SIST-TS ISO/TS 21748:2006
(Main)Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation
Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation
The Technical Specification gives guidance for - evaluation of measurement uncertainties using data obtained from studies conducted in accordance with ISO 5725-2:1994; - comparison of collaborative study results with measurement uncertainty (MU) obtained using formal principles of uncertainty propagation (see Clause 14). ISO 5725-3:1994 provides additional models for studies of intermediate precision. However, while the same general approach may be applied to the use of such extended models, uncertainty evaluation using these models is not incorporated in the present Technical Specification. This Technical Specification is applicable in all measurement and test fields where an uncertainty associated with a result has to be determined. This Technical Specification does not describe the application of repeatability data in the absence of reproducibility data. This Technical Specification assumes that recognized, non-negligible systematic effects are corrected, either by applying a numerical correction as part of the method of measurement, or by investigation and removal of the cause of the effect. The recommendations in this Technical Specification are primarily for guidance. It is recognized that while the recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is also possible to adopt other suitable approaches. In general, references to measurement results, methods and processes in this Technical Specification are normally understood to apply also to testing results, methods and processes.
Lignes directrices relatives à l'utilisation d'estimations de la répétabilité, de la reproductibilité et de la justesse dans l'évaluation de l'incertitude de mesure
L'ISO/TS 21748:2004 donne des lignes directrices en vue, d'une part, d'évaluer l'incertitude de mesure à partir de données obtenues lors d'études menées conformément à l'ISO 5725-2 et, d'autre part, de comparer les résultats d'une étude collaborative à l'incertitude de mesure obtenue en appliquant des principes formels de propagation de l'incertitude. L'ISO/TS 21748:2004 est applicable dans tous les domaines de mesure et d'essai nécessitant la détermination d'une incertitude associée à un résultat, mais ne décrit pas l'utilisation de données de répétabilité en l'absence de données de reproductibilité. Les recommandations de ce document sont avant tout indicatives.
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TECHNICAL ISO/TS
SPECIFICATION 21748
First edition
2004-03-15
Guidance for the use of repeatability,
reproducibility and trueness estimates in
measurement uncertainty estimation
Lignes directrices relatives à l'utilisation d'estimations de la répétabilité,
de la reproductibilité et de la justesse dans l'évaluation de l'incertitude
de mesure
Reference number
ISO/TS 21748:2004(E)
©
ISO 2004
---------------------- Page: 1 ----------------------
ISO/TS 21748:2004(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2004
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2004 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TS 21748:2004(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Symbols . 4
5 Principles . 7
5.1 Individual results and measurement process performance. 7
5.2 Applicability of reproducibility data. 7
5.3 Basic equations for the statistical model. 7
5.4 Repeatability data . 8
6 Evaluating uncertainty using repeatability, reproducibility and trueness estimates . 8
6.1 Procedure for evaluating measurement uncertainty. 8
6.2 Differences between expected and actual precision . 9
7 Establishing the relevance of method performance data to measurement results from a
particular measurement process . 9
7.1 General. 9
7.2 Demonstrating control of the laboratory component of bias. 9
7.3 Verification of repeatability. 11
7.4 Continued verification of performance. 12
8 Establishing relevance to the test item . 12
8.1 General. 12
8.2 Sampling . 12
8.3 Sample preparation and pre-treatment. 13
8.4 Changes in test-item type . 13
8.5 Variation of uncertainty with level of response . 13
9 Additional factors. 14
10 General expression for combined standard uncertainty. 14
11 Uncertainty budgets based on collaborative study data. 15
12 Evaluation of uncertainty for a combined result . 16
13 Expression of uncertainty information . 17
13.1 General expression. 17
13.2 Choice of coverage factor. 17
14 Comparison of method performance figures and uncertainty data . 17
14.1 Basic assumptions for comparison . 17
14.2 Comparison procedure. 18
14.3 Reasons for differences . 18
Annex A (informative) Approaches to uncertainty estimation. 19
Annex B (informative) Experimental uncertainty evaluation . 24
Annex C (informative) Examples of uncertainty calculations. 25
Bibliography . 29
© ISO 2004 – All rights reserved iii
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ISO/TS 21748:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of normative document:
an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TS 21748 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
iv © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
Introduction
Knowledge of the uncertainty associated with measurement results is essential to the interpretation of the
results. Without quantitative assessments of uncertainty, it is impossible to decide whether observed
differences between results reflect more than experimental variability, whether test items comply with
specifications, or whether laws based on limits have been broken. Without information on uncertainty, there is
a risk of misinterpretation of results. Incorrect decisions taken on such a basis may result in unnecessary
expenditure in industry, incorrect prosecution in law, or adverse health or social consequences.
