure (other than type evaluation) which results in the affixing of a verification mark and/or issuing of a verification certificate". The mark records that the instrument met the limit when it was checked. In legal metrology the word therefore has a third sense, apart from verification in the VIM's sense (Chapter 14) and from the design verification of a device's development (Chapters 23 and 25).

A measurement made in one country counts in another through three arrangements, each for a different link of the chain: the national institutes, the accredited laboratories and the instruments themselves. At the top, national institutes recognize each other's calibration and measurement capabilities, or CMCs (Chapter 16), under the CIPM MRA (Chapter 21). In May 2025 the arrangement had 258 participants, and its key comparison database, the KCDB, listed 26,135 CMCs in the report that the BIPM gave in June 2025.

One level down, an accredited laboratory's certificate can count in other countries because the bodies that accredit laboratories assess each other, under the Global ACI arrangement, which took over ILAC's on 1 January 2026 (Chapter 16). Global ACI lists two US accreditation bodies, A2LA and ANAB, and NABL, India's accreditation body, states that it is a signatory. A certificate for a maker's reference manometer from a laboratory that one of these bodies accredits is therefore recognized where the others work.

For the instrument itself, the route across borders is an OIML certificate, and it counts only in a state that accepts it. OIML describes its Certification System, OIML-CS, as "a system for issuing, registering and using OIML certificates and their associated OIML type evaluation/test reports" for types of measuring instruments. The system holds 37 OIML Recommendations, OIML's model rules for particular kinds of instrument, as NIST's office of weights and measures reported in 2026. On 14 April 2026 OIML and Global ACI signed a memorandum under which Global ACI endorses part of the system, which OIML names Scheme A, as one of its own schemes. A certificate still binds no state, because OIML writes model rules and only a state makes them law. Under India's Act, for one, the authority may approve a model already approved abroad without a test, or with whatever test it thinks fit.

73 — Three routes across a border

References and standardsLimits and decisionsFocal detail

OIML's model rules for sphygmomanometers

An automated monitor built to OIML's model rule must read the cuff pressure within ±0.4 kPa (±3 mmHg) or ±2 % of the reading, whichever is greater. The limit holds at any point of the measuring range, with the pressure rising or falling, between 10 and 40 °C and at 15 to 85 % relative humidity. OIML sets it in R 149, one of the two Recommendations for blood-pressure instruments that it published in 2020: R 148 is for non-automated sphygmomanometers, read with a stethoscope or by another manual method, and R 149 for automated ones. Each comes in three parts, for the requirements, the test procedures and the format of the test report, so R 149-1 holds the requirements. The two replaced R 16-1 and R 16-2 of 2002, which older studies in Chapters 2, 10 and 13 refer to.

In R 149-1, OIML also holds the monitor to that limit through its working life. The monitor must zero itself at least when it is switched on, and zero again, or switch itself off, when its zero drifts by one scale interval, 1 mmHg. Under electromagnetic disturbance it must stay within the limit, or signal an abnormality and resume normal operation within 30 s. After 10,000 simulated measurement cycles its reading may have changed by no more than 3 mmHg. Verification covers at least the cuff-pressure limit, the repeatability and the air-leakage test, and may be carried out in any room climate between 10 and 40 °C without a climatic chamber. OIML sets no wider limit in R 149-1 for a monitor in service, so the monitor must meet the same limit at every verification as when it was new.

OIML holds the non-automated instruments to the same figures in R 148-1, with one difference in temperature. An aneroid or electro-mechanical gauge must read within ±3 mmHg between 15 and 25 °C, and within ±3 mmHg or ±2 % of the reading, whichever is greater, between 10 and 40 °C, a wider band that does not apply to mercury manometers. A digital display must step in 0.1 kPa, or 1 mmHg, and at least three samples of a new type must be tested for its approval.

OIML also sets limits in R 149-1 for the automated monitor's estimate: a mean error of no more than ±5 mmHg and a standard deviation of no more than 8 mmHg. A maker shows that the estimate meets them by a clinical investigation, not on the bench (Chapter 24).

India writes the limits into its rules

In India a maker or importer must obtain approval of the model before manufacturing or importing a weight or measure, and a user must have each one verified before using it in a transaction. Both duties come from the Legal Metrology Act 2009, in force since 1 April 2011, whose purpose, in its long title, is "to establish and enforce standards of weights and measures". The Union, India's central government, sets the standards, the Union and the States share their enforcement, and each State frames its own enforcement rules. The General Rules of 2011, made under the Act, cover about 40 types of instrument, the sphygmomanometer and the clinical thermometer among them, by the account of the Department of Consumer Affairs, DoCA. Two Parts of the rules' Eighth Schedule hold the sphygmomanometers: Part VII-A the non-automated instruments and Part VII-B the automated monitors.

India's limits for the automated monitor are the same as OIML's. Under Part VII-B, the maximum permissible error of the cuff pressure is "±0.4 kPa (±3 mmHg) or ±2 % of the reading, whichever is greater", from 10 °C to 40 °C and for rising and for falling pressure. The monitor must zero itself at least at power-on, and zero again or switch off when its zero drifts by "one scale interval (0.1 kPa or 1 mmHg) or more". The estimate's limits are in the same Part, as limits for a clinical investigation, and for the reading and the estimate alike the figures are those of R 149-1. DoCA substituted this text for the Part on 28 July 2025, in force from publication.

The rule's cuff-pressure test, Test 1, follows OIML's procedure of Chapter 14. The tester replaces the cuff with a 500 mL metal vessel and compares the monitor with a reference manometer whose maximum permissible error is within ±0.1 kPa (±0.8 mmHg), stepping the pressure by no more than 6.7 kPa (50 mmHg) at a time. For model approval the authority tests at least three samples of each new model, and an officer or an approved test center may then verify each monitor in any climate from 10 to 40 °C, without a climatic chamber. Seals must guard the enclosure and the measuring parts against tampering, and the maker must mark each monitor with its model approval number, serial number, year of manufacture and country of origin.

India holds the non-automated instruments to the figures of R 148-1, in Part VII-A, which DoCA replaced on 7 January 2026, in force from publication. Such an instrument must read the cuff pressure within ±3 mmHg between 15 and 25 °C, and within ±3 mmHg or ±2 % of the reading from 10 to 40 °C, a band that excludes mercury manometers. The reference manometer is held to ±0.8 mmHg, the steps to 50 mmHg and model approval to three samples. These figures come from a reproduction of the text by TaxGuru, a website that reprints Indian notifications.

No Indian rule is known to name a period of re-verification for the monitor. Neither Part sets one, and rule 27 of the General Rules sets the periods for the whole Act. On 18 December 2025 DoCA substituted the rule's first clause, which now gives twenty-four months for weights, capacity measures, length measures, tapes, beam scales, counter machines and fuel dispensers, a list without the sphygmomanometer. By the accounts of law firms and a State regulator, the second clause gives sixty months for storage tanks and the third twelve months for every other weight or measure. Neither the new clause nor these accounts names sphygmomanometers, so twelve months under the third, catch-all clause is an inference from its wording, not a stated rule.

By DoCA's account, officers of the States, private test centers and a layer of regional laboratories share the checking. Privately run test centers, which the Central Government approves under the Act, may verify sphygmomanometers and clinical thermometers among other instruments. Five Regional Reference Standard Laboratories, at Ahmedabad, Bangalore, Bhubaneswar, Faridabad and Guwahati, link CSIR-NPL, the national institute, to the States' weights and measures laboratories, and two more are being set up at Nagpur and Varanasi. All five are accredited by NABL, so in DoCA's account the standards with which a State verifies instruments in use trace to CSIR-NPL through a regional laboratory.

74 — India's legal metrology for the monitor, with its dates

References and standardsLimits and decisionsReadingFocal detail

No legal-metrology rule found for the monitor in the US or the EU

In the United States no weights-and-measures code is known to apply to the monitor, and its accuracy falls instead under FDA's device rules (Chapter 31). NIST publishes Handbook 44, which provides "the specifications, tolerances and other technical requirements" for commercial weighing and measuring devices. Its current edition, of 2026, is the one that the National Conference on Weights and Measures adopted. The 2022 edition lists codes from 1.10 to 5.60, for scales, weights, liquid and gas meters, timing devices and grain moisture meters among others, and none for sphygmomanometers, blood-pressure instruments, clinical thermometers or medical devices.

In the European Union, too, device law and not the law on measuring instruments sets the requirements for the monitor's accuracy. Under the Medical Devices Regulation, the maker of a device with a measuring function must state the device's limits of accuracy (Chapter 31). The EU regulates measuring instruments through two directives, the Measuring Instruments Directive, the MID, and the directive on non-automatic weighing instruments, the NAWI directive, and neither is known to place a blood-pressure device under it. The European Parliament and the Council amended the MID on 11 March 2026 without changing that: the amendment, in force from 9 April 2026, concerns charging points for electric vehicles, dispensers of compressed gas, and meters for electricity, gas and thermal energy. The NAWI directive has no known amending act.

The rules side by side, with their dates

Each of India's limits is printed twice, in kilopascals with millimeters of mercury in brackets, and the two units do not always give the same number. That difference explains a shortfall in Chapter 12, where the engineer set OIML's reference manometer against the monitor's limit at 3.75 to one, short of the four to one.

75 — One limit in two units

References and standardsNoise and errorLimits and decisionsFocal detail

+ The questionHow do medical-device rules in the US, the EU and India treat a device that measures, and the equipment that tests it?

A Class I recall for readings that were too low

Some of Abbott's FreeStyle Libre 3 and 3 Plus sensors, the glucose sensors of its continuous monitoring systems, could read glucose too low, and on 13 January 2026 FDA classified their recall as Class I, its most serious type of recall. FDA gave the reason in one sentence: "Due to a manufacturing process issue that may cause carbon build up in the sensor that may result in incorrect low glucose results." Abbott had begun the recall on 24 November 2025, and FDA recorded it as one recall with a record for each of the four sensor models. In its own announcement Abbott traced the fault to "one production line among several" and stated that its internal testing had found it. By 7 January 2026 Abbott had reported 860 serious injuries and seven deaths, as FDA stated in a notice of February 2026.

The recall is a measurement case under device law. In the words of FDA's product classification, the sensor is factory calibrated: the person who wears it performs no calibration step, so the factory's calibration is the only one between the sensor's signal and the number on the screen. The faulty readings erred in one direction, low. The displayed number decides what a patient does next, so an error in that number alone can lead over time to wrong treatment decisions, such as eating excess carbohydrates or skipping or delaying insulin, as FDA's notice describes them. A maker traces a fault of this kind back through every unit it reached (Chapter 26).

76 — One recall, four records

Noise and errorFocal detail

The United States: a class II device and the standards FDA recognizes

In the United States the monitor is a class II device, and its maker reaches the market through a 510(k). In that premarket submission the maker shows that its device is "substantially equivalent" to one already legally marketed, and FDA clears a 510(k) rather than approving it. FDA groups devices of one type under a three-letter product code, and it lists the monitor under code DXN, "Noninvasive blood pressure measurement system", in class II. One maker whose monitor FDA cleared on 5 December 2023 states in its 510(k) summary: "The maximum error of the pressure measurement in the cuff should be ±0.4kPa(±3mmHg) at any measuring point" (Chapter 13). The figure is the maker's statement of the limit it tested against, and the maker names IEC 80601-2-30 and ISO 81060-2:2018 for its performance tests.

FDA names the standards it accepts in its list of recognized consensus standards, and a maker may support a premarket submission with a declaration that its device conforms to one of them. Such a declaration is a different document from the EU declaration of conformity of Chapter 29, which the manufacturer issues under the EU's device regulation. Since 6 July 2020 FDA has recognized the 2018 edition of IEC 80601-2-30, the particular standard for automated non-invasive sphygmomanometers. Since 23 December 2024 it has recognized ISO 81060-2, the standard for clinical validation of the estimate (Chapter 24), in its 2018 edition with amendments 1 and 2. FDA will accept declarations to its earlier recognition, of that edition with amendment 1 only, until 20 December 2026, so a maker that declares conformity after that date must cite both amendments. For the equipment that tests monitors, FDA recognizes in full ISO TS 81060-5, a specification for the repeatability and reproducibility of the simulators that test oscillometric monitors.

The equipment that tests a device falls under FDA's quality rule. FDA's Quality Management System Regulation, the QMSR, has been in force since 2 February 2026. The QMSR incorporates by reference ISO 13485:2016, the quality-system standard for device makers, and under the QMSR a maker must "Document a quality management system that complies with the applicable requirements of ISO 13485". The duty to control monitoring and measuring equipment is in clause 7.6 of that standard, so a maker's test stations and gauges come under the rule.

In its warning letters of 2026 (Chapter 26), FDA holds makers to that duty for their own calibration testing. On 27 May 2026 FDA wrote to Linemaster Switch Corporation, a maker of foot pedals that control medical lasers, that units "passed Linemaster's calibration testing" and were "subsequently returned because they failed customer calibration testing". FDA added that software errors in the test areas had been described as routine and "were not investigated".

The European Union: class IIa, and limits the maker states

In the European Union a home monitor is in class IIa, as two makers declare for their monitors under Rule 10 of the Medical Devices Regulation, the MDR. The MDR defines a device's class by rules. Under Rule 10, in its Annex VIII, active devices for diagnosis and monitoring are in class IIa "if they are intended to allow direct diagnosis or monitoring of vital physiological processes". They are in class IIb where they are "specifically intended for monitoring of vital physiological parameters" whose variations "could result in immediate danger to the patient". Joytech, which issues the EU declaration for the Beurer monitors of Chapter 29, names TÜV SÜD Product Service as its notified body, the independent organization designated to assess conformity, with a certificate valid to 27 April 2027. Ya Horng, which makes Garmin's Index BPM, names DNV Product Assurance, with a certificate valid to 30 August 2028.

The maker of a device with a measuring function, such as the monitor, must also state how accurate it is. Under the MDR such a device must be designed and made for sufficient accuracy, precision and stability for its intended purpose, and "The limits of accuracy shall be indicated by the manufacturer." Under the MDR, too, "The measurements made by devices with a measuring function shall be expressed in legal units", the units of the EU's units directive, 80/181/EEC (Chapter 3). Even a class I device with a measuring function needs a notified body, whose role under the MDR is limited "to the aspects relating to the conformity of the devices with the metrological requirements". A maker that otherwise declares the conformity of a class I device alone therefore calls in an outside assessor for the measurement.

The two makers declare conformity to the standards that FDA recognizes. Joytech lists IEC 80601-2-30:2018 with its European edition, EN IEC 80601-2-30:2019, and ISO 81060-2:2018 with amendment 2, also in its European edition, among 15 standards. Ya Horng lists the European edition of ISO 81060-2 and two older European standards for sphygmomanometers, EN 1060-1 and EN 1060-3, the second a predecessor of EN IEC 80601-2-30. A maker's list is not the Commission's list of harmonized standards, the EU's counterpart of FDA's list of recognized standards, and it is not known whether either European edition appears on the Commission's list for the MDR.

A maker of in vitro diagnostic devices, which test samples taken from the body, must assure traceability in the sense of Chapter 15. Under the IVDR, the parallel regulation for those devices, the metrological traceability of values assigned to calibrators and control materials "shall be assured through suitable reference measurement procedures and/or suitable reference materials of a higher metrological order". In January 2022 the Commission listed EN ISO 17511:2021, the standard for that traceability, among the IVDR's harmonized standards.

As of November 2026 the MDR as adopted governs the monitor, but both regulations may change. On 16 December 2025 the Commission proposed one regulation amending both. Among other changes, the proposal would remove the five-year limit on the validity of notified-body certificates. In September 2026 two committees of the European Parliament voted in favor, and a plenary vote is planned for early 2027, as the consultancy Emergo by UL reported on 9 October 2026.

India: a draft class and two regimes side by side

In India the monitor is in class B, but only in a draft list. India classifies medical devices under its Medical Devices Rules, 2017, and CDSCO, its medical-device regulator, administers those rules. In a list of cardiovascular devices dated 1 April 2025, CDSCO places every sphygmomanometer in class B: the aneroid manual instrument, the automatic-inflation electronic sphygmomanometer for professional use, portable or not, the electronic sphygmomanometer for home use and the long-term recorder. A non-invasive unit that measures several cardiovascular quantities goes to class C. The list is a draft issued for comments within 30 days, as the newspaper Business Standard and the regulatory services company CliniExperts report, and no final list is known.

The class decides the licensing route. A maker of class A or B devices applies on form MD-3 and receives its manufacturing license on form MD-5 from the State Licensing Authority. Classes C and D go through forms MD-7 and MD-9 to the Central Licensing Authority, and an importer of any class applies to the central authority on forms MD-14 and MD-15. CDSCO exempts from licensing only class A devices that are both non-sterile and non-measuring. A device with a measuring function therefore needs a license even in class A, and a class B monitor made in India needs one from its State.

The same monitor also falls under Part VII-B of the Eighth Schedule (Chapter 30), which DoCA administers under the Legal Metrology Act. No published text is known to say how the two regimes apply together: none states that a monitor needs both a CDSCO license and model approval under the Act, and none states that either exempts it from the other. A maker in India therefore settles each regime on its own. For the calibration of medical devices, NABL, India's accreditation body, gives specific criteria in its document NABL 126, issued in 2018 and amended in 2021.

Drafts on the way

Four drafts could change these rules, and none is in force as of November 2026. The vote on ISO/DIS 81060-2, the draft revision of the clinical validation standard, closed on 15 September 2026. The 2018 edition with its two amendments stays in force, and FDA does not recognize the draft. Edition 3 of IEC 80601-2-30 has reached a committee draft for vote, and on 29 May 2026 DIN, Germany's standards body, issued a German draft based on it. The 2018 edition of that standard also stays in force. CDSCO's cardiovascular list of 2025 and the Commission's proposal for the MDR and the IVDR are the other two. A maker who designs to a draft cannot be sure the final text will match it, so the records to rely on are the editions in force and the regulators' own lists, each with its date.

The correction fitted in December 1993

The correction of December 1993 cancelled the primary mirror's error without touching the mirror. On 2 December 1993 the Space Shuttle Endeavour lifted off with two instruments built to correct the Hubble Space Telescope (the opening story), and its crew installed them on spacewalks. The Wide Field and Planetary Camera 2, WFPC2, carried the correction on small relay mirrors inside the camera, which hold, in the words of its instrument handbook, "the same error (but with opposite sign)". COSTAR placed five pairs of corrective mirrors in front of three other instruments. The correction worked: "The operation to correct the telescope optics was a total success, and the differences are striking", ESA announced on 13 January 1994.

A correction of that kind needs the error itself, and three routes that did not depend on one another measured it. In 1991 Litvak of TRW, under contract to the Jet Propulsion Laboratory, inferred the primary mirror's conic constant, the number that fixes the shape of its curve, from star images taken in orbit. He found −1.0141 against a design value of −1.0023, a difference of 0.0118. In 1993 Meinel, Meinel and Schulte, of the Jet Propulsion Laboratory and Lockheed, measured the telescope's effective value from direct images as −1.0140 ± 0.0003. The third route went back to the factory. Lew Allen's board of investigation had measured the reflective null corrector where it stood. The field lens, about 1.3 mm out of place, "can account for the entire HST error", as George Rodney, NASA's head of safety and mission quality and a member of the board, recorded.

