ISO/IEC Guide 98-1:2024

Guide 98-1
Second edition
Guide to the expression of
2024-02
uncertainty in measurement —
Part 1:
Introduction
Guide pour l'expression de l'incertitude de mesure —
Partie 1: Introduction
Reference number
© ISO/IEC 2024
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ii
ISO/IEC Foreword
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— most conceptual and technical aspects have been removed.
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iii
Joint Committee for Guides in Metrology
Guide to the expression of uncertainty in measurement
— Part 1: Introduction
Guide pour l’expression de l’incertitude de mesure — Partie 1:
Introduction
JCGM GUM-1:2023
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ii JCGM GUM-1:2023
© JCGM 2023
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JCGM GUM-1:2023 iii
Contents
Page
Foreword iv
1 Scope 1
2 Rationale 1
3 Measurement 2
4 Guidance on evaluating measurement uncertainty 3
5 Parts of the GUM 5
5.1 Using the law of propagation of uncertainty (JCGM 100:2008) . . . . . . . . . . . . . 5
5.2 Conformity assessment (JCGM 106:2012) . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.3 Measurement models (JCGM GUM-6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5.4 Propagation of distributions (JCGM 101:2008) . . . . . . . . . . . . . . . . . . . . . . . 7
5.5 Extension to any number of output quantities (JCGM 102:2011) . . . . . . . . . . . . 8
Annexes 9
A Overview of the parts of the GUM 9
References 10
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iv JCGM GUM-1:2023
Foreword
In 1997 a Joint Committee for Guides in Metrology (JCGM), chaired by the Director of the
Bureau International des Poids et Mesures (BIPM), was created by the seven international
organizations that had originally in 1993 prepared the ‘Guide to the expression of uncer-
tainty in measurement’ and the ‘International vocabulary of basic and general terms in
metrology’. The JCGM assumed responsibility for these two documents from the Technical
Advisory Group 4 of the International Organization for Standardization (ISO/TAG4).
The Joint Committee is formed by the BIPM with the International Electrotechnical Com-
mission (IEC), the International Federation of Clinical Chemistry and Laboratory Medicine
(IFCC), the International Laboratory Accreditation Cooperation (ILAC), the International
Organization for Standardization (ISO), the International Union of Pure and Applied Chem-
istry (IUPAC), the International Union of Pure and Applied Physics (IUPAP) and the Inter-
national Organization of Legal Metrology (OIML).
JCGM has two Working Groups. Working Group 1, ‘Expression of uncertainty in mea-
surement’, has the task to promote the use of the ‘Guide to the expression of uncertainty
in measurement’ and to prepare documents for its broad application. Working Group 2,
‘Working Group on International vocabulary of basic and general terms in metrology’, has
the task to revise and promote the use of the ‘International vocabulary of basic and general
terms in metrology’ (the ‘VIM’).
In 2008 the JCGM made available a slightly revised version (mainly correcting minor er-
rors) of the ‘Guide to the expression of uncertainty in measurement’, labelling the docu-
ment ‘JCGM 100:2008’.
In 2017 the JCGM rebranded the documents in its portfolio that have been produced by
Working Group 1 or are to be developed by that Group. The whole suite of documents is
now known as the ‘Guide to the expression of uncertainty in measurement’ or ‘GUM’, and
is concerned with the evaluation and expression of measurement uncertainty, as well as
its application in science, trade, health, safety and other societal activities.
This part of the suite introduces the processes involved and the subsequent parts in this
suite giving specific guidance on these processes. This document replaces JCGM 104:2009.
This document has been prepared by Working Group 1 of the JCGM, and has benefited
from detailed reviews undertaken by member organizations of the JCGM and National
Metrology Institutes.
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JCGM GUM-1:2023 1
Guide to the expression of uncertainty in
measurement — Part 1: Introduction
1 Scope
The ‘Guide to the expression of uncertainty in measurement’ (GUM) establishes general
rules for evaluating and expressing uncertainty in measurement from the shop floor to
fundamental research. Therefore, the principles of this suite of documents are intended to
be applicable to a broad spectrum of measurements and their applications. An overview
of the parts of the GUM is given in table A.1 in Annex A.
NOTE Where the acronym GUM is used in this document, it refers to the suite of documents. An
individual part of the GUM is referred to by its corresponding JCGM numbering (e.g., part 6 of the
GUM is JCGM GUM-6:2020).