Laboratories operating under ISO 17025 accreditation and related systems are accordingly required to
evaluate measurement uncertainty for measurement and test results and report the uncertainty where relevant.
The Guide to the expression of uncertainty in measurement (GUM), published by ISO, is a widely adopted
standard approach. However, it applies to situations where a model of the measurement process is available.
A very wide range of standard test methods is, however, subjected to collaborative study in accordance with
ISO 5725-2:1994. This Technical Specification provides an appropriate and economic methodology for
estimating uncertainty associated with the results of these methods, which complies fully with the relevant
principles of the GUM, whilst taking account of method performance data obtained by collaborative study.
The general approach used in this Technical Specification requires that
estimates of the repeatability, reproducibility and trueness of the method in use, obtained by collaborative
study as described in ISO 5725-2:1994, be available from published information about the test method in
use. These provide estimates of the intra- and inter-laboratory components of variance, together with an
estimate of uncertainty associated with the trueness of the method;
the laboratory confirm that its implementation of the test method is consistent with the established
performance of the test method by checking its own bias and precision. This confirms that the published
data are applicable to the results obtained by the laboratory;
any influences on the measurement results that were not adequately covered by the collaborative study
be identified and the variance associated with the results that could arise from these effects be quantified.
An uncertainty estimate is made by combining the relevant variance estimates in the manner prescribed by
the GUM.
The dispersion of results obtained in a collaborative study is often also usefully compared with measurement
uncertainty estimates obtained using GUM procedures as a test of full understanding of the method. Such
comparisons will be more effective given a consistent methodology for estimating the same parameter using
collaborative study data.
© ISO 2004 – All rights reserved v
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TECHNICAL SPECIFICATION ISO/TS 21748:2004(E)
Guidance for the use of repeatability, reproducibility and
trueness estimates in measurement uncertainty estimation
1 Scope
The Technical Specification gives guidance for
evaluation of measurement uncertainties using data obtained from studies conducted in accordance with
ISO 5725-2:1994;
comparison of collaborative study results with measurement uncertainty (MU) obtained using formal
principles of uncertainty propagation (see Clause 14).
ISO 5725-3:1994 provides additional models for studies of intermediate precision. However, while the same
general approach may be applied to the use of such extended models, uncertainty evaluation using these
models is not incorporated in the present Technical Specification.
This Technical Specification is applicable in all measurement and test fields where an uncertainty associated
with a result has to be determined.
This Technical Specification does not describe the application of repeatability data in the absence of
reproducibility data.
This Technical Specification assumes that recognized, non-negligible systematic effects are corrected, either
by applying a numerical correction as part of the method of measurement, or by investigation and removal of
the cause of the effect.
The recommendations in this Technical Specification are primarily for guidance. It is recognized that while the
recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is
also possible to adopt other suitable approaches.
In general, references to measurement results, methods and processes in this Technical Specification are
normally understood to apply also to testing results, methods and processes.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms
ISO 5725-3:1994, Accuracy (trueness and precision) of measurement methods and results — Part 3:
Intermediate measures of the precision of a standard measurement method
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ISO/TS 21748:2004(E)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply. In addition, reference is made to
“intermediate precision conditions”, which are discussed in detail in ISO 5725-3:1994.
3.1
bias
difference between the expectation of the test results and an accepted reference value
NOTE Bias is the total systematic error as contrasted to random error. There may be one or more systematic error
components contributing to the bias. A larger systematic difference from the accepted reference value is reflected by a
larger bias value.
[ISO 3534-1]
3.2
combined standard uncertainty
u(y)
standard uncertainty of the result of a measurement when that result is obtained from the values of a number
of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariances of these other quantities weighted according to how the measurement result varies with changes
in these quantities
[GUM]
3.3
coverage factor
k
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty
NOTE A coverage factor, k, is typically in the range 2 to 3.
[GUM]
3.4
expanded uncertainty
U
quantity defining an interval about a result of a measurement expected to encompass a large fraction of the
distribution of values that could reasonably be attributed to the measurand
NOTE 1 The fraction may be regarded as the coverage probability or level of confidence of the interval.
NOTE 2 To associate a specific level of confidence with the interval defined by the expanded uncertainty requires
explicit or implicit assumptions regarding the probability distribution characterised by the measurement result and its
combined standard uncertainty. The level of confidence that may be attributed to this interval can be known only to the
extent to which such assumptions can be justified.
NOTE 3 Expanded uncertainty is termed overall uncertainty in Recommendation INC-1 (1980), paragraph 5.