77 — One error, measured three ways, then cancelled

The quantity being measuredReferences and standardsNoise and errorUncertaintyFocal detail

The camera's designers then set its prescription inside the error's stated bounds. They adopted "a prescription within the error bars for the HST primary mirror", as the Space Telescope Science Institute's handbook records, so that the camera's residual aberration is small. The correction also had to sit exactly in place: by the same handbook, a misalignment of 7 % of the pupil's diameter would bring back as much wavefront error as the uncorrected mirror had.

The correction of 1993 rested on three routes, each of which could have disagreed with the others. In 1981 Perkin-Elmer had polished the mirror against one instrument whose critical length was set once and never checked, and the two instruments that disagreed with it were discounted. The two measurements from images differed by 0.0001 and so agreed within their stated uncertainties, and the third, from the null corrector itself, accounted for the whole error.

The monitor's reading needs what the correction had. Inside the instrument, every stage from the sensor to the display adds an error that a budget bounds, as Chapter 11 bounded the reading at 150 mmHg to a standard uncertainty of 0.70 mmHg. Outside it, each reference must have been compared with a better one, link by link, from the maker's reference manometer through an accredited laboratory and a national institute's pressure balance and its masses to the Planck constant (Chapter 28). The uncertainty stated at the bench then includes the uncertainty of every link above it. That uncertainty must also be small enough for the decision the number serves: an expanded uncertainty of 1.4 mmHg, twice 0.70 mmHg, against a limit of ±3 mmHg (Chapter 12).

One further condition comes from the mirror's history: a second, independent check must be able to disagree with the first and be heard, as the two instruments of 1981 were not. The monitor's estimate of blood pressure also needs one proof more, a clinical validation against a reference method (Chapter 24), because a calibration of the cuff pressure does not test the algorithm. Hubble's primary mirror still has the shape it was polished to. In 1993 its error was known, measured, with its uncertainty stated, by independent methods that agreed, and a known error could be cancelled where the unknown one of 1981 could not.

The chapters reduce to sixteen working rules for anyone who designs, tests, calibrates, buys or regulates a device that measures. The rules follow a product's life in order, from design input through verification and clinical validation to calibration, supply and regulation, and each ends with the chapters it comes from.

1. Write separate accuracy requirements for the reading and the estimate, each with its own evidence. Calibration ties the cuff pressure to the SI, but an algorithm derives the systolic and diastolic values with ratios that no calibration of the cuff pressure tests, so only a clinical validation can prove them (Chapters 1, 9 and 28).
2. Write the uncertainty budget at the data-sheet stage, with every row in the display's unit. Each %FS figure, amplifier error and converter step is converted into mmHg before it is set beside the limit. The bare sensor's combined standard uncertainty, about 26 mmHg behind a 1 mmHg display, then shows which corrections the firmware must make and how good each must be (Chapters 4, 6 and 11).
3. Rank the rows after correction, and improve the largest first. Independent uncertainties add by their squares, so the largest rows decide the result. In the corrected budget the reference manometer, the sensor's hysteresis and the display step lead, and a 16-bit converter would change almost nothing (Chapters 5, 11 and 28).
4. Share the accuracy limit out as a budget before choosing parts, with a size, an owner and a test for every row. The method of combination decides how large each share may be. Added at their limits, the five numbered rows of the monitor's corrected budget leave each of the firmware's two corrections a residual of about ±0.43 mmHg. The root-sum-of-squares, which holds only for rows with no shared cause, leaves each about ±1.63 mmHg. Neither figure can go to the firmware in full, because the production test's guard band must fit inside the same 3 mmHg (Chapter 25).
5. Size the converter and the display from the channel's real resolution, and state accuracy as a separate figure. Bits measure resolution only, and a converter's nonlinearity can span hundreds of its own steps. The monitor's 12 bits give 0.109 mmHg per count behind a 1 mmHg display, while a maker's ±3 mmHg is a maximum permissible error, a limit rather than a measurement (Chapters 2 and 8).
6. Test the firmware as a stage of the measurement, across the whole input range. Abbott's FreeStyle InsuLinx glucose meters showed and stored results 1,024 mg/dL below the measured value, but only at very high glucose, and FDA recorded the cause as software design. Each monitor also needs its own zero and span, stored with a check value, because one unit read with typical coefficients is 55 mmHg wrong at 150 mmHg (Chapter 9).
7. Write the decision rule into the test procedure before the first unit is tested. Without one, a monitor whose measured error equals its 3 mmHg limit can be neither passed nor failed with confidence. Every rule trades the user's risk against the maker's yield, and a guard band equal to the test's expanded uncertainty of 1.4 mmHg moves the acceptance limit from 3.0 to 1.6 mmHg, so reducing the test's uncertainty comes before narrowing the limit further (Chapter 13).
8. Study the production test station before it sorts product, and again after any change to it. A station adds scatter of its own, and a gauge study separates its repeatability and reproducibility from the real differences between monitors. A station that records only PASS or FAIL needs an attribute study, which keeps agreement among technicians apart from agreement with the correct verdicts (Chapter 22).
9. Validate the test method before it is used, against acceptance criteria fixed in advance. A test's result cannot be checked afterward without a second, better station, so the maker proves the whole procedure, from fixture to decision, and then trusts each result. A simulator test shows only that the monitor's algorithm repeats, not that its answer is right (Chapter 23).
10. Prove the estimate in people, and state its claim so that a reader sees what one measurement may do. In a 2024 validation by Hernández Véliz and colleagues that analyzed 85 people, a monitor that passed both criteria of ISO 81060-2 with 1.2 ± 4.9 mmHg still allows about one measurement in twenty outside −8.6 to 11.0 mmHg. In a 2023 randomized crossover trial of 195 adults by Ishigami and colleagues, a cuff too small for the arm raised the systolic estimate by 19.5 mmHg in extra-large arms, so the claim names its cuff sizes and the conditions it assumes (Chapter 24).
11. Read a certificate's uncertainty with its coverage factor, and a laboratory's scope at the test point. A certificate's expanded uncertainty U is divided by its coverage factor k before it enters a budget, and U describes one calibration, not the instrument's accuracy in use. Two accredited scopes at the cuff's pressures differ widely, and one of them is too coarse to show that a monitor meets ±3 mmHg (Chapters 12 and 16).
12. Ask each calibration supplier for the chain, not the sticker. Traceability is a property of a result, related to a reference through a documented unbroken chain of calibrations, and the chain breaks where a link or an input cannot be shown or a reference is used without its date. The links above the bench add almost nothing to the reading's uncertainty, but a maker who skips one loses the tie to the unit (Chapters 15 and 28).
13. Set each calibration interval from risk and the as-found record, and check the span between calibrations. An accredited laboratory's certificate carries no due date unless the customer agrees one or a regulation requires one, so the interval is the owner's prediction. Auto-zero removes the offset but cannot see a change of span. In ACCU-RATE, a 2020 cross-sectional study of 327 home monitors by Hodgkinson and colleagues, those in use for more than four years failed five times as often as those in their first four years (Chapters 17 and 27).
14. Record each unit's measured error and each reference's as-found values, not only a pass. A reference found out of tolerance reaches back to every result it supported since its last good calibration. With each monitor's error on file, a reference found 2.0 mmHg high at 150 mmHg makes only the monitors recorded above +1.0 mmHg suspect, while a record of passes alone makes every monitor in the period suspect (Chapters 14 and 26).
15. Name beside each budget row the organization that states its figure, and take the current maker of each bought part or device from a dated record. More than four fifths of the monitor's corrected budget, counted in squares, rests on figures stated outside the monitor maker. A data sheet or a brand names who wrote or sold it on its date, and a part's maker can change while the part and its published figures stay the same (Chapter 29).
16. Build the cuff-pressure evidence once, then map it onto each jurisdiction's route. One bench method, with the reference manometer and its certificate recorded, can supply the accuracy file for the United States, the EU and India. Each route adds its own steps: in India a legal-metrology model approval beside the device license, and in the United States a check of FDA's recognition record, which may exclude some clauses of a standard (Chapters 30 and 31).

Terms are defined as they are used in this guide.

%GRR

The gauge's R&R divided by the total variation of a gauge study, as a percentage; by AIAG's manual, as Minitab and BPI reproduce it, under 10 % is generally acceptable and over 30 % unacceptable (Chapter 22).

1/f corner

The frequency below which 1/f noise exceeds an amplifier's flat noise floor; about 1 to 10 Hz for the best low-frequency amplifiers (Chapter 5).

1/f noise

Noise whose power is inversely proportional to frequency, so that it rises at low frequencies (Chapter 5).

510(k)

The premarket submission in which a US maker shows that its device is substantially equivalent to one already legally marketed; FDA clears it (Chapter 31).

Acceptance limit

The upper or lower bound of the measured values that a test will accept; it equals the tolerance limit under simple acceptance and lies inside it with a guard band (Chapter 13).

Accreditation

An independent body's assessment of a laboratory against a standard such as ISO/IEC 17025, followed by formal recognition that it is competent for a stated list of calibrations or tests; laboratories are accredited, quality systems certified (Chapter 16).

Accuracy

In the VIM, the closeness of a measured value to a true value; not a quantity and given no number. A maker's "accuracy ±3 mmHg" is a maximum permissible error (Chapter 2).

Adjustment

A set of operations that makes a measuring system give prescribed indications for given values of the quantity, such as zero, offset or span adjustment (VIM 3.11). Calibration comes before it, and the system is usually calibrated again after it (Chapter 14).

Alias

The false, slower frequency that a too-fast tone produces in sampled readings: mains hum at 50 Hz read 49 times a second gives an alias at 1 Hz (Chapter 7).

Aliasing

The distortion by which a frequency too fast for the readings appears in them as a slower one; once the readings are taken it is generally not recoverable (Chapter 7).

Aneroid sphygmomanometer

A mechanical dial gauge for blood pressure, used with a stethoscope; OIML R 148 covers it (Chapter 2).

Anti-alias filter

A low-pass filter ahead of a sampling converter that weakens frequencies above half the sampling rate before they can fold back as aliases (Chapter 7).

Aperture jitter

The variation, from one sample to the next, in the instant a sample-and-hold's switch opens; it matters for fast signals, not for a blood-pressure monitor's pulse band (Chapter 7).

Appraiser variation (AV)

In a gauge study, the reproducibility as a standard deviation: the spread between the averages of different operators on the same parts (Chapter 22).

Arms

A pulse oximeter's accuracy figure: the square root of the average squared difference from oxygen saturation measured in arterial blood, which counts bias and scatter together; FDA staff put 1 Arms at about one standard deviation (Chapter 24).

As found, as left

Trade names for the calibration results before and after an adjustment or repair; accreditation bodies describe ISO/IEC 17025 as asking for both on a certificate where they are available (Chapter 14).

As-maintained mass unit

The kilogram as the BIPM actually kept it in its working standards, found in 2014 to be offset by 35 µg from the international prototype (Chapter 18).

Attribute agreement

The test of a measuring system that reports a verdict, such as pass or fail: how often an operator repeats a verdict, how often operators agree, and how often the verdicts match the standard, the verdict known to be right for each item (Chapter 22).

Auscultation

Listening to the artery with a stethoscope; the reference method for the sounds by which an observer reads systolic and diastolic pressure (Chapter 7).

Auto-zero

In an amplifier, a technique in which the amplifier measures its own offset and subtracts it; because the noise changes slowly at low frequencies, subtracting consecutive samples cancels its low-frequency noise too (Chapter 5). In a monitor, its own zero: before measuring, at least at power-on, the firmware reads the sensor open to the air, stores that reading and subtracts it from later readings; an adjustment, not a calibration, which removes the offset but cannot see the span (Chapter 17).

Bandwidth

The range of frequencies over which a signal is measured; noise power grows in proportion to it (Chapter 5).

Bell curve

The normal distribution: values near its center are more likely than values far from it, it falls away alike on both sides, and its standard deviation sets its width (Chapter 10).

Bias

The value that a measurement assigns to a systematic error (Chapter 2).

Bias (of an estimate)

The mean of an estimate's differences from the reference, the first figure of ISO 81060-2's criterion 1 (Chapter 24); for a measuring system, the average difference between its results on a part and that part's known value (Chapter 22).

BIPM

The International Bureau of Weights and Measures, the laboratory and secretariat at Sèvres set up by the Metre Convention (Chapter 3).

Bridge

Four resistors joined in a square, powered across two opposite corners, whose output is the voltage between the other two; it is zero when the bridge is balanced (Chapter 4).

Calibration

In the VIM's definition (2.39), an operation in two steps: relating the values that measurement standards provide to an instrument's indications, each with its uncertainty, and then using that relation to obtain a measurement result from an indication. It is not adjustment (Chapter 14).

Calibration and measurement capability (CMC)

In ILAC's definition, a calibration and measurement capability available to customers under normal conditions, as a scope of accreditation describes it or as the BIPM's database publishes it; stated as an expanded uncertainty at about 95 %, the smallest uncertainty a certificate from the laboratory may state (Chapter 16).

Calibration coefficients

Numbers measured for each unit and stored in its firmware that turn counts into the displayed unit: chiefly a zero, measured again with the sensor open to the air, and a span factor from calibration against a reference (Chapter 9).

Calibration hierarchy

The sequence of calibrations from a reference to the final measuring system (VIM 2.40), along which the uncertainty necessarily increases (Chapter 15).

Calibration interval

The time an owner allows between successive calibrations of an instrument, chosen from risk and reviewed from the results; an accredited laboratory prints none unless the customer asks (Chapter 17).

Certified reference material

A material whose value a competent producer certifies with its uncertainty; the links of a traceability chain in chemistry and laboratory medicine (Chapter 15).

CGPM

The General Conference on Weights and Measures: delegates of every Member State, normally meeting every four years, whose resolutions decide the units; its 28th meeting was in October 2026 (Chapter 3).

Checksum

A number computed from stored data, such as a program and its calibration coefficients, so that a changed bit gives a different number (Chapter 26).

Chi-squared test of consistency

A statistical test of whether a set of results scatters around its common value by more than the results' stated uncertainties allow (Chapter 19).

CIPM

The International Committee for Weights and Measures: eighteen members from different States, meeting every year under the CGPM's authority, advised by ten Consultative Committees (Chapter 3).

CIPM MRA

The mutual recognition arrangement, signed on 14 October 1999, through which national metrology institutes demonstrate the international equivalence of their measurement standards and the certificates they issue (Chapters 3, 21).

Class E1

The most accurate class of weight in OIML R 111; a 1 kg weight of this class may differ from its nominal value by no more than 0.5 mg (Chapters 20, 21).

Class I recall

FDA's most serious type of recall, a classification of the recall action separate from the device's class (Chapters 9, 31).

Clinical validation

A study in people that compares a device's estimates with a reference method under a protocol fixed in advance; the only proof of a blood-pressure monitor's systolic and diastolic values (Chapter 24).

Combined standard uncertainty

The square root of the sum of the squared contributions of every row of an uncertainty budget; 0.70 mmHg for the monitor's corrected cuff-pressure reading at 150 mmHg (Chapter 11).

Common mode

The voltage that both inputs of a differential amplifier share; about 1 V at the monitor's bridge outputs (Chapter 6).

Common-mode rejection ratio (CMRR)

How well an amplifier ignores a common-mode voltage, stated in decibels; at least 85 dB for the INA350 (Chapter 6).

Conditional pass and conditional fail

ILAC's outcomes for a measured result inside the guard band below the tolerance limit, or above the tolerance limit but within the guard band beyond it: results the test cannot decide (Chapter 13).

Consensus value

The value of the kilogram that the CCM computes from the key comparisons of the realizations and from which mass has been disseminated since February 2021; since 1 March 2026 it puts the old prototype at 1 kg − 12 µg, with a standard uncertainty of 20 µg (Chapter 21).

Control solution

A liquid of known value that tests a glucose meter, not the patient (Chapter 27).

Corner frequency

The frequency at which a filter begins to weaken a signal (Chapter 6).

Correlated inputs

Inputs that share a cause and so move together; the simple sum of squares does not apply to them, and the GUM adds a term for each related pair (Chapter 11).

Coverage factor

The multiplier k that turns a combined standard uncertainty into an expanded uncertainty; accredited calibration laboratories use k = 2, about 95 % (95.45 % for a bell curve), and a larger k when a result rests on few readings (Chapter 12).

Coverage probability

The probability that the interval of plus or minus the expanded uncertainty contains the true value; about 95 % for k = 2. EA and UKAS call it a coverage probability, Mensor and NIST a confidence level (Chapter 12).

Criterion 1 (ISO 81060-2)

Over all paired readings, a mean difference from the reference of no more than 5 mmHg with a standard deviation of no more than 8 mmHg, as the AAMI/ESH/ISO collaboration states it (Chapter 24).

Criterion 2 (ISO 81060-2)

A limit on the standard deviation of each subject's averaged difference that falls as the mean difference grows, from 6.95 mmHg at a mean of zero to 4.79 mmHg at 5 mmHg, so that at least 85 % of errors stay within 10 mmHg (Chapter 24).

Decibel (dB)

A unit for ratios that counts tenfold steps: 20 dB for each tenfold step of a voltage ratio and 10 dB for each tenfold step of a power ratio (Chapter 5).

Decision rule

A rule that describes how measurement uncertainty is accounted for when stating conformity with a specified requirement, in ISO/IEC 17025's definition as ILAC reproduces it (Chapter 13).

Defining constants

The seven constants whose fixed numerical values define the SI since 20 May 2019, the Planck constant among them (Chapter 19).

Deflation method

The way a monitor lets air out of the cuff while its algorithm reads the oscillations (Chapter 27).

Degree of equivalence

The difference between an institute's result in a key comparison and the reference value, stated with the uncertainty of that difference (Chapter 21).

Degrees of freedom

The number of independent deviations behind a standard deviation, one less than the number of readings in the simple case; it sets the coverage factor when few readings are used (Chapters 10 and 12).

Design traceability

The documented link from each design requirement to the design output that answers it and to the verification that shows it is met; a different thing from metrological traceability (Chapters 15, 25).

Diagnostic sensitivity

The share of people with a condition whom a test detects; distinct from an instrument's sensitivity, its change in output for each unit of input (Chapters 4 and 24).

Diastolic pressure

The lowest pressure in the artery during a heartbeat; in an oscillometric monitor, an estimate derived by the algorithm from the envelope (Chapters 1, 9).

Differential nonlinearity (DNL)

The largest departure of any one converter step from its ideal size; a DNL worse than minus one step leaves a missing code (Chapter 8).

Disseminate

To pass a unit's value down to other standards by comparison, from a realization to national standards, accredited laboratories and factories (Chapter 21).

Dither

Noise added to a converter's input; about half a step rms randomizes the quantization error and lets averaging resolve finer than one step (Chapter 8).

Dominant contributor

The row of an uncertainty budget with the largest share of the total of squares: the offset, with 62 %, for the bare sensor. In the corrected channel it is the reference manometer, at 44 %, with the hysteresis close behind at 39 %, so no row supplies even half of the total (Chapters 11, 12).

Doubtful band

The measured values within one expanded uncertainty of a tolerance limit, the only ones whose true value, at about 95 % coverage, could lie on the other side of it (Chapter 13).