This document gives a rationale for evaluating, expressing and using measurement un-
certainty (Clause 2). A brief introduction is given to measurement (Clause 3) and to the
decisions involved when evaluating measurement uncertainty (Clause 4). In Clause 5, a
brief description of the contents of the parts of the GUM is given. In each of these clauses,
the relevant parts of the GUM are identified for further guidance.
2 Rationale
2.1 Measurement [12, Definition 2.1] is one of the most common processes in human
activity. Measured values of quantities [12, Definition 2.10] are required for a diverse
range of applications and, for each of these values, a statement is needed about its credi-
bility. Such a statement is usually expressed in terms of measurement uncertainty[12, Def-
inition 2.26]. The two components, the measured value and the associated uncertainty,
together constitute the most common way of reporting a measurement result[12, Defini-
tion 2.9]. In cases where values for more than one quantity are provided by the measure-
ment, a more elaborate statement of the uncertainty is often required (Clause 5.5; see also
Clause 3.1).
2.2 Measurements are performed in many branches of society for widely different pur-
poses. Many measurements performed on a daily basis, often in automated processes,
concern trade and commerce. Reliable measurement results are also needed for mak-
ing informed decisions in for example health, safety, weather forecasts, law enforcement
and science. Measurements are performed by for example greengrocers, technicians, en-
gineers, laboratory staff, health care professionals, scientists and individuals at home, in
very different contexts.
2.3 Many measurements are made for the purpose of comparison of results with speci-
fications. Such a comparison can be made for widely different purposes. This activity is
generally known as conformity assessment [3, Definition 4.1] [10, Definition 3.3.1]; see
also Clause 5.2.
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2 JCGM GUM-1:2023
2.4 Comparison of measurement results is an essential activity in science, calibration and
testing. Compatibility of measurement results [12, Definition 2.47] is the basis for being
able to reproduce scientific findings, performing quality assurance and quality control, and
providing the interpretation of measurement results and informed decision making. Many
standards that set requirements for demonstrating competence in measurement require
evaluating measurement uncertainty and identifying the major sources of uncertainty, for
example ISO/IEC 17025 (calibration and testing laboratories) [4], ISO 17034 (reference
material producers)[5], ISO/IEC 17043 (proficiency testing)[6] and ISO 15189 (medical
laboratories)[2].
2.5 Measurement uncertainty is of importance in various situations, including but not
limited to:
— comparison of measurement results,
— comparison of a measured value with specification limits (conformity assessment),
— establishing metrological traceability[12, Definition 2.41],
— applying a decision rule[10, Definition 3.3.12],
— calculating risks and risk assessment,
— comparison of model outputs and experiments,
— evaluating the validity of models,
— setting limits for the values of physical quantities,
— validating or developing scientific theories, and
— propagation of uncertainty from one measurement to another.
2.6 The GUM substantially contributes to the harmonization of methods for the evalua-
tion, expression and use of measurement uncertainty. It supports the mutual recognition
of calibration certificates and laboratory accreditations. The principles and methods of the
GUM have been adopted in many documentary standards of ISO, IEC and other standards
development organizations. Much software used by laboratories worldwide is based on
the provisions of the GUM.
3 Measurement
3.1 The quantity intended to be measured is called the measurand[12, Definition 2.3].
A measurement can have the objective of determining values and associated uncertainties
for a set of output quantities, rather than a single quantity. Then the measurand is said to
be multivariate. The measurement result is represented by the measured values and the
measurement uncertainty.
3.2 Measurement [12, Definition 2.1] can be described as an experimental or compu-
tational process that, by comparison with a measurement standard [12, Definition 5.1],
produces an estimate of the true value [12, Definition 2.11] of a property, together with
a statement of the uncertainty associated with that estimate, and intended for use in sup-
port of decision making. This property can be of a material or virtual object or collection
of objects, or of a process, event or series of events[19].
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JCGM GUM-1:2023 3
NOTE The GUM takes a broad view of ‘measurement’ in that it recognises that there are instances
where the process concerned is essentially computational or where the measurement result is of a
conceptual or theoretical nature[7, Clause 1.3].