[GUM]
3.5
precision
closeness of agreement between independent test results obtained under stipulated conditions
NOTE 1 Precision depends upon the distribution of random errors and does not relate to the true value or the specified
value.
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ISO/TS 21748:2004(E)
NOTE 2 The measure of precision is usually expressed in terms of imprecision and computed as a standard deviation
of the test results. Less precision is reflected by a higher standard deviation.
NOTE 3 “Independent test results” means results obtained in a manner not influenced by any previous result on the
same or similar test object. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability
and reproducibility conditions are particular examples of extreme stipulated conditions.
[ISO 3534-1]
3.6
repeatability
precision under repeatability conditions, i.e. conditions where independent test results are obtained with the
same method on identical test items in the same laboratory by the same operator using the same equipment
within short intervals of time
[ISO 3534-1]
3.7
repeatability standard deviation
standard deviation of test results obtained under repeatability conditions
NOTE This is a measure of dispersion of the distribution of test results under repeatability conditions. Similarly
“repeatability variance” and “repeatability coefficient of variation” can be defined and used as measures of the dispersion
of test results under repeatability conditions.
[ISO 3534-1]
3.8
reproducibility
precision under reproducibility conditions, i.e. conditions where test results are obtained with the same method
on identical test items in different laboratories with different operators using different equipment
NOTE A valid statement of reproducibility requires specification of the conditions changed. Reproducibility may be
expressed quantitatively in terms of the dispersion of the results.
[ISO 3534-1]
3.9
reproducibility standard deviation
standard deviation of test results obtained under reproducibility conditions
NOTE This is a measure of dispersion of the distribution of test results under reproducibility conditions. Similarly
“reproducibility variance” and “reproducibility coefficient of variation” could be defined and used as measures of the
dispersion of test results under reproducibility conditions.
[ISO 3534-1]
3.10
standard uncertainty
u(x )
i
uncertainty of the result of a measurement expressed as a standard deviation
[GUM]
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ISO/TS 21748:2004(E)
3.11
trueness
closeness of agreement between the average value obtained from a large set of test results and an accepted
reference value
NOTE The measure of trueness is normally expressed in terms of bias. The reference to trueness as “accuracy of
the mean” is not generally recommended.
[ISO 3534-1]
3.12
uncertainty
〈measurement〉 parameter, associated with the result of a measurement, that characterizes the dispersion of
the values that could reasonably be attributed to the measurand
NOTE 1 The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an
interval having a stated level of confidence.
NOTE 2 Uncertainty of measurement comprises, in general, many components. Some of these components may be
evaluated from the statistical distribution of the results of a series of measurements and can be characterized by
experimental standard deviations. Other components, which also can be characterized by standard deviations, are
evaluated from assumed probability distributions based on experience or other information.
NOTE 3 It is understood that the result of the measurement is the best estimate of the value of the measurand, and
that all components of uncertainty, including those arising from systematic effects such as components associated with
corrections and reference standards, contribute to the dispersion.
[GUM]
3.13
uncertainty budget
list of sources of uncertainty and their associated standard uncertainties, compiled with a view to evaluating a
combined standard uncertainty associated with a measurement result
NOTE The list often includes additional information such as sensitivity coefficients (rate of change of result with
change in a quantity affecting the result), degrees of freedom for each standard uncertainty, and an identification of the
means of evaluating each standard uncertainty in terms of a Type A or Type B evaluation.