Drift

A slow change in an instrument's output for the same input, such as a sensor's zero moving with temperature or time (Chapter 17).

Effective area

The area by which a pressure balance's piston turns a force into a pressure; about 3.357 cm² for CSIR-NPL's air piston gauge, known to nearly 11 parts per million at k = 2 (Chapter 15).

Effective degrees of freedom

A count derived by formula from the degrees of freedom of each contribution to a budget, from which EA-4/02's table gives the coverage factor (Chapter 12).

Effective number of bits (ENOB)

SINAD minus 1.76 dB, divided by 6.02 dB: the bit count of a perfect converter that would add as much noise and distortion; up to 11.1 for the converter in TI's monitor design (Chapter 8).

Envelope

The curve traced by the sizes of the oscillations plotted against the falling cuff pressure; the firmware receives one point on it per heartbeat (Chapter 7).

Equipment variation (EV)

In a gauge study, the repeatability as a standard deviation: the scatter when one operator measures the same part several times (Chapter 22).

Error budget (as a requirement)

An allocation of one instrument's accuracy limit into shares, each with its size, its owner and the test that proves it, set before the parts are chosen; for the monitor, seven shares of ±3 mmHg at 150 mmHg (Chapter 25).

Estimate

In this guide, the systolic and diastolic blood pressure that the monitor's algorithm derives from the oscillations in the cuff pressure; only a clinical validation can prove it (Chapters 1, 24).

EU declaration of conformity

The manufacturer's statement that a device meets the requirements of the EU's device regulation (Chapters 29, 31).

Excitation

The current or voltage that powers a bridge or other sensor; the 2SMPP-03 is driven by a constant 100 µA (Chapter 4).

Expanded uncertainty

The combined standard uncertainty multiplied by a coverage factor, written U and printed after the ± on a certificate; ±1.4 mmHg for the monitor's reading at 150 mmHg (Chapter 12).

Factory calibrated

FDA's product-classification wording for a sensor that its user does not calibrate, so the factory's calibration is the only one between its signal and the displayed number (Chapter 31).

False accept

Accepting an item that in fact lies outside its tolerance limit; ILAC states that under simple acceptance its probability may be as high as 50 %, which UKAS places at values on the tolerance limit (Chapters 12, 13).

Fault

In OIML's weighing recommendation, the difference between an instrument's error of indication and its intrinsic error, the error it shows minus the error it had when sound (Chapter 26).

Filter

A circuit that passes some frequencies and weakens others; a high-pass filter weakens slow changes, a low-pass filter weakens fast ones, and a band-pass filter weakens both (Chapter 6).

Fixed-ratio method

The common published oscillometric algorithm: systolic and diastolic pressure are read where the envelope falls to a population-based fraction of its peak, one fraction on each side; the makers' own fractions are proprietary (Chapter 9).

Gain

The factor by which an amplifier multiplies its input; 50 for the in-amp in TI's design (Chapter 6).

Gain error

The amount by which an amplifier's actual gain differs from its nominal gain; it scales every reading in proportion (Chapter 6).

Gauge

In manufacturing, any measuring instrument or test system, such as a production pressure test station (Chapter 22).

Gauge pressure

Pressure measured against the pressure of the surrounding air; the monitor's sensor reads the cuff's pressure above the room's (Chapter 4).

Gauge R&R (GRR)

Repeatability and reproducibility together: the variation that a measuring system adds to what it measures, the root-sum-of-squares of the equipment and appraiser variation (Chapter 22).

Gauge study

The study that measures a measuring system's gauge R&R (Chapter 22).

Global ACI MRA

The Multilateral Recognition Arrangement of Global Accreditation Cooperation Incorporated, into which the arrangements of ILAC and IAF passed on 1 January 2026 (Chapter 16).

Global risk

The probability, over the whole stream of items before any is measured, that a non-conforming item will be accepted (consumer's risk) or a conforming one rejected (producer's risk) (Chapter 13).

Guard band

The interval between a tolerance limit and the corresponding acceptance limit, often equal to the expanded uncertainty; with w = U the monitor's acceptance limit at 150 mmHg moves from 3.0 to 1.6 mmHg (Chapter 13).

Half-width

The distance from the center of a band of possible values to either of its limits (Chapter 11).

Harm

In ISO 14971's words, "Injury or damage to the health of people, or damage to property or the environment" (Chapter 26).

Harmonized standards

The standards on the European Commission's list, the EU's counterpart of FDA's list of recognized standards (Chapter 31).

Hazard

In ISO 14971's words, a "Potential source of harm" (Chapter 26).

Hazardous situation

In ISO 14971's words, a "Circumstance in which people, property or the environment is/are exposed to one or more hazards" (Chapter 26).

Hysteresis

The difference between a sensor's output at one pressure reached from below and from above; up to 0.2 %FS for the 2SMPP-03 (Chapter 4).

Image (of a tone)

A frequency at a whole multiple of the sampling rate, plus or minus a tone's own frequency, which sampled readings cannot tell apart from the tone; a tone above half the sampling rate always has an image below half that rate, where the readings show it as an alias (Chapter 7).

Indication

The quantity value an instrument provides; it need not be the same kind of quantity as the measurand, as with the sensor's millivolts and the converter's counts (Chapter 1).

Indirect measurement

A measurement made through a chain of signals and computations rather than by setting the quantity beside a scale, as the monitor turns an air pressure into millivolts, counts and mmHg (Chapter 1).

Influence quantity

A quantity other than the one measured that changes an instrument's output, such as temperature for a silicon bridge (Chapter 4).

Input-referred noise

Noise expressed as if it entered at the input of an amplifier or front end, so that it can be compared directly with the sensor's signal; under 10 µV peak to peak for the front end of TI's design (Chapters 5, 10, 11).

Instrumentation amplifier

Also in-amp: an amplifier built to measure the small difference between two inputs while rejecting the voltage they share (Chapter 6).

Integral nonlinearity (INL)

The largest departure of a converter's actual transfer characteristic from a straight line; an accuracy figure, separate from the converter's bit count (Chapter 8).

Interface

The boundary between two owners of a measuring chain, where one part's output becomes another's input, such as the sensor's microvolts for each millimeter of mercury at the amplifier (Chapter 25).

Interference

Noise with an outside cause, such as mains hum or the noise of the monitor's motors (Chapter 5).

Intermediate check

A check between full calibrations that an instrument still works and keeps its calibration status, such as a monitor read at zero and at one pressure (Chapter 17).

International prototype of the kilogram

The platinum-iridium cylinder kept at the BIPM that defined the kilogram from 1889 to 2019; since 2019 a mass like any other, with an uncertainty (Chapters 18, 19).

JCTLM

The Joint Committee for Traceability in Laboratory Medicine, which the BIPM set up in 2002 with ILAC and the International Federation of Clinical Chemistry and Laboratory Medicine; its database lists the reference materials, reference measurement procedures and reference measurement services at the upper links of the traceability chains of in-vitro diagnostic tests (Chapter 15).

Josephson effect

The effect by which a junction between two superconductors, driven at a known microwave frequency, holds a voltage set by that frequency and the Josephson constant, twice the elementary charge divided by h; used to realize the volt (Chapter 20).

Kappa

A statistic of agreement between verdicts that corrects the share of agreeing verdicts for the share that chance alone would produce; AIAG suggests at least 0.75, as Minitab reports (Chapter 22).

KCDB

The BIPM's key comparison database, which publishes the institutes' peer-reviewed calibration and measurement capabilities with the comparisons that support them (Chapter 21).

Key comparison

A comparison in which several national institutes measure the same quantity, usually on one transfer standard that travels between them, under a pilot laboratory (Chapter 21).

Key comparison reference value

The reference value that a key comparison yields, against which each participant's result is set (Chapter 21).

Kibble balance

An instrument, formerly called the watt balance, that weighs a mass against the force on a current-carrying coil and then moves the coil to measure the voltage it generates, so that the mass follows from the Planck constant, the meter and the second (Chapter 20).

Least significant bit (LSB)

A converter's step: its full range divided by its number of codes; one count of the monitor's 12-bit converter is 0.109 mmHg at the cuff (Chapter 8).

Least-squares adjustment

A calculation that finds the one set of values for several constants that best fits all the measurements together, as CODATA's task group did with the data available by 1 July 2017 (Chapter 19).

Legal metrology

In OIML's words, the "practice and process of applying statutory and regulatory structure and enforcement to metrology": the part of measurement a state makes law and checks; its scope differs from country to country (Chapter 30).

Limits of agreement

The bias plus and minus about twice the standard deviation of the differences from the reference: the band that holds about 95 % of single differences when they follow a bell curve (Chapter 24).

Linearity (of a measuring system)

The way a measuring system's bias changes across its range (Chapter 22).

Long-term stability

The drift of a sensor's output over months of use; the 2SMPP-03's data sheet gives none (Chapter 4).

Manometer

A pressure gauge (Chapters 1, 14).

Maximum permissible measurement error

The VIM's term for a limit within which an instrument's error must lie, such as OIML's ±3 mmHg for a monitor's cuff pressure (Chapter 2).

Measurand

The quantity a measurement is meant to find, in the VIM's words the "quantity intended to be measured"; for the monitor's reading, the air pressure in the cuff; for its estimate, the pressure in the artery (Chapter 1).

Measurement

In the VIM, the process of experimentally obtaining quantity values that can reasonably be attributed to a quantity; it implies a comparison (Chapter 1).

Measurement error

A measured value minus a reference value, with a sign; a difference, not a mistake (Chapter 2).

Measurement model

The written relation between a result and everything it depends on: for the monitor's reading, the cuff pressure and the error each stage of the chain can add (Chapter 11).

Measurement result

The value attributed to a measurand with the other relevant information, generally a measured value and its uncertainty; a number, its unit and its uncertainty together (Chapter 1).

Measurement uncertainty

A non-negative parameter, stated with the result, that characterizes the spread of values that can be attributed to the measurand on the information used; the stated doubt (Chapter 2).

Measurement-system analysis (MSA)

The discipline, set out in AIAG's reference manual, of testing a measuring system's bias, linearity, stability, repeatability and reproducibility before trusting its numbers (Chapter 22).

Measuring function

In the MDR, the property of a device that measures; its maker must state the limits of accuracy and express the measurements in legal units (Chapter 31).

MEMS

Microelectromechanical system: a sensor whose moving part and electrical elements are made in the same piece of silicon (Chapter 4).

Metre Convention

The treaty signed in Paris on 20 May 1875 by seventeen states, which created the BIPM and the bodies that decide the units (Chapter 3).

Metrological traceability

The property of a measurement result whereby it can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty (VIM 2.41); a property of a result, not of an instrument or a laboratory (Chapter 15).

Millimeter of mercury (mmHg)

The unit in which medicine states blood pressure, fixed by convention at 133.322 387 415 Pa; not listed in the SI Brochure's version 4.01 (2026) and kept for blood pressure by law (Chapter 3).

Missing code

A converter code that never appears because its step has no width (Chapter 8).

Model approval

India's term for type evaluation: approval of a weight or measure's model that the Legal Metrology Act requires before it is made or imported (Chapter 30).

Moving mode

Also velocity mode: the Kibble balance's measurement in which the coil sweeps through the field at a known speed while the voltage it generates is measured (Chapter 20).

National metrology institute

A country's laboratory for its national standards, which realizes the units and passes their values on; in India, CSIR-NPL in New Delhi (Chapter 3).

National prototype

A platinum-iridium copy of the kilogram held by a country, such as India's No. 57 at CSIR-NPL (Chapters 18, 21).

Noise

Any part of a signal that the measured quantity did not cause (Chapter 5).

Noise density

Noise stated for each square root of a hertz of bandwidth, such as 43 nV per root hertz (Chapter 5).

Noise floor

The level of noise below which no change in a channel can be told apart from it (Chapter 5).

Noise-free resolution

A maker's measure: the full range divided by the peak-to-peak noise, taken as 6.6 times the rms noise, stated in bits; the resolution at which the output code does not flicker (Chapter 8).

Nonlinearity

The departure of a sensor's output from a straight line through its range; up to 1.3 %FS for the 2SMPP-03 (Chapter 4).

Notch

A frequency that a filter blocks almost completely; at 50 readings a second, the filter of Analog Devices' AD7190 places notches at 50 Hz and at every multiple of 50 Hz (Chapter 7).

Notified body

An independent organization designated under EU law to assess a device's conformity; for a class I device with a measuring function, the MDR limits its role to the metrological requirements (Chapter 31).

Number of distinct categories (ndc)

An estimate of how many groups of parts a measuring system can tell apart: the part variation divided by the gauge's R&R, times 1.41, cut down to a whole number; AIAG recommends five or more (Chapter 22).

Nyquist rate

Twice the highest frequency in the signal that reaches the converter, hum included: the lowest sampling rate the sampling theorem allows (Chapter 7).

Official copies

The platinum-iridium copies of the international prototype kept with it at the BIPM: two at first, brought to six by the replacement of one and the addition of four others (Chapter 18).

Offset

A sensor's or amplifier's output with no input applied; typically −2.5 mV for the 2SMPP-03 (Chapter 4); as an error, it shifts every result by the same amount (Chapters 2, 11, 27).

OIML

The intergovernmental body that writes model rules for measuring instruments, its Recommendations, among them R 148 and R 149 (2020) for sphygmomanometers (Chapter 1).

OIML-CS

The OIML Certification System, a system for issuing, registering and using OIML certificates and type evaluation reports for types of measuring instruments; each state decides whether to accept them (Chapter 30).

Oscillometric signal

The cuff pressure together with the small oscillations, from less than 1 mmHg to 3 mmHg, that the pulsing artery adds to it at the pace of the heart; the steady part is the reading, and the oscillations carry what the firmware turns into the estimate (Chapter 4).

Out-of-tolerance impact assessment

The judgment, for each result a faulty reference supported, of whether the reference's error could have made it wrong by enough to matter, and what to do about the products involved (Chapter 26).

Oversampling

Reading far faster than the signal needs and averaging the readings down; four times the readings buy one more bit (Chapter 8).

Part per billion

One part in a billion; on a kilogram, one microgram (Chapter 18).

Part variation (PV)

In a gauge study, the spread of the parts' true values as a standard deviation, which the measuring system exists to see (Chapter 22).

Part VII-A

The Part of the Eighth Schedule for non-invasive non-automated sphygmomanometers, replaced on 7 January 2026 (Chapter 30).

Part VII-B

The Part of the Eighth Schedule to India's Legal Metrology (General) Rules, 2011, for non-invasive automated sphygmomanometers, substituted on 28 July 2025; it sets the cuff pressure's limit at ±0.4 kPa (±3 mmHg) or ±2 % of the reading, whichever is greater (Chapter 30).

Part-to-part variation

The real differences between the parts or monitors in a study, as distinct from the scatter that the measuring system adds (Chapter 22).

Pascal

The SI unit of pressure, one newton of force on one square meter, in base units a kilogram per meter per second squared; a kilopascal is 1,000 pascals (Chapter 3).

Peak to peak

The distance between the highest and lowest values of a signal over a stated time; for random noise, taken as 6.6 times the rms value (Chapter 5).

Percent contribution

A component of a gauge study as a share of the total variance rather than of the total standard deviation; 10 % and 30 % of the standard deviation are 1 % and 9 % of the variance (Chapter 22).

Percent of full scale (%FS)

A sensor's error stated as a share of its whole range rather than of the reading; 1 %FS of a 50 kPa sensor is about 3.75 mmHg (Chapter 4).

Percent within

The share of a device's results that fall inside a fixed band around the reference, such as 95 % of a glucose meter's results within ±15 % (Chapter 24).

Periodic verification

One of the three campaigns, which Schwitz and colleagues date 1899 to 1911, 1947 to 1954 and 1988 to 1992, in which the BIPM compared the national prototypes with the international prototype (Chapter 18).

Piezoresistance

The change in a material's electrical resistance when the material is strained (Chapter 4).

Piezoresistor

A resistor formed in silicon whose value changes when the silicon flexes; the monitor's sensor is a bridge of them (Chapters 1, 4).

Pilot laboratory

The laboratory that organizes a comparison and analyzes its results; CSIR-NPL for APMP.M.P-K6 (Chapter 21).

Planck constant

The constant h of quantum physics, which links the energy carried by light to its frequency; since 20 May 2019 exactly 6.626 070 15 ÷ 10³⁴ joule seconds, a value that defines the kilogram (Chapter 19).

Pounds per square inch (psi)

A unit of pressure used on some certificates, such as Mensor's for a barometric reference from 8 to 17 psi, about 55 to 117 kPa (Chapter 12).

Precision

The closeness of repeated readings to one another under stated conditions, usually given as a standard deviation; not accuracy (Chapter 2).

Predicate device

The legally marketed device to which a 510(k) claims substantial equivalence (Chapters 24, 31).

Pressure balance

Also piston gauge: a piston loaded with masses in a close-fitting cylinder, which makes a known pressure as the weight of piston and masses divided by the piston's effective area; a balance because the pressure balances a weight (Chapter 15).

Product code

FDA's three-letter label for a type of device, which ties it to a regulation and a class; the automated monitor's is DXN (Chapter 31).

Proficiency testing

A check of laboratories' results against each other: a provider sends the same item, or items of known value, to several laboratories and compares what each reports (Chapter 16).

Quantization error

The error of up to half a step either way that every converted reading carries; modeled as a sawtooth, a flat distribution with an rms value of the step divided by the square root of 12 (Chapter 8).

Quantum Hall effect

The effect by which a conducting layer in a strong magnetic field at low temperature shows a resistance set by the von Klitzing constant, h divided by the square of the elementary charge; used to realize the ohm (Chapter 20).

Random error

The part of an error that varies unpredictably from one repeated measurement to the next, such as amplifier noise; averaging reduces its effect (Chapter 2).

Ratiometric measurement

A measurement in which the converter's reference is derived from the sensor's own excitation, so that a change in the excitation cancels; TI's monitor design is not ratiometric (Chapter 6).

Re-verification after a repair

A check of a repaired instrument against the same limits as when new, before it goes back into use, because the repair may have changed the instrument its last calibration described (Chapter 27).

Reading

In this guide, the monitor's displayed cuff pressure in mmHg, which a chain of calibrations ties to the SI; kept apart from the estimate (Chapter 1).

Realize

To make a unit in practice in a laboratory, from its definition; national laboratories compare their realizations (Chapters 3, 21).

Recognized consensus standard

A standard on FDA's list, to which a maker may declare conformity in support of a premarket submission; FDA may recognize it only in part (Chapter 31).

Rectangular distribution

Also flat distribution: a band in which every value between two limits is equally likely; its standard deviation is the half-width divided by the square root of 3 (Chapter 11).

Reference

Whatever a measurement is compared with, from the marks on a ruler to a reference manometer or a national standard (Chapters 1, 24).

Reference manometer

The pressure gauge whose reading serves as the reference value when a monitor or gauge is calibrated; OIML and India's rules for automated sphygmomanometers allow it a maximum permissible error of ±0.8 mmHg (Chapter 14).

Reference method

An independent way of finding a quantity in the same subjects, trusted because a protocol fixes how it is done, such as two observers measuring blood pressure at the same time; distinct from a reference standard, which carries a traceable value (Chapter 24).