3.3 In the description of ‘measurement’ (see Clause 3.2), an estimate[1, Definition 1.31]
is an approximation of the true value [12, Definition 2.11] of the property of interest.
Another term sometimes used for estimate is measured value [12, Definition 2.10]. By
‘comparison with a measurement standard’ (see Clause 3.2), it is meant that somewhere
in the process a measurement standard is used to obtain an estimate that is metrologically
traceable to the relevant measurement unit[12, Definition 1.9].
3.4 Measurement uncertainty is the doubt about the true value of the measurand that re-
mains after making a measurement. Measurement uncertainty can be expressed in various
ways. Commonly used ways include:
— a standard uncertainty[12, Definition 2.30],
— an expanded uncertainty [7, Definition 2.3.5] with a coverage factor [7, Defini-
tion 2.3.6],
— a coverage interval[12, Definition 2.36] with a stated coverage probability[9, Defi-
nition 3.25], or
— a probability distribution describing the knowledge about the measurand[8, Defini-
tion 3.1], often expressed as a probability density function[8, Definition 3.3].
3.5 A measurement result should be presented in a way that is understandable and usable
by its recipient. The measurement result should therefore include all information needed
for its intended use[7, Clause 7]. The information available depends on whether the law
of propagation of uncertainty (Clause 5.1), the propagation of distributions (Clause 5.4),
or another method[11, Clause 11] has been used for the evaluation of measurement un-
certainty.
4 Guidance on evaluating measurement uncertainty
4.1 The evaluation of measurement uncertainty is neither a routine task nor a purely
mathematical one. It depends on detailed knowledge of the nature of the measurand and
the measurement. The quality and utility of the measurement result therefore ultimately
depend on the understanding, critical analysis, and diligence of those who contribute to
that result[7, Clause 3.4.8].
4.2 In selecting a method of uncertainty evaluation that suits the current needs, the user
should consider the following:
1. the information available,
2. the assumptions to be made,
3. the nature of the results required (see Clause 4.3),
4. the extent to which use is to be made of the information available.
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4 JCGM GUM-1:2023
4.3 Alongside the estimate of the measurand, results required from the uncertainty prop-
agation comprise some or all of:
1. standard uncertainty associated with the estimate,
2. coverage interval for the measurand for a stated coverage probability,
3. probability distribution for the measurand.
NOTE 1 The probability distribution for the measurand in Clause 4.3 bullet 3 is the most complete
description of the output quantity in terms of the information used. The estimate and the items 1
and 2 can be obtained from it.
NOTE 2 The propagation of distributions (see Clause 5.5) provides the probability distribution for
the measurand[8,9].
NOTE 3 In the case of a multivariate measurand, Clause 4.3 bullets 1 and 2 are generalized: see
also Clause 5.5.
4.4 The following information is required for uncertainty propagation:
— A measurement model (mathematical or algorithmic) suitable for the current ap-
plication, containing input quantities [12, Definition 2.50] of which the user has
knowledge and an output quantity (measurand) for which results are required[11],
— Either
* an estimate of each input quantity – from statistical analysis of observations or
provided by other means, and
* the standard uncertainty associated with each estimate and, when appropriate,
the degrees of freedom[1, Definition 2.54] and correlations[1, Definition 2.44]
between estimates, or
— a joint probability distribution for the input quantities.
NOTE 1 Guidance on quantifying correlation is given in[7, Clause 5.2] and[11, Clause 10.5].
NOTE 2 Probability distributions for the input quantities are often specified in uncertainty budgets
[12, Definition 2.33].
NOTE 3 Guidance on obtaining probability distributions for the input quantities is given in [8,
clause 6].
NOTE 4 Guidance on degrees of freedom in the simplest case of uncorrelated repeated observa-
tions of an input quantity is given in[7, Annex G] and[9, Clause 6.5.3] for a set of quantities.
4.5 To propagate measurement uncertainty using a measurement model (see also
Clause 5.3), it is important to consider what information is available and what is re-
quired[11, Clauses 5.1, 5.3, 5.8 and 5.9]. Also the resources necessary to take account of
the information are important. Such resources include, for example, human effort, math-
ematical or similar skills and computational capabilities. Finally, consideration should be
given to how the evaluated uncertainty will be used[11, Clauses 12 and 13].
4.6 Taking account of all available knowledge might require the services of a professional
statistician, a da
...