4 Symbols
a coefficient indicating an intercept in the empirical relationship sˆ =+abm
R
B laboratory component of bias
b coefficient indicating a slope in the empirical relationship sˆ =+abm
R
d
c coefficient in the empirical relationship sˆ = cm
R
c sensitivity coefficient ∂∂yx/
i i
d
d coefficient indicating an exponent in the empirical relationship sˆ = cm
R
e random residual error
e random residual error under repeatability conditions
r
k numerical factor used as a multiplier of the combined standard uncertainty u in order to obtain an
expanded uncertainty U
l laboratory number
4 © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
m mean value of the measurements
N number of contributions included in combined uncertainty calculations
′
n number of contributions incorporated in combined uncertainty calculations in addition to collaborative
study data
n number of replicates at one level by laboratory l
l
n number of replicate measurements
r
p number of laboratories
Q number of test items from a larger batch
q number of assigned values by consensus during a collaborative study
r correlation coefficient between x and x , in the range −1 to +1
ij i j
s between-group component of variance expressed as a standard deviation
b
2
s between-group component of variance
b
s estimated, or experimental, standard deviation of results obtained by repeated measurement on a
D
reference material used for checking control of bias
s repeatability standard deviation with ν degrees of freedom
i i
s uncertainty associated with the inhomogeneity of the sample
inh
2
s component of variance associated with the inhomogeneity of the sample
inh
s experimental or estimated inter-laboratory standard deviation
L
ˆ
s adjusted uncertainty associated with B where the contribution is dependent on the response
L
2
s the estimated variance of B
L
s intra-laboratory standard deviation
r
ˆ
s adjusted estimate of inter-laboratory standard deviation, where the contribution is dependent on the
r
response
2
s estimated variance of e
r
r
s estimated reproducibility standard deviation
R
′
s adjusted estimate of the reproducibility standard deviation
R
ˆ
s adjusted reproducibility standard deviation calculated from an empirical model, where the contributions
R
are dependent on the response
s intra-laboratory standard deviation derived from replicates or other repeatability studies
w
2
s intra-group component of variance (often an intra-laboratory component of variance)
w
s(∆ ) laboratory standard deviation of differences during a comparison of a routine method with a definitive
y
method
x value of the ith input value in the determination of a result
i
'
x deviation of the ith input value from the nominal value of x
i
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ISO/TS 21748:2004(E)
x the jth input value in the determination of a result
j
ˆ
u()δ uncertainty associated with δ due to the uncertainty of estimating δ by measuring a reference
ˆ
measurement standard or reference material with certified value µ
ˆ ˆ
u( µ ) uncertainty associated with the certified value µ
22
u(y) combined standard uncertainty associated with y where uy() = c u (x )
∑ii
in=1,
2
u(Y) combined uncertainty for the result Y = f(y , y , .) where uY() = c u(y )
1 2 ∑ ii
i
2
u (y) combined standard uncertainty associated with y, expressed as a variance
u uncertainty associated with sample inhomogeneity
inh
U expanded uncertainty, equal to k times the standard uncertainty u
U(y) expanded uncertainty in y where U(y) = ku(y), where k is a coverage factor
y result for test item i from the definitive method during a comparison of methods
i
ˆ
y result for test item i from the routine test method during a comparison of methods
i
y assigned value for proficiency testing
0
∆ laboratory bias
ˆ
∆ estimate of bias of laboratory l, equal to the laboratory mean, m, minus the certified value, µ
l
∆ mean laboratory bias during a comparison of a routine method with a definitive method
y
δ bias intrinsic to the measurement method in use
ˆ
δ estimated or measured bias
µ unknown expectation of the ideal result
ˆ
µ certified value of a reference material
σ standard deviation for proficiency testing
0
σ true value of the standard deviation of results obtained by repeated measurement on a reference
D
material used for checking control of bias
σ inter-laboratory standard deviation; standard deviation of B
L
2
σ variance of B; inter-laboratory variance
L
σ intra-laboratory standard deviation; standard deviation of e
r r
2
σ variance of e ; intra-laboratory variance
r
r
σ within-group standard deviation
w
σ standard deviation required for adequate performance (ISO Guide 33)
w0
ν effective degrees of freedom for the standard deviation of, or uncertainty associated with input value x
eff i
6 © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
ν number of degrees of freedom
i
5 Principles
5.1 Individual results and measurement process performance
5.1.1 Measurement uncertainty relates to individual results. Repeatability, reproducibility, and bias, by
contrast, relate to the performance of a measurement or testing process. For studies under all parts of
ISO 5725, the measurement or testing process will be a single measurement method, used by all laboratories
taking part in the study. Note that for the purposes of this Technical Specification, the measurement method is
assumed to be implemented in the form of a single detailed procedure (as defined in the International
Vocabulary of Basic and General Terms in Metrology). It is implicit in this Technical Specification that process-
performance figures derived from method-performance studies are relevant to all individual measurement
results produced by the process. It will be seen that this assumption requires supporting evidence in the form
of appropriate quality control and assurance data for the measurement process (Clause 7).
5.1.2 It will be seen below that differences between individual test items may additionally need to be taken
into account, but, with that caveat, it is unnecessary to undertake individual and detailed uncertainty studies
for every test item for a well characterized and stable measurement process.
5.2 Applicability of reproducibility data
The application of the principles of this Technical Specification is based on two principles.
First, the reproducibility standard deviation obtained in a collaborative study is a valid basis for
measurement uncertainty evaluation (see A.2.1).
Second, effects not observed within the context of the collaborative study must be demonstrably
negligible or explicitly allowed for. The latter principle is implemented by an extension of the basic model
used for collaborative study (see A.2.3).