Relative standard uncertainty

A standard uncertainty expressed as a fraction of the value, such as 10 parts per billion (Chapter 19).

Repeatability (of a measuring system)

The spread between results when one operator measures the same part several times with the same system, under repeatability conditions; a gauge study states it as the equipment variation (Chapters 2 and 22).

Repeatability conditions

Repeated measurements with the same procedure, operators, measuring system, conditions and location over a short period (Chapter 2).

Reproducibility (of a measuring system)

The spread between results when different operators measure the same part with the same system (Chapters 2 and 22).

Reproducibility conditions

Repeated measurements in which the locations, operators and measuring systems differ (Chapter 2).

Resolution

The smallest change in a measured quantity that perceptibly changes the indication; for a display, the smallest step it can show, such as 1 mmHg. It is not a limit on error (Chapters 2, 8).

Reverse traceability

The search backward from a reference found wrong to every result and every product that rested on it since its last good calibration (Chapter 26).

Rms

Root mean square: the square root of the average of a signal's squared values; for noise, its standard deviation (Chapter 5).

Robustness (of a test method)

In ICH's list of validation characteristics, a method's capacity to keep meeting its criteria despite the small changes that daily use brings, such as a slightly different vessel, a longer wait or a warmer room (Chapter 23).

Root-difference-square guard band

An acceptance limit set at the square root of the specification squared minus the expanded uncertainty squared, one of the four methods that Fluke's policy names; 2.65 mmHg for the monitor at 150 mmHg (Chapter 13).

Root-sum-of-squares

The rule for adding independent uncertainties: square each contribution, add the squares and take the square root of the total (Chapter 11).

Same-arm sequential method

In a blood-pressure validation, taking the observers' readings and the monitor's one after another on the same arm, the method the AAMI/ESH/ISO collaboration prefers (Chapter 24).

Sample-and-hold

A circuit that follows the input, then disconnects a small capacitor from it and holds that voltage while the converter works, so that each reading records one instant (Chapter 7).

Sampling rate

The number of readings a converter takes each second (Chapter 7).

Scope of accreditation

The list of calibrations an accreditation covers, each with its quantity, range, method and CMC; a certificate outside it does not carry the accreditation's weight (Chapter 16).

Self-heating

The warming of a sensor by the excitation that measures it, an error the sensor makes by being measured (Chapter 6).

Sensitivity (of an instrument)

The change in an instrument's output for a given change in the quantity it measures; 112 µV for each mmHg for the 2SMPP-03 (Chapter 4). Distinct from a diagnostic test's sensitivity (Chapter 24).

Sensitivity coefficient

In an uncertainty budget, the rate at which the result changes when one input changes, which converts each standard uncertainty into the unit of the result; distinct from an instrument's sensitivity (Chapter 11).

Service mode

A monitor's test mode, reserved for service personnel, in which the vent valve stays closed so that an outside pump sets the pressure and the display shows what the sensor reads (Chapter 14).

Shot noise

Noise from the separate, randomly arriving charges that make up a current (Chapter 5).

SI

The International System of Units: seven base units, the units derived from them and 24 prefixes, resting since 20 May 2019 on seven defining constants (Chapter 3).

Sigma-delta converter

A converter that compares its input with a 1-bit feedback loop running far faster than the signal, shapes its quantization noise out of the band of interest and filters the bit stream into slower readings of many bits; it averages over each conversion rather than sampling an instant (Chapters 7, 8).

Signal chain

The six stages between a physical quantity and a reported number, named by what each does: sense, condition, digitize, compute, connect, decide (Chapter 1; Part II).

Signal-to-noise ratio (SNR)

The size of a signal against the size of the noise that accompanies it, usually stated in decibels (Chapter 5).

Significant fault

In OIML's weighing recommendation, a fault greater than one verification scale interval, e; in the recommendation's 1992 edition, since superseded, OIML required the instrument to stop automatically or warn on one (Chapter 26).

Simple acceptance

A decision rule that accepts an item whose measured value does not exceed the tolerance limit, without allowing for uncertainty; the JCGM notes that it is also known as shared risk (Chapter 13).

SINAD

The ratio of a converter's rms signal to the root-sum-of-squares of everything else in its output, noise and distortion together, as Analog Devices defines it (Chapter 8).

Span (of a sensor)

The sensor's output at full scale minus its output at zero; typically 42.0 mV over 50 kPa for the Omron 2SMPP-03 (Chapters 4, 11).

Specific risk

The probability that one particular accepted item does not conform, or that one particular rejected item does, given its measured value (Chapter 13).

Specificity (of a test method)

In ICH's list of validation characteristics, a method's response to the property it tests and to nothing else; for the pressure test, to the monitor's error and not to a leak, a moving pressure or a change of temperature (Chapter 23).

Stability (of a measuring system)

The way a measuring system's bias changes over time (Chapter 22).

Standard deviation

The measure of how widely single readings scatter around their mean: square each reading's deviation from the mean, add the squares, divide by one less than the number of readings and take the square root; 0.44 mmHg for the ten generated readings of Chapter 10's example (Chapter 10).

Standard deviation of the mean

The standard deviation of single readings divided by the square root of their number; it describes how well a mean locates the quantity, not how one reading scatters (Chapter 10).

Standard uncertainty

An uncertainty expressed as a standard deviation, in the GUM's definition (Chapters 2, 11).

Systematic error

The part of an error that stays constant or varies predictably when a measurement is repeated, such as a sensor's offset; a known one can be corrected (Chapter 2).

Systolic pressure

The highest pressure in the artery during a heartbeat; in an oscillometric monitor, an estimate derived by the algorithm from the envelope (Chapters 1, 9).

Temperature coefficient

The change of a figure, such as an offset or a reference voltage, for each degree of temperature (Chapter 6).

Test method

The complete procedure by which a maker decides whether a product meets a requirement: equipment, settings, steps, conditions, sample size, calculation and acceptance criteria (Chapter 23).

Test uncertainty ratio

The tolerance of a quantity divided by the 95 % expanded uncertainty of the measurement that tests it; the four-to-one rule dates from MIL-STD-45662A (1988) (Chapter 12).

Test-method validation

Evidence, fixed in advance, that a test method run as written gives results that are right and that repeat (Chapter 23).

Thermal noise

Also Johnson noise: the random voltage that the thermal motion of charges produces in every conductor, growing with resistance, absolute temperature and bandwidth (Chapter 5).

Tolerance limit

The upper or lower bound of the values that a property itself may take, such as the monitor's ±3 mmHg at 150 mmHg (Chapters 12 and 13).

Tone

A signal at a single frequency (Chapter 7).

Total variation (TV)

In a gauge study, the root-sum-of-squares of the gauge's R&R and the part variation (Chapter 22).

Transducer

A device that turns one physical quantity into another, such as a pressure into a voltage (Chapter 4).

Transfer standard

The artifact that travels between the laboratories of a comparison, such as the piston and cylinder of APMP.M.P-K6 (Chapter 21).

True quantity value

A value consistent with the definition of a quantity; in the VIM's traditional approach unique and, in practice, unknowable (Chapter 2).

Trueness

The closeness of the average of many repeated readings to a reference value; it reflects systematic error, not random error (Chapter 2).

Type A evaluation

Evaluation of a standard uncertainty by statistical analysis of a series of observations (Chapters 2, 10).

Type B evaluation

Evaluation of a standard uncertainty by any other means: a data sheet, a certificate, a standard's limit or the step of a display (Chapters 2, 11).

Type evaluation

An authority's tests on samples of a new design of measuring instrument before it is sold; India's law calls the step approval of the model (Chapter 30).

Uncertainty budget

The table of every input to a measurement with its standard uncertainty, distribution, divisor and sensitivity coefficient, from which the combined standard uncertainty is computed (Chapter 11).

Variance

The square of a standard deviation (Chapter 22).

Verification (legal metrology)

In OIML's vocabulary, a conformity assessment procedure, other than type evaluation, that ends in a verification mark or certificate on an instrument; a third sense of the word, apart from the VIM's verification and design verification (Chapter 30).

Verification (metrological)

Objective evidence that an item meets specified requirements, such as a maker's limit (VIM 2.44); distinct from calibration, and from design verification (Chapter 14).

VIM

The International Vocabulary of Metrology, the shared dictionary of measurement terms; its third edition, JCGM 200:2012, is still in force as of November 2026, and a draft of the fourth went to a vote in January 2026 (Chapter 1).

Voltage reference

The part that holds the voltage against which a converter counts, and so acts as the instrument's internal standard (Chapter 6).

Weighing mode

Also force mode: the Kibble balance's measurement in which a current through the coil balances the weight of a mass (Chapter 20).

Working standard

A reference used routinely to calibrate other standards; the BIPM's 1 kg working standards lost 18 to 88 µg through use between 1992 and 2014 (Chapter 18).

Worst case

A way of combining an error budget that adds every share at its limit, as if every error sat at its edge in the same direction at once (Chapter 25).

XRCD (X-ray crystal density)

The method that realizes the kilogram by counting the atoms in a silicon-28 sphere from the sphere's volume and the size of one crystal cell (Chapter 20).

Sources are listed by the chapter in which they are first used. Status and prices are as of the month the guide is current to.