5.3 Basic equations for the statistical model
5.3.1 The statistical model on which this guidance is based is formulated as in Equation (1):
yB=+µδ+ +cx′+e (1)
∑ ii
where
y is an observed result, assumed to be calculated from the equation: y = f(x , x , …, x );
1 2 n
µ is the (unknown) expectation of ideal
...
TECHNICAL ISO/TS
SPECIFICATION 21748
First edition
2004-03-15
Guidance for the use of repeatability,
reproducibility and trueness estimates in
measurement uncertainty estimation
Lignes directrices relatives à l'utilisation d'estimations de la répétabilité,
de la reproductibilité et de la justesse dans l'évaluation de l'incertitude
de mesure
Reference number
ISO/TS 21748:2004(E)
©
ISO 2004
---------------------- Page: 1 ----------------------
ISO/TS 21748:2004(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2004
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2004 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TS 21748:2004(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Symbols . 4
5 Principles . 7
5.1 Individual results and measurement process performance. 7
5.2 Applicability of reproducibility data. 7
5.3 Basic equations for the statistical model. 7
5.4 Repeatability data . 8
6 Evaluating uncertainty using repeatability, reproducibility and trueness estimates . 8
6.1 Procedure for evaluating measurement uncertainty. 8
6.2 Differences between expected and actual precision . 9
7 Establishing the relevance of method performance data to measurement results from a
particular measurement process . 9
7.1 General. 9
7.2 Demonstrating control of the laboratory component of bias. 9
7.3 Verification of repeatability. 11
7.4 Continued verification of performance. 12
8 Establishing relevance to the test item . 12
8.1 General. 12
8.2 Sampling . 12
8.3 Sample preparation and pre-treatment. 13
8.4 Changes in test-item type . 13
8.5 Variation of uncertainty with level of response . 13
9 Additional factors. 14
10 General expression for combined standard uncertainty. 14
11 Uncertainty budgets based on collaborative study data. 15
12 Evaluation of uncertainty for a combined result . 16
13 Expression of uncertainty information . 17
13.1 General expression. 17
13.2 Choice of coverage factor. 17
14 Comparison of method performance figures and uncertainty data . 17
14.1 Basic assumptions for comparison . 17
14.2 Comparison procedure. 18
14.3 Reasons for differences . 18
Annex A (informative) Approaches to uncertainty estimation. 19
Annex B (informative) Experimental uncertainty evaluation . 24
Annex C (informative) Examples of uncertainty calculations. 25
Bibliography . 29
© ISO 2004 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO/TS 21748:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of normative document:
an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TS 21748 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
iv © ISO 2004 – All rights reserved
---------------------- Page: 4 ----------------------
ISO/TS 21748:2004(E)
Introduction
Knowledge of the uncertainty associated with measurement results is essential to the interpretation of the
results. Without quantitative assessments of uncertainty, it is impossible to decide whether observed
differences between results reflect more than experimental variability, whether test items comply with
specifications, or whether laws based on limits have been broken. Without information on uncertainty, there is
a risk of misinterpretation of results. Incorrect decisions taken on such a basis may result in unnecessary
expenditure in industry, incorrect prosecution in law, or adverse health or social consequences.
Laboratories operating under ISO 17025 accreditation and related systems are accordingly required to
evaluate measurement uncertainty for measurement and test results and report the uncertainty where relevant.
The Guide to the expression of uncertainty in measurement (GUM), published by ISO, is a widely adopted
standard approach. However, it applies to situations where a model of the measurement process is available.
A very wide range of standard test methods is, however, subjected to collaborative study in accordance with
ISO 5725-2:1994. This Technical Specification provides an appropriate and economic methodology for
estimating uncertainty associated with the results of these methods, which complies fully with the relevant
principles of the GUM, whilst taking account of method performance data obtained by collaborative study.
The general approach used in this Technical Specification requires that
estimates of the repeatability, reproducibility and trueness of the method in use, obtained by collaborative
study as described in ISO 5725-2:1994, be available from published information about the test method in
use. These provide estimates of the intra- and inter-laboratory components of variance, together with an
estimate of uncertainty associated with the trueness of the method;
the laboratory confirm that its implementation of the test method is consistent with the established
performance of the test method by checking its own bias and precision. This confirms that the published
data are applicable to the results obtained by the laboratory;
any influences on the measurement results that were not adequately covered by the collaborative study
be identified and the variance associated with the results that could arise from these effects be quantified.
An uncertainty estimate is made by combining the relevant variance estimates in the manner prescribed by
the GUM.
The dispersion of results obtained in a collaborative study is often also usefully compared with measurement
uncertainty estimates obtained using GUM procedures as a test of full understanding of the method. Such
comparisons will be more effective given a consistent methodology for estimating the same parameter using
collaborative study data.
© ISO 2004 – All rights reserved v
---------------------- Page: 5 ----------------------
TECHNICAL SPECIFICATION ISO/TS 21748:2004(E)
Guidance for the use of repeatability, reproducibility and
trueness estimates in measurement uncertainty estimation
1 Scope
The Technical Specification gives guidance for
evaluation of measurement uncertainties using data obtained from studies conducted in accordance with
ISO 5725-2:1994;
comparison of collaborative study results with measurement uncertainty (MU) obtained using formal
principles of uncertainty propagation (see Clause 14).
ISO 5725-3:1994 provides additional models for studies of intermediate precision. However, while the same
general approach may be applied to the use of such extended models, uncertainty evaluation using these
models is not incorporated in the present Technical Specification.
This Technical Specification is applicable in all measurement and test fields where an uncertainty associated
with a result has to be determined.
This Technical Specification does not describe the application of repeatability data in the absence of
reproducibility data.
This Technical Specification assumes that recognized, non-negligible systematic effects are corrected, either
by applying a numerical correction as part of the method of measurement, or by investigation and removal of
the cause of the effect.
The recommendations in this Technical Specification are primarily for guidance. It is recognized that while the
recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is
also possible to adopt other suitable approaches.
In general, references to measurement results, methods and processes in this Technical Specification are
normally understood to apply also to testing results, methods and processes.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms
ISO 5725-3:1994, Accuracy (trueness and precision) of measurement methods and results — Part 3:
Intermediate measures of the precision of a standard measurement method
© ISO 2004 – All rights reserved 1
---------------------- Page: 6 ----------------------
ISO/TS 21748:2004(E)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply. In addition, reference is made to
“intermediate precision conditions”, which are discussed in detail in ISO 5725-3:1994.
3.1
bias
difference between the expectation of the test results and an accepted reference value
NOTE Bias is the total systematic error as contrasted to random error. There may be one or more systematic error
components contributing to the bias. A larger systematic difference from the accepted reference value is reflected by a
larger bias value.
[ISO 3534-1]
3.2
combined standard uncertainty
u(y)
standard uncertainty of the result of a measurement when that result is obtained from the values of a number
of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariances of these other quantities weighted according to how the measurement result varies with changes
in these quantities
[GUM]
3.3
coverage factor
k
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty
NOTE A coverage factor, k, is typically in the range 2 to 3.
[GUM]
3.4
expanded uncertainty
U
quantity defining an interval about a result of a measurement expected to encompass a large fraction of the
distribution of values that could reasonably be attributed to the measurand
NOTE 1 The fraction may be regarded as the coverage probability or level of confidence of the interval.
NOTE 2 To associate a specific level of confidence with the interval defined by the expanded uncertainty requires
explicit or implicit assumptions regarding the probability distribution characterised by the measurement result and its
combined standard uncertainty. The level of confidence that may be attributed to this interval can be known only to the
extent to which such assumptions can be justified.
NOTE 3 Expanded uncertainty is termed overall uncertainty in Recommendation INC-1 (1980), paragraph 5.
[GUM]
3.5
precision
closeness of agreement between independent test results obtained under stipulated conditions
NOTE 1 Precision depends upon the distribution of random errors and does not relate to the true value or the specified
value.
2 © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
NOTE 2 The measure of precision is usually expressed in terms of imprecision and computed as a standard deviation
of the test results. Less precision is reflected by a higher standard deviation.
NOTE 3 “Independent test results” means results obtained in a manner not influenced by any previous result on the
same or similar test object. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability
and reproducibility conditions are particular examples of extreme stipulated conditions.
[ISO 3534-1]
3.6
repeatability
precision under repeatability conditions, i.e. conditions where independent test results are obtained with the
same method on identical test items in the same laboratory by the same operator using the same equipment
within short intervals of time
[ISO 3534-1]
3.7
repeatability standard deviation
standard deviation of test results obtained under repeatability conditions
NOTE This is a measure of dispersion of the distribution of test results under repeatability conditions. Similarly
“repeatability variance” and “repeatability coefficient of variation” can be defined and used as measures of the dispersion
of test results under repeatability conditions.
[ISO 3534-1]
3.8
reproducibility
precision under reproducibility conditions, i.e. conditions where test results are obtained with the same method
on identical test items in different laboratories with different operators using different equipment
NOTE A valid statement of reproducibility requires specification of the conditions changed. Reproducibility may be
expressed quantitatively in terms of the dispersion of the results.