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19. Ch. 1 — OIML. Non-invasive automated sphygmomanometers. Part 2: Test procedures. OIML R 149-2, Edition 2020. https://www.oiml.org/en/files/pdf_r/r149-2-e20.pdf
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34. Ch. 3 — CGPM. Resolution 3 of the 27th CGPM (2022). On the extension of the range of SI prefixes. https://www.bipm.org/en/-/resolution-cgpm-27-3
35. Ch. 3 — CGPM. Declaration of the 1st CGPM (1889). Sanction of the international prototypes of the metre and the kilogram. https://doi.org/10.59161/CGPM1889DECLE (the first CGPM met in Paris from 24 to 28 September 1889)
36. Ch. 3 — CSIR-National Physical Laboratory. Mass Metrology Section. Accessed 31 Oct 2026. https://www.nplindia.in/index.php/science-technology/physico-mechanical-metrology/mass-metrology-section/
37. Ch. 3 — Pražák D., Sedlák V., Sınır E., et al. Changing the status of mmHg. Accreditation and Quality Assurance 25, 81–82 (2020). doi:10.1007/s00769-019-01414-7 (letter; EMPIR project 16RPT03, co-funded by the EU; the letter records that the SI Brochure's 8th edition listed the millimeter of mercury among other non-SI units, and that the 9th edition of 2019 dropped it; it also records that ISO 80000-4 listed the unit as not recommended in 2013, before dropping it in 2019)
38. Ch. 3 — BIPM. Updated SI Brochure clarifies the status of non-SI units (news). 4 Jun 2026. https://www.bipm.org/en/-/2026-06-04-updated-si-brochure-clarifies-the-status-of-non-si-units
39. Ch. 3 — Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to units of measurement, as amended by Council Directive 85/1/EEC of 18 December 1984. OJ of 15 Feb 1980. https://eur-lex.europa.eu/eli/dir/1980/181/oj/eng (Annex, Chapter I, section 4, read in the version of 13 Jun 2020 as reproduced on legislation.gov.uk: https://legislation.gov.uk/eudr/1980/181/annex/2020-06-13)
40. Ch. 3 — Ireland. European Communities (Units of Measurement) (Amendment) Regulations, 1985. S.I. No. 228/1985. Irish Statute Book. https://www.irishstatutebook.ie/1985/en/si/0228.html (explanatory note read; revoked by S.I. No. 255/1992; Ireland's 1985 amendment kept the millimeter of mercury as the unit for blood pressure and other body fluids, as its explanatory note states; the 1992 Regulations revoked and replaced it)
41. Ch. 3 — Ireland. European Communities (Units of Measurement) Regulations, 1992. S.I. No. 255/1992. 9 Sep 1992 (in force as amended). Irish Statute Book. https://www.irishstatutebook.ie/1992/en/si/0255.html
42. Ch. 4 — OIML. Metrological regulation for load cells. Part 1: Metrological and technical requirements. OIML R 60-1:2021 (E). 2021. https://www.oiml.org/en/files/pdf_r/r060-1-e21.pdf
43. Ch. 4 — TDK Electronics. Pressure sensors C32 series: Gauge low pressure sensor die C32/2, data sheet Version 7. 18 December 2024. https://www.tdk-electronics.tdk.com/inf/57/ds/c32_2_gauge_lp.pdf (manufacturer)
44. Ch. 4 — Hottinger Brüel & Kjaer GmbH. PW6D single point load cell, data sheet B01996 04 E00. 3 September 2024. https://www.Hbm.com/fileadmin/mediapool/hbmdoc/technical/B01996.pdf (manufacturer)
45. Ch. 4 — Wu J. (Texas Instruments). A Basic Guide to RTD Measurements. Application note SBAA275A, June 2018, revised March 2023. https://ti.com/lit/SBAA275 (manufacturer; reports the IEC 60751 coefficients)
46. Ch. 4 — Moghimi R. (Analog Devices). Seven Steps To Successful Ultralow Light Signal Conversion. Technical article MS-2394. 2013. https://wcm-cce.cldnet.analog.com/media/en/technical-documentation/tech-articles/seven-steps-to-successful-ultra-low-light-signal-conversion-ms-2394.pdf (manufacturer)
47. Ch. 4 — Kitamura M., et al. Sphygmomanometer. Patent JP5141650B2 (application JP2011030748A). Omron Healthcare Co., Ltd. Filed 31 July 2009; granted 13 February 2013. https://patents.google.com/patent/JP5141650B2/en (patent; Omron Healthcare staff)
48. Ch. 5 — Johnson J.B. Thermal Agitation of Electricity in Conductors. Physical Review 32(1):97–109. July 1928. https://doi.org/10.1103/PhysRev.32.97 (abstract read; author at Bell Telephone Laboratories)
49. Ch. 5 — Nyquist H. Thermal Agitation of Electric Charge in Conductors. Physical Review 32(1):110–113. July 1928. https://doi.org/10.1103/PhysRev.32.110 (abstract read; author at AT&T)
50. Ch. 5 — Analog Devices. Op Amp Noise. Tutorial MT-047, Rev. 0. October 2008. https://www-cce.cldnet.analog.com/media/en/training-seminars/tutorials/MT-047.pdf (manufacturer)
51. Ch. 5 — National Institute of Standards and Technology. CODATA Recommended Values of the Fundamental Physical Constants: 2022. NIST SP 961. May 2024. https://www.physics.nist.gov/cuu/pdf/wall_2022.pdf
52. Ch. 5 — Analog Devices. Op Amp Noise Relationships: 1/f Noise, RMS Noise, and Equivalent Noise Bandwidth. Tutorial MT-048, Rev. 0, October 2008. https://wcm-cce.cldnet.analog.com/media/en/training-seminars/tutorials/MT-048.pdf (manufacturer)
53. Ch. 5 — Benz S.P., Pollarolo A., Qu J., Rogalla H., Urano C., Tew W.L., Dresselhaus P.D., White D.R. An electronic measurement of the Boltzmann constant. Metrologia 48(3):142–153, published 30 March 2011. doi:10.1088/0026-1394/48/3/008 (NIST-supported; authors' preprint arXiv:1101.0312)
54. Ch. 5 — Johnson J.B. The Schottky Effect in Low Frequency Circuits. Physical Review 26(1):71–85. July 1925. https://doi.org/10.1103/PhysRev.26.71 (abstract read; author at Bell Telephone Laboratories; in this paper Johnson measured the noise of vacuum-tube filaments and found it much larger at low frequencies than the theory of the day predicted; Johnson's 1925 paper credits Schottky with the discovery of shot noise; for a tungsten filament the measured noise was about 0.7 times the theoretical value above 200 Hz and rose to about 50 times it at 10 Hz)
55. Ch. 5 — Kiely R. (Analog Devices). Understanding and Eliminating 1/f Noise. Analog Dialogue 51(2). May 2017. https://www.analog.com/en/resources/analog-dialogue/articles/understanding-and-eliminating-1-f-noise.html (manufacturer; author is company staff)
56. Ch. 5 — Analog Devices. Instrumentation Amplifier (In-Amp) Basics. Tutorial MT-061, Rev. 0. October 2008. https://www.analog.com/MT-061 (manufacturer)
57. Ch. 5 — Sanchez G. Blood Pressure Monitor Using Flexis QE128. Freescale Semiconductor application note AN3500, Rev. 0. August 2007. https://NXP.com/docs/en/application-note/AN3500.pdf (manufacturer; author is Freescale staff)
58. Ch. 5 — National Institute of Standards and Technology. Guide for the Use of the International System of Units (SI). NIST SP 811, Chapter 8, section 8.7. Web page updated 18 August 2025. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8
59. Ch. 5 — Texas Instruments. ADS123x 2- and 4-Channel, 24-Bit, Delta-Sigma ADCs for Bridge Sensors. Data sheet SBAS350H, June 2005, revised June 2025. https://www.ti.com/product/ADS1232 (manufacturer; design-example passage)
60. Ch. 5 — Kester W. (Analog Devices). The Good, the Bad, and the Ugly Aspects of ADC Input Noise: Is No Noise Good Noise? Tutorial MT-004, Rev. A. October 2008. https://www.analog.com/MT-004 (manufacturer)
61. Ch. 6 — Analog Devices. Precision Weigh Scale Design Using the AD7190 24-Bit Sigma-Delta ADC with Internal PGA. Circuit Note CN-0102, Rev. A. December 2012. https://wcm-cce.cldnet.analog.com/media/en/reference-design-documentation/reference-designs/CN0102.pdf (manufacturer)
62. Ch. 6 — Analog Devices. ADR4520/ADR4525/ADR4530/ADR4533/ADR4540/ADR4550 Ultralow Noise, High Accuracy Voltage References, data sheet Rev. G. https://www.analog.com/media/en/technical-documentation/data-sheets/adr4520_4525_4530_4533_4540_4550.pdf (manufacturer)
63. Ch. 6 — NXP Semiconductors. MPXx2050 product page ("temperature compensated over 0 to +85 °C"; output "Ratiometric to supply voltage"; accessed 31 Oct 2026). https://nxp.com/products/MPXx2050 (manufacturer)
64. Ch. 7 — Goto M., Nishibayashi H., Narimatsu K., Yokozeki A. Blood pressure monitor. US patent application US 2001/0037068 A1, Colin Corp. Published 1 Nov 2001. https://patents.google.com/patent/US20010037068 (manufacturer's patent; read to 100,000 of 120,186 characters)
65. Ch. 7 — Unser M. Sampling—50 Years After Shannon. Proceedings of the IEEE 88(4):569–587 (2000). https://doi.org/10.1109/5.843002 (secondary: review; read at the author's group page, EPFL; Unser records that Shannon coined the term "Nyquist frequency" in recognition of Nyquist's contributions to communication theory; Nyquist's own 1928 paper concerned telegraph transmission, and Unser does not credit him with the sampling theorem)
66. Ch. 7 — Analog Devices. Aperture Time, Aperture Jitter, Aperture Delay Time: Removing the Confusion. Tutorial MT-007, Rev. A. October 2008. https://www.analog.com/MT-007 (manufacturer)
67. Ch. 7 — Shannon C.E. Communication in the Presence of Noise. Proceedings of the IRE 37(1):10–21 (1949). https://doi.org/10.1109/JRPROC.1949.232969 (reprinted Proceedings of the IEEE 86(2):447–457, 1998; the theorem's wording read through Unser 2000)
68. Ch. 7 — Kester W. What the Nyquist Criterion Means to Your Sampled Data System Design. Analog Devices Tutorial MT-002, Rev. A. October 2008. https://www.analog.com/MT-002 (manufacturer)
69. Ch. 7 — Nyquist H. Certain Topics in Telegraph Transmission Theory. Transactions of the AIEE 47(2):617–644 (1928). https://doi.org/10.1109/T-AIEE.1928.5055024 (metadata only)
70. Ch. 7 — Lopez S. Blood Pressure Monitor Fundamentals and Design. Freescale Semiconductor application note AN4328, Rev. 2. December 2012. https://NXP.com/docs/en/application-note/AN4328.pdf (manufacturer; Freescale staff)
71. Ch. 7 — Oh H.S., Chee Y.J., Lee J.S., Kim I.Y., Kim S.I., Kim Y.S. The Modified Step-Wise Deflation Method in Blood Pressure Measurement. Computers in Cardiology 35:169–172 (2008). https://www.cinc.org/old/Proceedings/2008/pdf/0169.pdf (Hanyang University; funded by the Korean Science and Engineering Foundation)
72. Ch. 7 — Analog Devices. AD7190 4.8 kHz, Ultralow Noise, 24-Bit Sigma-Delta ADC with PGA, data sheet Rev. C. February 2013. https://www-cce.cldnet.analog.com/media/en/technical-documentation/data-sheets/AD7190.pdf (manufacturer)
73. Ch. 7 — Analog Devices. Tutorial on Technical and Performance Benefits of AD719x Family (slide set, undated). https://www-cce.cldnet.analog.com/media/en/training-seminars/tutorials/ad719x_tutorial.pdf (manufacturer; includes the maker's worked weigh-scale example)
74. Ch. 7 — Kester W. ADC Architectures III: Sigma-Delta ADC Basics. Analog Devices Tutorial MT-022, Rev. A. October 2008. https://www.analog.com/MT-022 (manufacturer)
75. Ch. 7 — Microlife AG. Instruction manual, WatchBP Office (BP3SK1-3B), IB WatchBP Office EN 0226. https://www.microlife.com/media/3442/download/IB%20WatchBP%20Office%202G_EN_0226.pdf?v=7 (manufacturer)
76. Ch. 7 — Celler B.G., Argha A., Le P.N., Ambikairajah E. Novel methods of testing and calibration of oscillometric blood pressure monitors. PLoS One 13(8):e0201123 (2018). https://doi.org/10.1371/journal.pone.0201123 (UNSW Sydney; funded by the Australian Research Council, LP160101202; no competing interests declared)
77. Ch. 7 — Ministry of Consumer Affairs, Food and Public Distribution (Department of Consumer Affairs), India. Legal Metrology (General) Third Amendment Rules, 2025, G.S.R. 498(E), substituting Part VII-B of the Eighth Schedule (non-invasive automated sphygmomanometers; clause 5(1), the maximum permissible error of the cuff pressure; clause 5(2), the limits for the clinical investigation). 28 Jul 2025. https://consumeraffairs.gov.in/public/upload/files/Sphygmomanomneters%20General%20Rules_1754973919.pdf (issuer's publication of the gazette notification)
78. Ch. 7 — Gui Y., Chen F., Murray A., Zheng D. Pulse Interval Modulation-based Method to Extract the Respiratory Rate from Oscillometric Cuff Pressure Waveform During Blood Pressure Measurement. Computing in Cardiology 44 (2017). https://pprd.cinc.org/archives/2017/pdf/326-252.pdf (SUSTech; funded by NSFC and EPSRC)
79. Ch. 8 — Renesas Electronics. RL78/H1D microcontrollers, product page; Specifications of the blood pressure monitoring evaluation kit (RTK0EH0003S02001BR). Accessed 31 Oct 2026. https://renesas.com/en/document/pre/specifications-blood-pressure-monitoring-evaluation-kit (manufacturer)
80. Ch. 8 — Kester W. The Importance of Data Converter Static Specifications: Don't Lose Sight of the Basics! Analog Devices Tutorial MT-010, Rev. A. October 2008. https://www.analog.com/MT-010 (manufacturer)
81. Ch. 8 — Kester W. Taking the Mystery out of the Infamous Formula, "SNR = 6.02N + 1.76dB," and Why You Should Care. Analog Devices Tutorial MT-001, Rev. A. October 2008. https://www.analog.com/MT-001 (manufacturer)
82. Ch. 8 — Kester W. Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor. Analog Devices Tutorial MT-003, Rev. A. October 2008. https://www.analog.com/MT-003 (manufacturer)
83. Ch. 8 — IEEE. IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters. IEEE 1241-2023. 6 Oct 2023. https://standards.ieee.org/ieee/1241/6797 (catalogue page; the standard's text not read)
84. Ch. 9 — U.S. Food and Drug Administration. Medical Device Recalls database: Class 1 Device Recall FreeStyle InsuLinx Blood Glucose Monitoring System, recall Z-1245-2013. Posted 9 May 2013; terminated 3 Aug 2015. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfRES/res.cfm?id=117228
85. Ch. 9 — Parmar A. FDA Designates Abbott's Recall of FreeStyle InsuLinx Glucose Meter As Class I. MD+DI, 20 May 2013. https://www.mddionline.com/regulatory-quality/fda-designates-abbott-s-recall-of-freestyle-insulinx-glucose-meter-as-class-i (secondary: reproduces the recall notice; MD+DI reproduced the recall notice on 20 May 2013, the day it reported FDA's announcement of the Class I designation)
86. Ch. 9 — McCaffrey K. Class 1 Recall: Abbott Diabetes Care, FreeStyle InsuLinx Blood Glucose Meters. MedWrench, dated 15 Apr 2013 on the page. https://www.medwrench.com/article/35883/class-1-recall-abbott-diabetes-care-freestyle-insulinx-blood-glucose-meters (secondary)
87. Ch. 9 — Shenzhen CHK Technology Co Ltd. Electronic sphygmomanometer and its calibrating method. WO 2010/130189 A1. Published 18 Nov 2010. https://patents.google.com/patent/WO2010130189A1/en (manufacturer's patent application; machine translation; status "Ceased" on Google Patents)
88. Ch. 9 — Sawanoi Y., Tokko Y. Electronic sphygmomanometer. US 2011/0301476 A1, granted as US 9,149,194 B2 (6 Oct 2015). Omron Healthcare Co., Ltd. https://patents.google.com/patent/US20110301476 (manufacturer's patent; read to 100,000 of 125,784 characters; Omron Healthcare first filed the application in 2009; it was granted in the US in 2015)
89. Ch. 9 — Welch Allyn. Ambulo 2400 Ambulatory Blood Pressure Monitor Service Manual, 9516-182-50-ENG Rev F. October 2019. https://www.hillrom.com/content/dam/hillrom-aem/us/en/sap-documents/LIT/9516-/9516-182-50-ENGLITPDF.pdf (manufacturer)
90. Ch. 9 — Grotov Y. Blood Pressure Monitor Calibration. US 2016/0095557 A1, granted as US 10,194,872 B2 (5 Feb 2019). https://patents.google.com/patent/US20160095557A1/en (an individual inventor's patent)
91. Ch. 9 — Agarwal N. Low-Power BP Meter Reference Design. Electronics For You, 15 Oct 2024 (modified 20 May 2025). https://www.electronicsforu.com/electronics-projects/low-power-bp-meter-reference-design (secondary: reports Microchip's reference design)
92. Ch. 9 — Chandrasekhar A., Yavarimanesh M., Hahn J.-O., Sung S.-H., Chen C.-H., Cheng H.-M., Mukkamala R. Formulas to Explain Popular Oscillometric Blood Pressure Estimation Algorithms. Frontiers in Physiology 10:1415 (2019). https://doi.org/10.3389/fphys.2019.01415 (Michigan State University; funded by the US National Institutes of Health; no conflicts declared)
93. Ch. 9 — Welch Allyn. CSB – Clearing CVSM/CIWS NIBP EEPROM Error. DIR 20012832 Rev A. 19 Jan 2012. https://www.hillrom.com/content/dam/hillrom-aem/us/en/sap-documents/LIT/20012/20012832LITPDF.pdf (manufacturer's customer service bulletin)
94. Ch. 9 — IEC. IEC 62304:2006 Medical device software – Software life cycle processes; Amendment 1:2015; consolidated version IEC 62304:2006+AMD1:2015. IEC webstore, checked 31 Oct 2026. https://webstore.iec.ch/en/publication/6792
95. Ch. 9 — Johner Institute. IEC 62304 2nd edition: all areas of application and changes. 8 Jul 2026. https://blog.johner-institute.com/iec-62304-medical-software/iec-62304-2nd-edition-all-areas-of-application-and-changes/ (secondary: consultancy; on the draft second edition)
96. Ch. 9 — Critical Software. IEC 62304 Edition 2 changes (August 2026). Undated news page, accessed 31 Oct 2026. https://asd.criticalsoftware.com/en/newsroom/iec-62304-edition-2-changes-august-2026 (secondary: consultancy; on the draft second edition)
97. Ch. 10 — LRM – Laboratório de Referência Metrológica (São Paulo). Certificado de calibração L 3687/20, Rigel Uni-SiM patient simulator, non-invasive pressure. 2 Mar 2020. Posted by the Government of Rondônia (Brazil) in "7 parte 3", 2020. https://rondonia.ro.gov.br/wp-content/uploads/2020/10/7-parte-3.pdf (text extract only; column headings and error sign not verified on the page image; the government of the Brazilian state of Rondônia later posted this certificate publicly)
98. Ch. 10 — European co-operation for Accreditation. Evaluation of the Uncertainty of Measurement in Calibration. EA-4/02 M:2022. 4 Apr 2022. https://european-accreditation.org/wp-content/uploads/2018/10/EA-4-02.pdf
99. Ch. 10 — Louvel D. USP General Chapter <41> (slides). Mettler-Toledo pharma event, Cairo, 18 Nov 2015. https://www.mt.com/dam/SIPharmaEvent/How%20to%20Comply%20with%20the%20new%20USP41%20Standard.pdf (manufacturer; secondary description of USP <41>)
100. Ch. 10 — Troemner LLC. USP 41 Weighing Requirements for Balances (undated web page). https://www.troemner.com/reference-center/weights-reference-center/USP-41-Weighing-Requirements-for-Balances (manufacturer; secondary description of USP <41>)
101. Ch. 10 — UKAS. The expression of uncertainty and confidence in measurement. M3003, Edition 6. March 2024. https://www.ukas.com/wp-content/uploads/2023/05/M3003-The-expression-of-uncertainty-and-confidence-in-measurement.pdf
102. Ch. 11 — NIST Physical Measurement Laboratory. International and US perspectives on measurement uncertainty. The NIST Reference on Constants, Units, and Uncertainty (undated page; accessed 31 Oct 2026). https://pml.nist.gov/cuu/Uncertainty/international2.html (secondary: NIST's account of the GUM's history)
103. Ch. 11 — JCGM. Guide to the expression of uncertainty in measurement — Part 5: Examples. JCGM GUM-5:2026. 2026. https://www.bipm.org/en/doi/10.59161/JCGMGUM-5-2026
104. Ch. 11 — JCGM. Amendment 1 to the GUM: Nonlinearity in measurement models. JCGM 100:2008/Amd.1:2026 (Evaluation of measurement data — Guide to the expression of uncertainty in measurement). 2026. https://www.bipm.org/en/doi/10.59161/JCGM100-Amd-2026