[ISO 3534-1]
3.9
reproducibility standard deviation
standard deviation of test results obtained under reproducibility conditions
NOTE This is a measure of dispersion of the distribution of test results under reproducibility conditions. Similarly
“reproducibility variance” and “reproducibility coefficient of variation” could be defined and used as measures of the
dispersion of test results under reproducibility conditions.
[ISO 3534-1]
3.10
standard uncertainty
u(x )
i
uncertainty of the result of a measurement expressed as a standard deviation
[GUM]
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ISO/TS 21748:2004(E)
3.11
trueness
closeness of agreement between the average value obtained from a large set of test results and an accepted
reference value
NOTE The measure of trueness is normally expressed in terms of bias. The reference to trueness as “accuracy of
the mean” is not generally recommended.
[ISO 3534-1]
3.12
uncertainty
〈measurement〉 parameter, associated with the result of a measurement, that characterizes the dispersion of
the values that could reasonably be attributed to the measurand
NOTE 1 The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an
interval having a stated level of confidence.
NOTE 2 Uncertainty of measurement comprises, in general, many components. Some of these components may be
evaluated from the statistical distribution of the results of a series of measurements and can be characterized by
experimental standard deviations. Other components, which also can be characterized by standard deviations, are
evaluated from assumed probability distributions based on experience or other information.
NOTE 3 It is understood that the result of the measurement is the best estimate of the value of the measurand, and
that all components of uncertainty, including those arising from systematic effects such as components associated with
corrections and reference standards, contribute to the dispersion.
[GUM]
3.13
uncertainty budget
list of sources of uncertainty and their associated standard uncertainties, compiled with a view to evaluating a
combined standard uncertainty associated with a measurement result
NOTE The list often includes additional information such as sensitivity coefficients (rate of change of result with
change in a quantity affecting the result), degrees of freedom for each standard uncertainty, and an identification of the
means of evaluating each standard uncertainty in terms of a Type A or Type B evaluation.
4 Symbols
a coefficient indicating an intercept in the empirical relationship sˆ =+abm
R
B laboratory component of bias
b coefficient indicating a slope in the empirical relationship sˆ =+abm
R
d
c coefficient in the empirical relationship sˆ = cm
R
c sensitivity coefficient ∂∂yx/
i i
d
d coefficient indicating an exponent in the empirical relationship sˆ = cm
R
e random residual error
e random residual error under repeatability conditions
r
k numerical factor used as a multiplier of the combined standard uncertainty u in order to obtain an
expanded uncertainty U
l laboratory number
4 © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
m mean value of the measurements
N number of contributions included in combined uncertainty calculations
′
n number of contributions incorporated in combined uncertainty calculations in addition to collaborative
study data
n number of replicates at one level by laboratory l
l
n number of replicate measurements
r
p number of laboratories
Q number of test items from a larger batch
q number of assigned values by consensus during a collaborative study
r correlation coefficient between x and x , in the range −1 to +1
ij i j
s between-group component of variance expressed as a standard deviation
b
2
s between-group component of variance
b
s estimated, or experimental, standard deviation of results obtained by repeated measurement on a
D
reference material used for checking control of bias
s repeatability standard deviation with ν degrees of freedom
i i
s uncertainty associated with the inhomogeneity of the sample
inh
2
s component of variance associated with the inhomogeneity of the sample
inh
s experimental or estimated inter-laboratory standard deviation
L
ˆ
s adjusted uncertainty associated with B where the contribution is dependent on the response
L
2
s the estimated variance of B
L
s intra-laboratory standard deviation
r
ˆ
s adjusted estimate of inter-laboratory standard deviation, where the contribution is dependent on the
r
response
2
s estimated variance of e
r
r
s estimated reproducibility standard deviation
R
′
s adjusted estimate of the reproducibility standard deviation
R
ˆ
s adjusted reproducibility standard deviation calculated from an empirical model, where the contributions
R
are dependent on the response
s intra-laboratory standard deviation derived from replicates or other repeatability studies
w
2
s intra-group component of variance (often an intra-laboratory component of variance)
w
s(∆ ) laboratory standard deviation of differences during a comparison of a routine method with a definitive
y
method
x value of the ith input value in the determination of a result
i
'
x deviation of the ith input value from the nominal value of x
i
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ISO/TS 21748:2004(E)
x the jth input value in the determination of a result
j
ˆ
u()δ uncertainty associated with δ due to the uncertainty of estimating δ by measuring a reference
ˆ