105. Ch. 11 — JCGM. Evaluation of measurement data — Supplement 1 to the GUM — Propagation of distributions using a Monte Carlo method. JCGM 101:2008. 2008. https://doi.org/10.59161/JCGM101-2008 (text read to clause 6.4.8)
106. Ch. 11 — BIPM. JCGM publications: Guides in metrology (catalogue page). Accessed 31 Oct 2026. https://www.bipm.org/en/web/guest/publications/guides
107. Ch. 12 — Mensor. Calibration certificate, CPG2400 s/n 410004SU, Cal Cert ID 241514 (accredited by A2LA). 9 Feb 2024. Published by Washington State Patrol, 2025. https://wsp.wa.gov/wp-content/uploads/2025/06/2024-02-09.pdf (manufacturer: the maker's own laboratory; uncertainty column heading not legible in the copy read, units taken as psi; the Washington State Patrol, the customer, later published this certificate among the records of its breath-test program)
108. Ch. 12 — NIST Office of Weights and Measures. SOP 1, Appendix A – Example Certificate. In: NISTIR 6969, Selected Laboratory and Measurement Practices and Procedures. 2019. https://doi.org/10.6028/NIST.IR.6969-2019 (template; illustrative values)
109. Ch. 12 — Rigel Medical (Seaward Group). Uni-SiM User Manual, Rev 2, section 14, Technical Specifications. 2021. https://www.seaward.com/us/support/medical/uni-sim/manual/uni-sim-manual (manufacturer)
110. Ch. 12 — Japan Meteorological Agency, Meteorological Instrument Center. Calibration certificate (barometer), SAMPLE (accredited by IAJapan). Undated. https://www.jma.go.jp/jma/jma-eng/jma-center/ric/ISOIEC%2017025/Certificate/Certificate-barometer.pdf (values masked)
111. Ch. 12 — Central Electronics Centre, IIT Madras. Scope of accreditation, certificate CC-2918 (MEDICAL scope), valid 17 Nov 2024 to 16 Nov 2028, amended 16 Feb 2025. https://cec.iitm.ac.in/wp-content/uploads/2025/04/MEDICAL-scope.pdf (accreditation body not named in the extract read)
112. Ch. 12 — ILAC. Guidelines on Decision Rules and Statements of Conformity. ILAC G8:09/2019. September 2019. https://ilac.org/?ddownload=122722
113. Ch. 12 — Department of Defense. Calibration Systems Requirements. MIL-STD-45662A. August 1988. https://apps.dtic.mil/sti/tr/pdf/ADA286358.pdf (cancelled; status: ANSI Webstore, MIL-STD-45662A Notice 2, https://webstore.ansi.org/standards/dod/milstd45662anot)
114. Ch. 12 — Song J.-F. The Guidelines for Expressing Measurement Uncertainties and the 4:1 Test Uncertainty Ratio. NCSL Workshop & Symposium, 1997. https://www.nist.gov/node/661216 (NIST author; abstract only)
115. Ch. 12 — Mimbs S. A New NASA Preferred Standard: ANSI/NCSL Z540.3-2006. Measurement Science Conference, Anaheim, 13–14 Mar 2008. NASA NTRS 20130012068. https://ntrs.nasa.gov/api/citations/20130012068/downloads/20130012068.pdf (NASA Kennedy Space Center author; quotes Z540.3, which was not opened; Mimbs records that NASA adopted ANSI/NCSL Z540-1 in 1995)
116. Ch. 12 — SIMCO Electronics. What the 4:1 Calibration Ratio Was Meant to Do and What It Wasn't (undated, unsigned web page). https://www.simco.com/?p=26409 (company page; secondary account of the 1954–1955 papers)
117. Ch. 12 — NCSL International. Z540.3 Standard (status page: withdrawn October 2020, superseded by ISO/IEC 17025:2017). Accessed 31 Oct 2026. https://ncsli.org/page/z5403
118. Ch. 12 — JCGM. Evaluation of measurement data — The role of measurement uncertainty in conformity assessment. JCGM 106:2012. 2012. https://doi.org/10.59161/JCGM106-2012
119. Ch. 12 — Bundesamt für Justiz. Verordnung über das Betreiben und Benutzen von Medizinprodukten (Medizinprodukte-Betreiberverordnung, MPBetreibV), § 15 Messtechnische Kontrollen. 2025. https://www.gesetze-im-internet.de/mpbetreibv_2025/__15.html
120. Ch. 12 — Global ACI. Recognised accreditation bodies (list), last modified 21 Jul 2026. https://globalaci.org/
121. Ch. 13 — IEC. IEC 80601-2-30:2018, Medical electrical equipment — Part 2-30: Particular requirements for the basic safety and essential performance of automated non-invasive sphygmomanometers, edition 2.0, 22 Mar 2018 (IEC Webstore catalogue page; in force on 31 Oct 2026). https://webstore.iec.ch/publication/29812
122. Ch. 13 — Zhuhai Yueja Medical Device Technology Co., Ltd. 510(k) summary, K232814, Electronic Blood Pressure Monitor (cleared 5 Dec 2023). https://www.accessdata.fda.gov/cdrh_docs/pdf23/K232814.pdf (manufacturer's summary, FDA-hosted)
123. Ch. 13 — Physikalisch-Technische Bundesanstalt (for the Deutscher Kalibrierdienst). Calibration of Pressure Gauges. DKD-R 6-1, edition 03/2014, revision 3. https://doi.org/10.7795/550.20210422
124. Ch. 13 — ISO. ISO/IEC 17025:2017 General requirements for the competence of testing and calibration laboratories (catalogue page; confirmed 2023). https://www.iso.org/standard/66912.html (paid standard; clauses used as ILAC and accreditation bodies describe them)
125. Ch. 13 — UKAS. Decision rules and statements of conformity. LAB 48, Edition 5. July 2024. https://ukas.com/wp-content/uploads/2023/05/LAB-48-Decision-rules-and-statements-of-conformity.pdf
126. Ch. 13 — Bureau of Standards, Metrology and Inspection (Taiwan). Technical Specification of Verification and Inspection for Non Invasive Mechanical Sphygmomanometers, CNMV 16-1, Rev 2. Promulgated 14 Oct 2006, enforced 1 Jan 2008. English translation. https://www.bsmi.gov.tw/wSite/public/Data/f1555659238245.pdf
127. Ch. 13 — Fluke Corporation. Policy for Making Statements of Conformity in Calibration Certificates. FCM 7008.1 Rev 002 (hosted by Fluke Biomedical). https://www.flukebiomedical.com/media/133623/download (company's own policy)
128. Ch. 13 — Silva Junior S.H. Estudo da Confiabilidade Metrológica de Esfigmomanômetros. Master's dissertation, Programa de Pós-Graduação em Metrologia (PósMQI), PUC-Rio, 2008 (advisor E. Costa Monteiro). https://www.maxwell.vrac.puc-rio.br/12319/12319_1.PDF (abstract and front matter read)
129. Ch. 13 — UKAS. Reporting Calibration Results. LAB 5, Edition 5. January 2025. https://www.ukas.com/wp-content/uploads/2021/11/LAB-5-Reporting-Calibration-Results.pdf
130. Ch. 13 — Southern African Development Community Accreditation Service. Technical Requirements ISO/IEC 17025:2017 (assessment checklist), SADCAS F 60 (b), Issue 3. 2023. https://www.sadcas.org/sites/default/files/pdf-documents/SADCAS%20F%2060b%20-%20Technical%20Requirements%20ISO%20IEC%2017025-2017%20[Issue%203].pdf
131. Ch. 14 — Supreme Court of New Jersey. State v. Cassidy, A-58-16 (078390). Decided 13 November 2018, with the Special Master's report appended. https://www.njcourts.gov/system/files/court-opinions/2018/a_58_16.pdf
132. Ch. 14 — Fluke Biomedical. ProSim 8 App Note: ProSim 8 NIBP test optimization: dynamic pressure simulation and pressure leak test. Undated (accessed 31 Oct 2026). https://www.flukebiomedical.com/resource/prosim-8-app-note-prosim-8-nibp-test-optimization-dynamic-pressure-simulation-and-pressure (manufacturer)
133. Ch. 14 — Rossmax Swiss GmbH. Instruction Manual, Model CalPro, Mobile Calibration System for Blood Pressure Monitor. File OBM_IB_CalPro_EN_SW_ver2126, undated. https://rossmax.rs/wp-content/uploads/downloads/OBM_IB_CalPro_EN.pdf (manufacturer; host's relation to Rossmax not verified)
134. Ch. 14 — Shenzhen Mindray Bio-Medical Electronics. VS-900 Vital Signs Monitor Service Manual, V6.0. April 2019. https://www.mindray.com/content/dam/xpace/en_gb/education/Service-Manuals/VS900_Service_Manual_V6.0_EN.pdf (manufacturer)
135. Ch. 14 — FDA Office of Regulatory Affairs. ORA Laboratory Manual Volume II: Traceability. ORA-LAB.5.6, Revision 02, revised 15 May 2019. https://fda.gov/media/73956/download
136. Ch. 14 — NIST Office of Weights and Measures. SOP 1 – 2019, Appendices B and C (Appendix B, Calibration Certificate Review Checklist for ISO/IEC 17025:2017 section 7.8). 2019. https://www.nist.gov/document/sop-1-calibration-certificate-eval-app-b-c-20190506pdf (restates the standard; secondary)
137. Ch. 14 — Yang P. (Health and Life Co., Ltd.). Electronic sphygmomanometer calibrating tool. US 6,984,212 B1. Filed 21 September 2004, granted 10 January 2006 (lapsed 2010). https://patents.google.com/patent/US6984212 (manufacturer's patent)
138. Ch. 14 — Frick G., Lee T.-H. (Microlife Intellectual Property GmbH). Blood pressure monitor calibrating device. US 6,733,462 B1. Filed 9 November 2000, granted 11 May 2004 (lapsed 2012). https://patents.google.com/patent/US6733462 (manufacturer's patent)
139. Ch. 15 — NIST. Metrological Traceability: Frequently Asked Questions and NIST Policy (policy text of NIST Directive P 5800.00, Metrological Traceability, effective 31 May 2019; page updated 27 May 2026). https://www.nist.gov/metrology/metrological-traceability-frequently-asked-questions-and-nist-policy
140. Ch. 15 — ILAC. ILAC Policy on Metrological Traceability of Measurement Results. ILAC-P10:07/2020. July 2020 (ILAC's arrangement passed to Global ACI on 1 January 2026). https://ilac.org/?ddownload=123220
141. Ch. 15 — NPL (UK). Pressure and barometers: UKAS accredited calibration and bespoke services (service page, accessed 31 Oct 2026). https://www.npl.co.uk/products-services/force-pressure-mass-density/pressure-barometers
142. Ch. 15 — Bean V.E. NIST Measurement Services: NIST Pressure Calibration Service. NIST Special Publication 250-39. February 1994. https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication250-39.pdf (historical)
143. Ch. 15 — OIML. Weights of classes E1, E2, F1, F2, M1, M1–2, M2, M2–3 and M3. Part 1: Metrological and technical requirements. OIML R 111-1, Edition 2004, with Amendment 2025. https://www.oiml.org/en/files/pdf_r/r111-1-e04.pdf ; https://www.oiml.org/en/files/pdf_r/r111-1-e04_amend25.pdf
144. Ch. 15 — Thakur V.N., Yadav S., Kumar A. Establishment of air piston gauge as primary pressure standard at CSIR-National Physical Laboratory INDIA. Acta IMEKO 9(5) (2020) 329–333. https://doi.org/10.21014/acta_imeko.v9i5.994 (abstract only; authors are CSIR-NPL staff)
145. Ch. 15 — CSIR-National Physical Laboratory, India. Report to the CCM (CCM-23_R27_NPLI_Report). BIPM document, undated (late 2022). https://www.bipm.org/documents/20126/85540139/CCM-23_R27_NPLI_Report.pdf/03bbd22a-c963-4530-d1a7-d2968e25104a (the institute's own report)
146. Ch. 15 — ISO. ISO 17511:2020 In vitro diagnostic medical devices — Requirements for establishing metrological traceability of values assigned to calibrators, trueness control materials and human samples. Edition 2, April 2020 (confirmed 2026). https://www.iso.org/standard/69984.html (catalogue page)
147. Ch. 15 — JCTLM. About us. Accessed 2 Nov 2026. https://jctlm.org/about-us/ (the BIPM, ILAC and the IFCC established the JCTLM in 2002)
148. Ch. 16 — Wenke F. Labortechnik (Branchen, Indien). Germany Trade & Invest (GTAI), 30 September 2026. https://www.gtai.de/de/trade/indien/branchen/labortechnik-847294 (secondary: a German federal trade agency's market report, reading NABL's register)
149. Ch. 16 — NABL. Home page and About page (accessed 31 Oct 2026). https://nabl-india.org/ ; https://nabl-india.org/about-us/
150. Ch. 16 — Kramer M. (PJLA). Requirements in Section 6.4 "Equipment". Perry Johnson Laboratory Accreditation, webinar slides, 26 October 2023. https://www.pjlabs.com/downloads/webinar_slides/10.26.2023_Equipment64.pdf (accreditation body; describes the standard)
151. Ch. 16 — ILAC. ILAC Policy for Measurement Uncertainty in Calibration. ILAC-P14:09/2020. September 2020. https://ilac.org/?ddownload=123348
152. Ch. 16 — UKAS. Schedule of accreditation, S M Gauge Company Ltd, 9152 Calibration, Issue 018, 16 June 2026. https://ukas.com/wp-content/uploads/schedule_uploads/00001/9152Calibration-Single.pdf
153. Ch. 16 — PSG Centre for Industrial Research and Development (PSG CIRD), PSG College of Technology, Coimbatore. Scope of accreditation, annexure to certificate CC-4660, valid 30 January 2026 to 29 January 2030. https://cird.psgtech.ac.in/files/certificates/Scope.pdf (the laboratory's own copy; accreditation body not named in its text)
154. Ch. 16 — ILAC. ILAC Policy for Proficiency Testing and/or Interlaboratory comparisons other than Proficiency Testing. ILAC-P9:01/2024. January 2024. https://ilac.org/?ddownload=3259
155. Ch. 16 — NABL. NABL documents list (NABL 142, 143, 164 and others; accessed 31 Oct 2026). https://nabl-india.org/nabl-documents/
156. Ch. 16 — ILAC Secretariat. Update from the Secretariat. 1 December 2025. https://ilac.org/?p=126756
157. Ch. 16 — ILAC. Facts & Figures (last modified 11 December 2024). https://ilac.org/about-ilac/facts-and-figures/
158. Ch. 16 — ILAC, IAF and Global ACI. Press release: Global ACI commences full operations. 1 January 2026. https://ilac.org/wp-content/uploads/Press-Release-Global.pdf
159. Ch. 16 — UKAS. Technical Bulletin: Transition to the Global ACI MRA Mark. 15 May 2026. https://www.ukas.com/resources/technical-bulletins/transition-to-the-global-aci-mra-mark/
160. Ch. 16 — Canlobo A. Medical device calibration: ISO 13485 requirements. Micro Precision Calibration blog, 4 June 2026 (updated 7 June 2026). https://microprecision.com/blog/medical-device-calibration-iso-13485-requirements/ (company: a calibration provider)
161. Ch. 16 — Lewandowski-Walker K. (CDRH, FDA). MDSAP: Production and Service Controls Process: Part 2. Training slides, undated. https://fda.gov/media/147549/download
162. Ch. 17 — FDA. Quality System Regulation, 21 CFR 820.72 Inspection, measuring, and test equipment. CFR 2021 edition (revised as of 1 April 2021); superseded by the Quality Management System Regulation on 2 February 2026. https://www.govinfo.gov/content/pkg/CFR-2021-title21-vol8/pdf/CFR-2021-title21-vol8-sec820-70.pdf (withdrawn rule, cited as such); also reproduced by the Legal Information Institute, Cornell Law School, https://www.law.cornell.edu/cfr/text/21/820.72
163. Ch. 17 — FDA. Medical Devices; Quality System Regulation Amendments. Final rule, 89 FR 7496, 2 February 2024 (effective 2 February 2026). https://www.federalregister.gov/documents/2024/02/02/2024-01709/medical-devices-quality-system-regulation-amendments
164. Ch. 17 — OIML and ILAC. Guidelines for the determination of recalibration intervals of measuring equipment. OIML D 10:2022 / ILAC-G24:2022. Edition 2022 (supersedes the 2007 edition). https://www.oiml.org/en/files/pdf_d/d010-e22.pdf
165. Ch. 17 — Mackenzie C.J., Piggin T.J. (Baker Hughes Oilfield Operations LLC). Automatic zero reset for a pressure transducer. US 11,221,266 B2. Granted 11 January 2022. https://patents.google.com/patent/US11221266 (industrial sensor, not a blood-pressure monitor)
166. Ch. 17 — Kato H., Tanaka T., Sano Y., Oku S. (Omron Corporation). Electronic sphygmomanometer. US 6,872,182 B2. 29 March 2005. https://patents.google.com/patent/US6872182 (manufacturer's patent)
167. Ch. 17 — Air Quality Research Center, University of California, Davis. Reference Weights. UCD IMPROVE Technical Information #251A, version 3.0, 15 July 2022. https://airquality.ucdavis.edu/sites/g/files/dgvnsk1671/files/inline-files/IMPROVE_TI_251A_v3.0_Reference_Weights.pdf
168. Ch. 17 — Devine C.J. MHLW MO 169 – Chapter 2/Section 5 – Control of Monitoring & Measuring Devices. MedTech Intelligence, 19 September 2012. https://medtechintelligence.com/?p=193 (trade article quoting Japan's Ministerial Ordinance No. 169, Article 53, in English; text aligned with ISO 13485:2003)
169. Ch. 17 — ISO. ISO 13485:2016 Medical devices — Quality management systems — Requirements for regulatory purposes. Edition 3, March 2016 (confirmed 2025). https://www.iso.org/standard/59752.html (catalogue page; clause 7.6 as FDA's MDSAP training, Micro Precision, Advisera and MO 169 describe it)
170. Ch. 17 — Advisera 13485Academy. Calibration requirements in ISO 13485. 8 March 2019, updated 28 August 2023. https://advisera.com/13485academy/wp-json/wp/v2/posts/11338 (consultancy; describes the standard)
171. Ch. 17 — NIST Office of Weights and Measures. GMP 11, Good Measurement Practice for Assignment and Adjustment of Calibration Intervals for Laboratory Standards. In NISTIR 6969, Selected Laboratory and Measurement Practices and Procedures, 2019 edition. https://www.nist.gov/document/gmp-11-calibration-intervals-20190506pdf
172. Ch. 17 — PMDA (Pharmaceuticals and Medical Devices Agency, Japan). Regulatory information (English page: the second chapter of MHLW Ministerial Ordinance No. 169 revised 26 Mar 2021 to align with ISO 13485:2016). Accessed 2 Nov 2026. https://www.pmda.go.jp/english/review-services/regulatory-info/0004.html (regulator's own page)
173. Ch. 18 — Jabbour Z.J., Yaniv S.L. (NIST). The kilogram and measurements of mass and force. J. Res. NIST 106(1), 25–46 (2001). https://www.nist.gov/document/j61jabpdf (secondary: a review by NMI staff; Johnson Matthey delivered three platinum-iridium cylinders, KI, KII and KIII, in 1879, and KIII was chosen as the international prototype; KIII had been kept in a safe at the BIPM since 1882, seven years before its sanction)
174. Ch. 18 — Schwitz W., Jeckelmann B., Richard P. (METAS). Towards a new kilogram definition based on a fundamental constant. C. R. Physique 5, 881–892 (2004). https://doi.org/10.1016/j.crhy.2004.05.005 (secondary: a review by NMI staff)
175. Ch. 18 — BIPM. The BIPM announces the death of Georges Girard. News, 24 Jun 2022 (date from the URL). https://www.bipm.org/en/-/2022-06-24-georges-girard (Georges Girard joined the BIPM as a 17-year-old trainee in October 1945, headed its mass section from the 1970s and retired in 1993)
176. Ch. 18 — Stock M. et al. (BIPM). Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram, part I: comparison of the international prototype with its official copies. Metrologia 52, 310 (2015). https://doi.org/10.1088/0026-1394/52/2/310 (CC BY 3.0)
177. Ch. 18 — Girard G. (BIPM). Le nettoyage-lavage des prototypes du kilogramme au BIPM. BIPM Monographie 1990/1, October 1990. https://www.bipm.org/utils/common/pdf/monographies-misc/Monographie1990-1-FR.pdf
178. Ch. 18 — CIPM. Recommendation 4 (CI-1993), Monitoring the stability of the international prototype of the kilogram. Proceedings of the 82nd CIPM (1993), 1994, p. 134. https://www.bipm.org/committees/ci/cipm/82-1993/resolution-4 (official text French)
179. Ch. 18 — CGPM. Resolution 5 of the 20th CGPM (1995), Monitoring the stability of the international prototype of the kilogram. https://doi.org/10.59161/CGPM1995RES5E (official text French; the CGPM's endorsement is Resolution 5 of its 20th meeting, 1995)
180. Ch. 18 — CCM. Recommendation 1 of the 14th CCM (2013), On a new definition of the kilogram. https://www.bipm.org/en/-/ccm-2013-recommendation-1 (official text French)
181. Ch. 18 — Stock M. (BIPM). Extraordinary Calibrations (slides). 15th meeting of the CCM, 26–27 Feb 2015. BIPM working document ID-6911. https://www.bipm.org/documents/20126/28428460/working-document-ID-6911/7b5b5898-df71-cf42-97be-8aef56d8bd79
182. Ch. 18 — Stock M. (BIPM). Overview of mass calibration work and maintenance of BIPM working standards (slides). CCM-21-05, 20 May 2021. https://www.bipm.org/documents/20126/56189656/CCM-21-05_BIPM-Maintenance-WorkingStandards.pdf/a2d851c2-1f57-0ff2-1a7b-2f8e3ae1bccb
183. Ch. 18 — Schlamminger S., Steiner R.L., Haddad D., Newell D.B., Seifert F., Chao L.S., Liu R., Williams E.R., Pratt J.R. (NIST). A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST. arXiv:1501.06796 (2015), authors' preprint. https://arxiv.org/pdf/1501.06796 (NIST staff)
184. Ch. 18 — CCM. Recommendation to NMIs on managing the consequences of the corrections to the BIPM as-maintained mass unit. 15th meeting of the CCM, 2015. BIPM working document ID-6909. https://bipm.org/documents/20126/28428361/working-document-ID-6909/40c81149-3c55-88e6-ef0f-73ef837966d1
185. Ch. 18 — CIPM. Recommendation 1 (CI-2015), Recommendation to NMIs on managing the consequences of the corrections to the BIPM as-maintained mass unit. 104th meeting of the CIPM, 2015. https://bipm.org/committees/ci/cipm/104-_1-2015/resolution-1
186. Ch. 18 — Wood B., Sanchez C. (NRC). The NRC watt balance: Planck constant determination (slides). FC 2015, Eltville, 4 Feb 2015. https://www.bipm.org/documents/20126/43535504/Wood.pdf/362fb8cf-784f-93c8-72ad-c29d21425389 (NRC staff)
187. Ch. 18 — BIPM. The international prototype of the kilogram (IPK page, mass metrology). Undated, accessed 2 Nov 2026. https://www.bipm.org/mass-metrology/ipk
188. Ch. 19 — CGPM. Resolution 1 of the 26th CGPM (2018), On the revision of the International System of Units (SI). https://www.bipm.org/en/-/resolution-cgpm-26-1 (official text French; the revision is Resolution 1 of the 26th CGPM, 16 November 2018)
189. Ch. 19 — CGPM. Resolution 1 of the 13th CGPM (1967), SI unit of time (second). https://www.bipm.org/en/-/resolution-cgpm-13-1
190. Ch. 19 — CGPM. Resolution 1 of the 17th CGPM (1983), Definition of the metre. https://www.bipm.org/en/-/resolution-cgpm-17-1
191. Ch. 19 — CCM. Recommendation 1 of the 16th CCM (2017), For a new definition of the kilogram in 2018. https://www.bipm.org/en/-/ccm-2017-recommendation-1
192. Ch. 19 — Newell D.B., Mohr P.J., Taylor B.N., Tiesinga E. (NIST, for the CODATA Task Group on Fundamental Constants). Data and analysis for the CODATA 2017 special fundamental constants adjustment for the revision of the SI. Metrologia 55, 125–146 (2018). NIST record https://www.nist.gov/node/1324931 (abstract read)
193. Ch. 19 — CODATA Task Group on Fundamental Constants. Minutes of the meeting of 4 September 2017, BIPM. https://www.bipm.org/documents/20126/43516424/Minutes_CODATA_TGFC_September2017_final.pdf/4734764b-051d-75c4-94e6-532783f17d48 (the CODATA Task Group on Fundamental Constants met at the BIPM on 4 September 2017 and recorded its inputs for h in the minutes of that meeting)
194. Ch. 19 — NIST. 2019 Gold Medal Award (citation page). 14 Nov 2019. https://www.nist.gov/node/1594646 (secondary: the date, place and unanimity of the 2018 vote)
195. Ch. 19 — Fujii K. (NMIJ), Massa E. (INRIM), Bettin H. (PTB), Kuramoto N. (NMIJ), Mana G. (INRIM). Avogadro constant measurements using enriched 28Si monocrystals. Metrologia 55, L1–L4 (2018), published 12 Dec 2017. https://doi.org/10.1088/1681-7575/aa9abd (CC BY 3.0; NMI staff)
196. Ch. 19 — CODATA. CODATA Strategic Plan 2013–2018. April 2013. https://codata.org/CODATA_Strategic_%20Plan_2013-2018.pdf
197. Ch. 19 — CODATA. CODATA Constitution (Statutes and By-Laws), as modified up to the 31st General Assembly, Gaborone, 2018. https://codata.org/wp-content/uploads/2021/02/CODATA_CONSTITUTION_2018-CLEAN-FINAL.pdf
198. Ch. 20 — Schlamminger S., Haddad D. (NIST). The Kibble balance and the kilogram. C. R. Physique 20, 55–63 (2019). https://doi.org/10.1016/j.crhy.2018.11.006 (abstract and references read; NIST staff; after Kibble's death in 2016 the metrology community renamed the watt balance the Kibble balance)
199. Ch. 20 — National Physical Laboratory. Bryan Kibble (famous NPL people page). Undated. https://www.npl.co.uk/famous/bryan-kibble (NPL dates the first moving-coil watt balance to 1978)
200. Ch. 20 — Haddad D., Seifert F., Chao L.S., Possolo A., Newell D.B., Pratt J.R., Williams C.J., Schlamminger S. (NIST; Seifert and Williams also JQI, University of Maryland). Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017. Metrologia 54, 633–641 (2017). https://doi.org/10.1088/1681-7575/aa7bf2 (read as the authors' preprint, arXiv:1708.02473; NIST staff)
201. Ch. 20 — CCEM. Mise en pratique for the definition of the ampere and other electric units in the SI. SI Brochure, 9th edition (2019), Appendix 2, 20 May 2019. https://www.bipm.org/utils/en/pdf/si-mep/SI-App2-ampere.pdf
202. Ch. 20 — Bettin H. (PTB), Fujii K. (NMIJ/AIST), Nicolaus A. (PTB). Silicon spheres for the future realization of the kilogram and the mole. C. R. Physique 20, 64–76 (2019). https://doi.org/10.1016/j.crhy.2018.12.005 (NMI staff)
203. Ch. 20 — BIPM KCDB. CCM.M-K8.2024, third key comparison of realizations of the kilogram (final report page). Published 20 Feb 2026. https://www.bipm.org/en/d/-ccm-m-k8-2024 (abstract read)
204. Ch. 20 — National Research Council Canada. The kilogram hangs in the balance. News release, 16 Nov 2017. https://www.canada.ca/en/national-research-council/news/2017/11/the_kilogram_hangsinthebalance.html (NRC bought its balance from the UK's National Physical Laboratory in 2008)
205. Ch. 20 — Cowen R. NIST's Kibble balance: a mass revolution. NIST, 2 Jun 2025. https://www.nist.gov/node/1882566 (NIST's own article)
206. Ch. 20 — First international comparison of three different tabletop Kibble balances from 1 mg to 10 g. Metrologia 63(4) (2026), published 27 Jul 2026. https://doi.org/10.1088/1681-7575/ae890c ; NIST record https://www.nist.gov/node/1917511 (abstract read; authors from TU Ilmenau, PTB and NIST)
207. Ch. 20 — Li N., Liu W., Qupasie E.E.E., Zhao W., Huang S., Li S. (Tsinghua University). Design of a miniature Kibble balance for kilogram-scale mass calibration — KBmini. arXiv:2601.18054 (January 2026), preprint submitted to Metrologia; not peer-reviewed as read.
208. Ch. 21 — Mandal G., Kumar A., Sharma D.C., Kumar H. (CSIR-NPL). Variation in mass values of Indian prototype kilogram. XX IMEKO World Congress, Busan, 9–12 Sep 2012. https://imeko.org/proceedings/variation-in-mass-values-of-indian-prototype-kilogram (abstract read; NMI staff)
209. Ch. 21 — BIPM. Beginning a new phase of the dissemination of the kilogram. News, January 2021. https://bipm.org/en/-/2021-kg-consensus
210. Ch. 21 — Stock M. (BIPM), Davidson S. (NPL). Report on the calculation of the CCM consensus value for the kilogram 2026. BIPM, 7 Jan 2026. https://www.bipm.org/documents/20126/286252520/Report+on+the+Calculation+of+the+Consensus+Value+2026/d842a06e-2fbb-0175-c004-84a9968f41b1
211. Ch. 21 — BIPM. Third consensus value of the kilogram to be implemented from 1 March 2026. News, 24 Feb 2026 (the URL reads 2025-02-24). https://www.bipm.org/en/-/2025-02-24-third-consensus-value-of-the-kilogram-to-be-implemented-1
212. Ch. 21 — Davidson S. (NPL). Report of the CCM Working Group on Mass (inc. CCM-TGPfD-kg) (slides). 20th meeting of the CCM, 26–27 June 2025. https://www.bipm.org/documents/20126/275177277/CCM-25_06-7_WGM_TGPfD-Kg-Report/44896737-0dae-2711-fe32-3493e211c763
213. Ch. 21 — Bandyopadhyay A.K. (CSIR-NPL), Woo S.Y., Fitzgerald M., Man J., Ooiwa A., Jescheck M., Wu Jian, Chen Soo Fatt, Chan T.K., Moore K. Results of the APMP pressure key comparison in gas media and gauge mode from 20 kPa to 105 kPa: APMP.M.P-K6 final report (also APMP-IC-2-97). BIPM KCDB document, undated (after September 2001). The report's table and abstract list ten laboratories; one later section states that eleven took part. https://www.bipm.org/documents/20126/48150841/APMP.M.P-K6.pdf/7547b633-4e46-c3f7-e558-7fee19198ff5
214. Ch. 21 — BIPM. CIPM MRA (page). Undated, accessed 31 Oct 2026. https://www.bipm.org/en/cipm-mra
215. Ch. 21 — Milton M.J.T. (Director, BIPM). Report from the BIPM (slides). 26 Jun 2025. BIPM document CCM-25_03-2. https://www.bipm.org/documents/20126/275187393/CCM-25_03-2_BIPM-report/31dbdd23-b52d-3e60-9be6-1d7e46f3d797
216. Ch. 21 — CSIR-National Physical Laboratory, India. NPLI report to the CCM (CCM-21-R25). Undated, latest events mid-2021. https://www.bipm.org/documents/20126/55868032/CCM-21-R25_NPLI-Report.pdf/3ceb24fe-fbcc-6db9-0145-49a1237c86ca (the NMI's own report)
217. Ch. 21 — Mandal G., Gopan C.K. (CSIR-NPL). Improvement of measurement capabilities of multiple mass standards of 1 kg at NPLI. IMEKO TC3 conference, Pattaya, 21–25 Nov 2010. https://imeko.org/proceedings/improvement-of-measurement-capabilities-of-multiple-mass-standards-of-1-kg-at-npli (abstract read; NMI staff)
218. Ch. 21 — CIPM. Mutual recognition of national measurement standards and of calibration and measurement certificates issued by national metrology institutes (CIPM MRA). Paris, 14 October 1999; 2003 edition. https://www.bipm.org/documents/20126/43742162/CIPM-MRA-2003.pdf (the CIPM MRA's text is dated Paris, 14 October 1999; CSIR-NPL has taken part since that day (Chapter 3))
219. Ch. 22 — Automotive Industry Action Group (AIAG). Measurement Systems Analysis (MSA) Reference Manual, 4th edition, AIAG MSA-4. June 2010. Catalogue page, ANSI Webstore: https://webstore.ansi.org/standards/aiag/aiagmsa2010 (paid manual, not read; its criteria as Minitab and BPI Consulting reproduce them)
220. Ch. 22 — Minitab, LLC. Is my measurement system acceptable? Minitab Support, undated (accessed 31 Oct 2026). https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/supporting-topics/gage-r-r-and-wheeler-s-emp-studies/is-my-measurement-system-acceptable/ (company's own help page; cites AIAG MSA-4)
221. Ch. 22 — McNeese B. Three Ways to Analyze a Gage R&R Study. BPI Consulting, LLC (SPC for Excel), 2015. https://www.spcforexcel.com/Downloads/pdf/Three-Ways-to-Analyze-a-Gage-RR.pdf (company's own tutorial; the 90-reading data set of the solved example; cites AIAG MSA-4, p. 78)
222. Ch. 22 — Minitab, LLC. Example of Gage Linearity and Bias Study. Minitab Support, undated (accessed 31 Oct 2026). https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/gage-linearity-and-bias-study/before-you-start/example/ (company's own example)
223. Ch. 22 — Minitab, LLC. What is the number of distinct categories? Minitab Support, undated (accessed 31 Oct 2026). https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/supporting-topics/gage-r-r-and-wheeler-s-emp-studies/using-the-number-of-distinct-categories-in-a-gage-r-r-study/ (company's own help page)
224. Ch. 22 — Minitab, LLC. Interpret the key results for Attribute Agreement Analysis. Minitab Support, undated (accessed 31 Oct 2026). https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/attribute-agreement-analysis/attribute-agreement-analysis/interpret-the-results/key-results/ (company's own help page)
225. Ch. 22 — International Automotive Task Force (IATF). IATF 16949:2016 Frequently Asked Questions (FAQs), November 2025 issue. https://www.iatfglobaloversight.org/wp/wp-content/uploads/2025/11/IATF-16949-FAQs_November-2025.pdf (FAQ 6, on clause 7.1.5.1.1; the clause text itself not read)
226. Ch. 22 — International Automotive Task Force (IATF). Stakeholder Communiqué SC-2026-005: IATF 16949 2nd edition update information. July 2026. https://www.iatfglobaloversight.org/wp/wp-content/uploads/2026/07/Stakeholder-Communique-SC-2026-005_IATF-16949-2nd-Edition-status.pdf (dates indicative)
227. Ch. 22 — Global Harmonization Task Force, Study Group 3. Quality Management Systems – Process Validation Guidance. GHTF/SG3/N99-10:2004, Edition 2. January 2004. Archived by IMDRF: https://www.imdrf.org/sites/default/files/docs/ghtf/final/sg3/technical-docs/ghtf-sg3-n99-10-2004-qms-process-guidance-04010.doc
228. Ch. 22 — ISO. ISO 22514-7:2021 Statistical methods in process management — Capability and performance — Part 7: Capability of measurement processes, with Amd 1:2024; third edition at ISO/FDIS 22514-7 (approval stage on 31 Oct 2026). https://www.iso.org/standard/89276.html (catalogue page of the FDIS)
229. Ch. 23 — US Food and Drug Administration (CDRH, CBER). Recommended Content and Format of Non-Clinical Bench Performance Testing Information in Premarket Submissions. Final guidance, docket FDA-2018-D-1329. 20 Dec 2019. https://www.fda.gov/media/113230/download
230. Ch. 23 — US Food and Drug Administration. Quality Management System Regulation (QMSR). Page content current as of 2 Feb 2026. https://www.fda.gov/medical-devices/postmarket-requirements-devices/quality-management-system-regulation-qmsr
231. Ch. 23 — Tartal J. (CDRH, FDA). Quality Management System Regulation (QMSR) – Design and Development. Training slides, undated. https://www.fda.gov/media/189041/download (the regulator's summary of ISO 13485:2016, 7.3.6 and 7.3.7; not the standard's text)
232. Ch. 23 — US Food and Drug Administration. Warning Letter 707997 to Mectronic Medicale S.R.L. 27 Jun 2025. https://www.fda.gov/inspections-compliance-enforcement-and-criminal-investigations/warning-letters/mectronic-medicale-srl-707997-06272025 (issued under the Quality System Regulation, before the QMSR took effect; a warning letter states FDA's allegations)
233. Ch. 23 — US Food and Drug Administration (CDER, CBER) / ICH. Q2(R2) Validation of Analytical Procedures. Guidance for industry, final. March 2024 (ICH Step 4, November 2023). https://www.fda.gov/media/161201/download (a text for medicines, used for its list of validation characteristics)
234. Ch. 23 — US Food and Drug Administration. Recognized Consensus Standards: ISO TS 81060-5 First edition 2020-02, Non-invasive sphygmomanometers — Part 5: Requirements for the repeatability and reproducibility of NIBP simulators, recognition 3-167, entered 6 Jul 2020. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfStandards/detail.cfm?standard__identification_no=41189
235. Ch. 23 — Kumar R., Dubey P.K., Zafer A., Kumar A., Yadav S. (CSIR-NPL). Control and Automation Software for Calibration and Testing of Blood Pressure Measuring Devices. IEEE DataPort, v1.0.0, created 7 Oct 2023. https://doi.org/10.21227/jm1q-5350 (dataset page by NMI staff; abstract only, files not opened)
236. Ch. 24 — Stergiou G.S. (chair), et al., AAMI/ESH/ISO Collaboration (members include Alpert B., Asmar R., Atkins N., Ioannidis J.P., O'Brien E.). A Universal Standard for the Validation of Blood Pressure Measuring Devices. Hypertension 71 (2018) 368–374. https://doi.org/10.1161/HYPERTENSIONAHA.117.10237 (statement by the collaboration that set the standard's universal protocol; not the standard's text)
237. Ch. 24 — ISO. ISO 81060-2:2018 Non-invasive sphygmomanometers — Part 2: Clinical investigation of intermittent automated measurement type; Amd 1:2020; Amd 2:2024; revision at ISO/DIS 81060-2, stage 40.60, 15 Sep 2026. https://committee.iso.org/standard/89733.html (paid standard, not read)
238. Ch. 24 — US Food and Drug Administration. Recognized Consensus Standards: ISO 81060-2 Third edition 2018-11 [including AMD1:2020 and AMD2:2024], recognition 3-196, entered 23 Dec 2024, partial recognition. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfstandards/detail.cfm?standard__identification_no=45813
239. Ch. 24 — Noh S.A., Kim H.-S., Kang S.-H., Yoon C.-H., Youn T.-J., Chae I.-H. History and evolution of blood pressure measurement. Clinical Hypertension 30(1) (April 2024), Table 1. https://clinicalhypertension.biomedcentral.com/articles/10.1186/s40885-024-00268-7/tables/1 (secondary: a review's table; authors as the DOAJ record gives them, https://doaj.org/article/95b0eb410bf34606b2c6225c2e0048ee)
240. Ch. 24 — Hernández Véliz D., Valdés González Y., et al. (with Ringrose J., Padwal R.). Validation of combiomed hipermax-BF model A7101 automatic oscillometric upper-arm sphygmomanometer in general population: AAMI/ESH/ISO universal standard (ISO 81060-2:2018/Amd 1:2020). Journal of Human Hypertension 38 (2024) 779–785. https://doi.org/10.1038/s41371-024-00948-9 (abstract only; funded by the Cuban Ministry of Public Health; no competing interests declared; the maker is not an author)
241. Ch. 24 — Ishigami J., Charleston J., Miller E.R. 3rd, Matsushita K., Appel L.J., Brady T.M. Effects of Cuff Size on the Accuracy of Blood Pressure Readings: The Cuff(SZ) Randomized Crossover Trial. JAMA Internal Medicine (2023) e233264. https://doi.org/10.1001/jamainternmed.2023.3264 (secondary: read through the authors' institution's summary, Johns Hopkins Medicine Matters, https://medicine-matters.blogs.hopkinsmedicine.org/?p=19225; the paper itself not opened)
242. Ch. 24 — ISO. ISO 15197:2013 In vitro diagnostic test systems — Requirements for blood-glucose monitoring systems for self-testing in managing diabetes mellitus; revision at ISO/CD 15197, stage 30.60, 12 Mar 2026. https://committee.iso.org/standard/91142.html (paid standard, not read)
243. Ch. 24 — Hwang H. (SD Biosensor), Leonardi L. (PIKDARE), Nicolucci A. (CORESEARCH). Accuracy of the Standard GlucoNavii Mentor in Blood Glucose Monitoring According to International Organization for Standardization 15197:2013 Criteria. JMIR Diabetes 7(2) (2022) e20774. https://doi.org/10.2196/20774 (manufacturer study: funded by SD Biosensor, first author an SD Biosensor employee, medical writing funded by PIKDARE)
244. Ch. 24 — US Food and Drug Administration (CDRH). Self-Monitoring Blood Glucose Test Systems for Over-the-Counter Use. Final guidance, docket FDA-2013-D-1446. 29 Sep 2020. https://www.fda.gov/media/87721/download
245. Ch. 24 — Withings. 510(k) summary, K252474, Withings BeamO (model SCT02), cleared 10 Nov 2025. https://www.accessdata.fda.gov/cdrh_docs/pdf25/K252474.pdf (manufacturer's summary, FDA-hosted)
246. Ch. 24 — ISO. ISO 80601-2-56:2017 Medical electrical equipment — Part 2-56: Particular requirements for basic safety and essential performance of clinical thermometers for body temperature measurement, with Amd 1:2018 (to be revised). https://committee.iso.org/standard/67348.html (paid standard, not read)
247. Ch. 24 — ISO. ISO 12487:2026 Medical electrical equipment — Clinical performance evaluation of clinical thermometers. Edition 1, 21 May 2026. https://committee.iso.org/standard/85205.html (catalogue page)
248. Ch. 24 — US Food and Drug Administration (CDRH). Pulse Oximeters – Premarket Notification Submissions [510(k)s]. Final guidance. 4 Mar 2013. https://www.fda.gov/media/72470/download
249. Ch. 24 — Lee J.J., Quinn B., Patel N. (CDRH, FDA). Pulse Oximeters: Technology, Accuracy Limitations, and Regulation. Advisory panel slides, 2 Feb 2024. https://www.fda.gov/media/176236/download (regulator's slides)
250. Ch. 25 — NASA. NASA Systems Engineering Handbook. NASA/SP-2016-6105 Rev2. 2016. https://www.nasa.gov/sites/default/files/atoms/files/nasa_systems_engineering_handbook_0.pdf
251. Ch. 25 — NASA. Measurement Uncertainty Analysis Principles and Methods. NASA-HDBK-8739.19-3. 13 Jul 2010 (revalidated 1 Mar 2018). https://standards.nasa.gov/sites/default/files/standards/NASA/Baseline/0/nasa-hdbk-873919-3.pdf (NASA's 2010 handbook records that before the GUM many data analysts and engineers added uncertainties linearly, while statisticians and measurement scientists combined them by root-sum-of-squares)
252. Ch. 25 — Eicke W.G., Riley J.P., Riley K.J. (NASA Metrology and Calibration Working Group). Metrology—Measurement Assurance Program Guidelines. NASA Reference Publication 1364. March 1995. https://ntrs.nasa.gov/api/citations/19950018123/downloads/19950018123.pdf
253. Ch. 25 — OIML. R 76-1 Non-automatic weighing instruments. Part 1: Metrological and technical requirements – Tests. Edition 2006 (E). https://www.oiml.org/en/files/pdf_r/r076-1-e06.pdf
254. Ch. 25 — Detecto (Cardinal Scale). Composition of Modules, platform scale FP-125KG. Undated worksheet. https://detecto.com/themes/ee/site/default/asset/img/resources/resources_brochures/icon_Composition-of-Modules.pdf (company document)
255. Ch. 25 — FDA. 21 CFR Part 820, Quality Management System Regulation. eCFR, up to date as of 16 Jul 2026 (section 820.10(c), design and development under ISO 13485 clause 7.3). https://www.ecfr.gov/current/title-21/chapter-I/subchapter-H/part-820
256. Ch. 26 — FDA CDRH. Warning letter to Nipro Renal Solutions USA, Corporation. CMS 732874. 16 Jul 2026 (page header 24 Jul 2026). https://www.fda.gov/inspections-compliance-enforcement-and-criminal-investigations/warning-letters/nipro-renal-solutions-usa-corporation-732874-07242026
257. Ch. 26 — MDSAP. MDSAP Audit Approach. MDSAP AU P0002.009. Revision date 6 Aug 2024. https://www.fda.gov/media/166672/download (the version FDA's MDSAP page links; revisions .010 of 2 Feb 2026 and .011 of 3 Aug 2026 are reported by Complife and NSF, not read at source)
258. Ch. 26 — OIML. D 31 General requirements for software-controlled measuring instruments. Edition 2023 (E). https://www.oiml.org/en/files/pdf_d/d031-e23.pdf
259. Ch. 26 — FDA. openFDA device enforcement record Z-1074-2013, LifeScan OneTouch Verio IQ, Class I, classified 12 Apr 2013, terminated. https://api.fda.gov/device/enforcement.json?search=product_description:Verio+AND+recalling_firm:Lifescan&limit=5 ; recall record https://api.fda.gov/device/recall.json?search=product_description:VerioIQ&limit=5
260. Ch. 26 — FDA. Applying Human Factors and Usability Engineering to Medical Devices. Guidance, issued 3 Aug 2026 (originally 3 Feb 2016); reproduces definitions from ANSI/AAMI/ISO 14971:2019. https://www.fda.gov/media/80481/download
261. Ch. 27 — FDA. 510(k) decision summary K193340, GoChek and GoChek Connect Blood Glucose Monitoring Systems (MicroTech Medical, Inc.). https://www.accessdata.fda.gov/cdrh_docs/reviews/K193340.pdf
262. Ch. 27 — Sartorius. Entris II Essential Line analytical balance with internal adjustment, BCE64I-1S. Product page, undated, read 31 Oct 2026. https://shop.sartorius.com.cn/us/p/BCE64I-1S (manufacturer)
263. Ch. 27 — Imlab BV. Automatic Calibration/Adjustment with isoCAL. 19 Jun 2023 (modified 2 Sep 2025). https://www.imlab.eu/nl/nieuws/automatic-calibration-adjustment-with-isocal/ (secondary: a distributor of the maker's products)
264. Ch. 27 — Hodgkinson J.A., et al. Accuracy of blood-pressure monitors owned by patients with hypertension (ACCU-RATE study). Br J Gen Pract 70(697):e548–e554 (2020). https://doi.org/10.3399/bjgp20X710381 (funded by NIHR; no monitor-maker funding; one author declared research support in blood-pressure monitors from Omron and Lloyds Pharmacies)
265. Ch. 27 — Chopra R., Bareja A. (S.S. Rana & Co.). Verification of Weights & Measures under the Legal Metrology Act. 6 Dec 2021 (modified 16 Aug 2023). https://ssrana.in/articles/verification-of-weights-measures-legal-metrology-act/ (secondary: law firm)
266. Ch. 27 — FDA. Medical Device Recalls, Z-3217-2026 to Z-3220-2026, Midmark IQvitals Zone vital-signs monitors, Class II, initiated 21 Aug 2026, posted 18 Sep 2026. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfRes/res.cfm?id=222051 ; openFDA device enforcement, recall number Z-3218-2026
267. Ch. 28 — Olson D.A., Driver R.G., Bowers W.J. (NIST). A Gas Pressure Scale Based on Primary Standard Piston Gauges. J. Res. Natl. Inst. Stand. Technol. 115(6):393–412 (2010). https://nvlpubs.nist.gov/nistpubs/jres/115/6/V115.N06.A01.pdf
268. Ch. 29 — Ministry of Economy, Trade and Industry (METI), Japan. Public notice under Measurement Act Article 159(1)(x): revocation of designated verification bodies (A&D Company, Limited), 14 Jul 2026; and public notice of the hearing on the revocation (Article 38, item 2, applied by Article 106(3)), held 3 Jul 2026. METI page on designated verification bodies, last updated 22 Jul 2026 (in Japanese; regulator's record; METI designated A&D as a designated verification body in October 2021)
269. Ch. 29 — A&D Company, Limited. Notice of an administrative disposition in a case of violation of the Measurement Act (in Japanese). 14 Jul 2026; earlier notices of 30 Sep 2025 (updated 22 Jan 2026) and of the designation granted 18 Oct 2021 (company's own)
270. Ch. 29 — A&D HOLON Holdings Co., Ltd. Semi-annual securities report (EDINET), 14 Nov 2025: Measurement Act violations in repair work at A&D Company (Article 49, duty to remove verification marks) (statutory filing, in Japanese)
271. Ch. 29 — A&D Company, Limited. Product range (company site, in Japanese), accessed 31 Oct 2026. https://www.aandd.co.jp/ (manufacturer)
272. Ch. 29 — Aratas. About Aratas (company page), accessed 31 Oct 2026. https://www.aratas.com/en-global/corporate/aratas (company's own)
273. Ch. 29 — Microchip Technology. MCP3564 Weight Scale Demo (ARD00906), development-tool page, accessed 31 Oct 2026 (manufacturer)
274. Ch. 29 — Texas Instruments. Texas Instruments to acquire Silicon Labs (release). 4 Feb 2026 (company's own; closing expected in the first half of 2027)
275. Ch. 29 — Analog Devices, Inc. Form 8-K (Items 7.01, 9.01): definitive agreement to acquire Alif Semiconductor. 9 Sep 2026 (company filing; closing expected in the fourth quarter of 2026)
276. Ch. 29 — JOYTECH Healthcare Co., Ltd. EU Declaration of Conformity, Blood Pressure Monitor (Beurer models SBC 35, SBC 39, BM 92 and others). Hangzhou, 23 Sep 2025; notified body TÜV SÜD Product Service GmbH (0123), certificate G10 109940 0002. https://www.beurer.com/ (manufacturer)
277. Ch. 29 — Garmin / Ya Horng Electronic Co., Ltd. EU Declaration of Conformity, Index BPM (BP707); notified body DNV Product Assurance AS (2460), certificate 30 Aug 2023 to 30 Aug 2028 (manufacturer)
278. Ch. 29 — Fluke Biomedical. BP Pump 2 Non-Invasive Blood Pressure Simulator and Tester, data sheet 2817822-en. Oct 2023. https://flukebiomedical.com/sites/default/files/bp_pump_2_datasheet_en.pdf (manufacturer)
279. Ch. 29 — Fortive Corporation. Annual report on Form 10-K for 2025: segments Intelligent Operating Solutions (Fluke) and Advanced Healthcare Solutions (Fluke Biomedical); separation of Ralliant, 28 Jun 2025 (company filing)
280. Ch. 29 — Crane Company. Form 8-K: completion of the acquisition of Baker Hughes's Precision Sensors & Instrumentation business. 5 Jan 2026 (completion 1 Jan 2026); Form 10-Q, Q3 2026: Druck, Panametrics and Reuter-Stokes (company filings)
281. Ch. 29 — Druck (a Crane Company brand). Multifunction calibrators (product category page), © 2026. https://druck.com/product-category/test-and-calibration-instrumentation/portable-calibrators/multifunction-calibrators (manufacturer)
282. Ch. 29 — Beamex Oy Ab. Calibrators and calibration software (company pages), modified 19 Aug 2026 (manufacturer)
283. Ch. 29 — Fluke Corporation. Fluke launches CalStudio (release). Everett, Washington, 3 Nov 2025 (company's own)
284. Ch. 29 — Nagman Instruments and Electronics Private Limited, Chennai. Company page, modified 10 Jan 2026 (manufacturer)
285. Ch. 29 — Mettler-Toledo. Job posting for Troemner, LLC, Thorofare, New Jersey ("Mettler-Toledo acquired Troemner in 2016"), accessed 31 Oct 2026 (owner's own page)
286. Ch. 29 — Troemner. Accreditations (company page), accessed 31 Oct 2026. https://Troemner.com/accreditations (manufacturer)
287. Ch. 29 — CSIR-National Physical Laboratory, India. Calibration and testing (CFCT) pages, accessed 31 Oct 2026. https://www.nplindia.org/ (national institute's own pages; counts undated)
288. Ch. 29 — EQT. Trescal - EQT Portfolio Company (EQT Infrastructure V), © EQT AB 2026 (owner's own page)
289. Ch. 29 — Trade press report on Trescal's 14 acquisitions and entry into India (Bengaluru and Hyderabad), Jan 2026 (secondary; Trescal's own release not available)
290. Ch. 29 — Transcat, Inc. Annual report on Form 10-K for the fiscal year ended 28 Mar 2026; release on the acquisition of SCM Metrology and Laboratories S.A., effective 9 Apr 2026 (company filing; company release)
291. Ch. 29 — ADI ARTECH Transducers Pvt. Ltd., Vadodara. Home page, © 2024. https://adiartech.com/ (manufacturer)
292. Ch. 29 — Essae-Teraoka, Bengaluru. Company page, modified 27 Oct 2026 (manufacturer)
293. Ch. 29 — Tempsens Instruments, Udaipur. Company page, news items of October 2026 (manufacturer)
294. Ch. 29 — Omron. OMRON Healthcare to Set Up Its First Manufacturing Factory in India. 7 Jun 2023. https://www.omron.com/apac/en/stories/health-care/OMRON-Healthcare-Factory-In-India (company's own)
295. Ch. 29 — Omron Healthcare Co., Ltd. OMRON Healthcare Plans India-Based Factory. 2 Jun 2023. https://healthcare.omron.com/news-media/press-release/49 (company's own)
296. Ch. 29 — BioSpectrum Asia. Japan's Omron Healthcare to soon roll out Made-in-India blood pressure monitors. 11 Jul 2025. https://www.biospectrumasia.com/news/49/26334/japans-omron-healthcare-to-soon-roll-out-made-in-india-blood-pressure-monitors.html (secondary, quoting Omron Healthcare India)
297. Ch. 29 — Morepen Laboratories Ltd. Intimation of analyst/investor call, Q2 FY2021-22. 10 Nov 2021. https://bseindia.com/xml-data/corpfiling/AttachHis/11dfff65-d040-44dc-a45f-c25f61a6f225.pdf (company's exchange filing)
298. Ch. 29 — Morepen Laboratories Ltd. Morepen Labs Q1 FY25 Profit Surges by 147%, Revenue Grows by 14%. 12 Aug 2024. https://morepen.com/public/uploads/media/Morepen66b9bc60d76da.pdf (company's own)
299. Ch. 29 — BPL Medical Technologies. BPL 120/80 B21. https://www.bplmedicaltechnologies.com/product-details/bp-monitors/bpl-120-80-b21/ (seller's product page)
300. Ch. 29 — Nemko Scandinavia AS. ISO 9001:2015 certificate NO-801491, Skanray Technologies Limited. 29 Aug 2024. https://skanray.com/wp-content/uploads/2024/09/ISO-9001-2015-1.pdf
301. Ch. 29 — Skanray Technologies. About us. https://world.skanray.com/about-us/ (company's own)
302. Ch. 30 — CIPM President. Statement to the 28th CGPM. Oct 2026. https://www.bipm.org/documents/d/guest/statement-cipm-president-cgpm-2026
303. Ch. 30 — OIML. International vocabulary of terms in legal metrology (VIML). OIML V 1, Edition 2022 (E/F), entries 1.01, 2.01, 2.09. https://www.oiml.org/
304. Ch. 30 — Global ACI. Recognised accreditation bodies (list), last modified 21 Jul 2026; OIML–Global ACI memorandum of understanding, 14 Apr 2026. https://globalaci.org/
305. Ch. 30 — NIST Office of Weights and Measures. OIML update to the National Conference on Weights and Measures annual meeting, 2026 (US national legal-metrology body)
306. Ch. 30 — Government of India. The Legal Metrology Act, 2009 (Act No. 1 of 2010), India Code. https://www.indiacode.nic.in/handle/123456789/2102
307. Ch. 30 — Department of Consumer Affairs, Government of India. The Legal Metrology Act, 2009, and rules (overview and rules pages). https://consumeraffairs.gov.in/pages/legal-metrology-act (regulator's own pages)
308. Ch. 30 — TaxGuru (Editor6). Legal Metrology (General) Amendment Rules, 2026, G.S.R. 10(E), 7 Jan 2026 (reproduction of the notification replacing Part VII-A). https://taxguru.in/?p=1017895 (secondary reproduction)
309. Ch. 30 — TaxGuru (Editor6). Draft rules for non-invasive non-automated sphygmomanometers, DoCA public notice of 31 Jul 2025. https://taxguru.in/?p=979264 (secondary reproduction of a draft; DoCA published the new Part VII-A in draft for public comment on 31 July 2025, with comments due by 30 August 2025, and its limits, test method and three-sample requirement are those of the final rule of 7 January 2026)
310. Ch. 30 — Department of Consumer Affairs. Legal Metrology (General) Seventh Amendment Rules, 2025, G.S.R. 905(E), 18 Dec 2025, substituting rule 27(2)(a). https://consumeraffairs.gov.in/ (issuer's own publication)
311. Ch. 30 — NIST Office of Weights and Measures. NIST Handbook 44, Current Edition (2026), page updated 6 Jan 2026; table of contents of the 2022 edition. https://www.nist.gov/pml/owm/publications/nist-handbooks/handbook-44
312. Ch. 30 — European Union. Directive (EU) 2026/706 of the European Parliament and of the Council of 11 March 2026 amending Directive 2014/32/EU. CELEX 32026L0706. https://eur-lex.europa.eu/eli/dir/2026/706/oj
313. Ch. 30 — Department of Consumer Affairs, Government of India. Legal Metrology (overview). Last updated 22 Sep 2026. https://consumeraffairs.gov.in/pages/legal-metrology-overview (regulator's own page)
314. Ch. 30 — Government of India, Ministry of Consumer Affairs, Food and Public Distribution. Notification of 31 Jan 2011 appointing 1 April 2011 for the coming into force of the Legal Metrology Act, 2009, and rescinding S.O. 1(E) of 31 Dec 2010. Republished in Manipur Gazette Extraordinary No. 525A, 14 Feb 2011. https://www.manipurgovtpress.nic.in/media/gazzete/EOG_525A_14-02-2011.pdf (State government's republication)
315. Ch. 31 — US Food and Drug Administration. Medical device recall database and openFDA enforcement records, event 98049: FreeStyle Libre 3 and 3 Plus sensors, four Class I records, initiated 24 Nov 2025, classified 13 Jan 2026. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfRES/res.cfm (regulator's record)
316. Ch. 31 — FDA. Glucose Monitor Sensor Recall: Abbott Diabetes Care Removes Certain FreeStyle Libre 3 and FreeStyle Libre 3 Plus Sensors. 5 Feb 2026. https://www.fda.gov/medical-devices/medical-device-recalls-and-early-alerts/glucose-monitor-sensor-recall-abbott-diabetes-care-removes-certain-freestyle-libre-3-and-freestyle
317. Ch. 31 — Abbott. Abbott Initiates Medical Device Correction for Certain FreeStyle Libre 3 and FreeStyle Libre 3 Plus Sensors in the U.S. 24 Nov 2025 (posted by FDA 15 Jan 2026). https://www.fda.gov/safety/recalls-market-withdrawals-safety-alerts/abbott-initiates-medical-device-correction-certain-freestyle-librer-3-and-freestyle-libre-3-plus (company's own)
318. Ch. 31 — US Food and Drug Administration. Product Classification, product code DXN, Noninvasive blood pressure measurement system, 21 CFR 870.1130. https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfPCD/classification.cfm?ID=DXN
319. Ch. 31 — US Food and Drug Administration. Recognized Consensus Standards: IEC 80601-2-30 Edition 2.0 2018-03, recognition 3-123, entered 6 Jul 2020, partial recognition (clause 211.8.3.1, ingress of water or particulate matter, not recognized). https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfStandards/detail.cfm?standard__identification_no=41130
320. Ch. 31 — FDA. Warning letter to Linemaster Switch Corporation. CMS #730215. 27 May 2026. https://www.fda.gov/inspections-compliance-enforcement-and-criminal-investigations/warning-letters/linemaster-switch-corporation-730215-05272026
321. Ch. 31 — European Union. Regulation (EU) 2017/746 on in vitro diagnostic medical devices (IVDR), as adopted: Annex I section 9.3. https://www.legislation.gov.uk/eur/2017/746
322. Ch. 31 — European Commission. Implementing Decision (EU) 2022/15 of 6 January 2022 amending Implementing Decision (EU) 2021/1195 as regards harmonised standards (metrological traceability of values assigned to calibrators). https://eur-lex.europa.eu/eli/dec_impl/2022/15/oj
323. Ch. 31 — Covington & Burling. European Commission announces long-awaited proposal to simplify EU medical device regulations. 16 Dec 2025. https://www.covingtonblogs.com/2025/12/16/european-commission-announces-long-awaited-proposal-to-simplify-eu-medical-device-regulations/ (law firm)
324. Ch. 31 — Emergo by UL (A. van Raamsdonk). Europe targets revised MDR and IVDR adoption Q2–Q3 2027. 9 Oct 2026. https://www.emergobyul.com/news/europe-targets-revised-mdr-and-ivdr-adoption-q2-q3-2027 (consultancy)
325. Ch. 31 — CDSCO. Updation of existing risk based classification list, Cardiovascular (Annexure I), file dated 1 Apr 2025, F. No. MED-16015(11)/1/2025-eoffice. https://cdsco.gov.in/ (regulator's draft list)
326. Ch. 31 — Koul S. CDSCO issues revised risk classification list for cardiovascular devices. Business Standard. 2 Apr 2025 (newspaper)
327. Ch. 31 — DIN Media. DIN EN IEC 80601-2-30 (VDE 0750-2-30):2026-06, draft, issued 29 May 2026, based on IEC 62D/2201/CDV:2025 (national publisher; draft)
328. Ch. 31 — Fricke R.W. Jr. STS-61 Space Shuttle Mission Report. NASA-TM-110545, NSTS-08288. 1 Feb 1994. https://ntrs.nasa.gov/citations/19950016770 (WFPC2, built at NASA's Jet Propulsion Laboratory, was installed on the mission's third spacewalk)
329. Ch. 31 — NASA Science. Servicing Mission 1 (SM1). 5 Oct 2022, updated 16 Apr 2024. https://science.nasa.gov/mission/hubble/observatory/missions-to-hubble/servicing-mission-1 (agency public page; COSTAR, built by Ball Aerospace, was installed on the fourth spacewalk)
330. Ch. 31 — Space Telescope Science Institute. WFPC2 Instrument Handbook, section 5.2, Aberration Correction. https://www.stsci.edu/instrument-news/handbooks/wfpc2/W2_47.html
331. Ch. 31 — NASA Science. The Camera That Saved Hubble. 4 Dec 2018, updated 4 Oct 2023. https://science.nasa.gov/missions/hubble/the-camera-that-saved-hubble (agency public page; the first raw data from WFPC2 came down on 18 December 1993)
332. Ch. 31 — ESA. Hubble Space Telescope can see clearly now. Press Release N° 3-1994. 13 Jan 1994. https://www.esa.int/Newsroom/Press_Releases/Hubble_Space_Telescope_can_see_clearly_now
333. Ch. 31 — Litvak M.M. (TRW, for JPL). Image Inversion Analysis of the HST OTA, Technical Final Report, Phase A. 15 Mar 1991, revised 18 Jul 1991. https://ntrs.nasa.gov/citations/19920020116 (contractor report)
334. Ch. 31 — Meinel A.B., Meinel M.P., Schulte D.H. Determination of the Hubble Space Telescope effective conic-constant error from direct image measurements. Applied Optics 32(10), 1993. https://ntrs.nasa.gov/citations/19930050633
335. Ch. 31 — Rodney G.A. (NASA Office of Safety and Mission Quality). Hubble Space Telescope SRM&QA Observations and Lessons Learned. NASA. https://ntrs.nasa.gov/citations/19920008654
336. Ch. 31 — European Union. Regulation (EU) 2017/745 of the European Parliament and of the Council of 5 April 2017 on medical devices (MDR), as adopted: Annex I sections 15.1 and 15.2; Annex VIII Rule 10; Article 52(7). https://www.legislation.gov.uk/eur/2017/745 (reproduction of the adopted text; Annex I read at https://www.legislation.gov.uk/eur/2017/745/annex/I/adopted)