measurement standard or reference material with certified value µ
ˆ ˆ
u( µ ) uncertainty associated with the certified value µ
22
u(y) combined standard uncertainty associated with y where uy() = c u (x )
∑ii
in=1,
2
u(Y) combined uncertainty for the result Y = f(y , y , .) where uY() = c u(y )
1 2 ∑ ii
i
2
u (y) combined standard uncertainty associated with y, expressed as a variance
u uncertainty associated with sample inhomogeneity
inh
U expanded uncertainty, equal to k times the standard uncertainty u
U(y) expanded uncertainty in y where U(y) = ku(y), where k is a coverage factor
y result for test item i from the definitive method during a comparison of methods
i
ˆ
y result for test item i from the routine test method during a comparison of methods
i
y assigned value for proficiency testing
0
∆ laboratory bias
ˆ
∆ estimate of bias of laboratory l, equal to the laboratory mean, m, minus the certified value, µ
l
∆ mean laboratory bias during a comparison of a routine method with a definitive method
y
δ bias intrinsic to the measurement method in use
ˆ
δ estimated or measured bias
µ unknown expectation of the ideal result
ˆ
µ certified value of a reference material
σ standard deviation for proficiency testing
0
σ true value of the standard deviation of results obtained by repeated measurement on a reference
D
material used for checking control of bias
σ inter-laboratory standard deviation; standard deviation of B
L
2
σ variance of B; inter-laboratory variance
L
σ intra-laboratory standard deviation; standard deviation of e
r r
2
σ variance of e ; intra-laboratory variance
r
r
σ within-group standard deviation
w
σ standard deviation required for adequate performance (ISO Guide 33)
w0
ν effective degrees of freedom for the standard deviation of, or uncertainty associated with input value x
eff i
6 © ISO 2004 – All rights reserved
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ISO/TS 21748:2004(E)
ν number of degrees of freedom
i
5 Principles
5.1 Individual results and measurement process performance
5.1.1 Measurement uncertainty relates to individual results. Repeatability, reproducibility, and bias, by
contrast, relate to the performance of a measurement or testing process. For studies under all parts of
ISO 5725, the measurement or testing process will be a single measurement method, used by all laboratories
taking part in the study. Note that for the purposes of this Technical Specification, the measurement method is
assumed to be implemented in the form of a single detailed procedure (as defined in the International
Vocabulary of Basic and General Terms in Metrology). It is implicit in this Technical Specification that process-
performance figures derived from method-performance studies are relevant to all individual measurement
results produced by the process. It will be seen that this assumption requires supporting evidence in the form
of appropriate quality control and assurance data for the measurement process (Clause 7).
5.1.2 It will be seen below that differences between individual test items may additionally need to be taken
into account, but, with that caveat, it is unnecessary to undertake individual and detailed uncertainty studies
for every test item for a well characterized and stable measurement process.
5.2 Applicability of reproducibility data
The application of the principles of this Technical Specification is based on two principles.
First, the reproducibility standard deviation obtained in a collaborative study is a valid basis for
measurement uncertainty evaluation (see A.2.1).
Second, effects not observed within the context of the collaborative study must be demonstrably
negligible or explicitly allowed for. The latter principle is implemented by an extension of the basic model
used for collaborative study (see A.2.3).
5.3 Basic equations for the statistical model
5.3.1 The statistical model on which this guidance is based is formulated as in Equation (1):
yB=+µδ+ +cx′+e (1)
∑ ii
where
y is an observed result, assumed to be calculated from the equation: y = f(x , x , …, x );
1 2 n
µ is the (unknown)
...
SLOVENSKI STANDARD
SIST-TS ISO/TS 21748:2006
01-april-2006
Napotek za uporabo ocen ponovljivosti, obnovljivosti in pravilnosti pri
ocenjevanju merilne negotovosti
Guidance for the use of repeatability, reproducibility and trueness estimates in
measurement uncertainty estimation
Lignes directrices relatives à l'utilisation d'estimations de la répétabilité, de la
reproductibilité et de la justesse dans l'évaluation de l'incertitude de mesure
Ta slovenski standard je istoveten z: ISO/TS 21748:2004
ICS:
17.020 Meroslovje in merjenje na Metrology and measurement
splošno in general
SIST-TS ISO/TS 21748:2006 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST-TS ISO/TS 21748:2006
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SIST-TS ISO/TS 21748:2006
TECHNICAL ISO/TS
SPECIFICATION 21748
First edition
2004-03-15
Guidance for the use of repeatability,
reproducibility and trueness estimates in
measurement uncertainty estimation
Lignes directrices relatives à l'utilisation d'estimations de la répétabilité,
de la reproductibilité et de la justesse dans l'évaluation de l'incertitude
de mesure
Reference number
ISO/TS 21748:2004(E)
©
ISO 2004
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
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Published in Switzerland
ii © ISO 2004 – All rights reserved
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Symbols . 4
5 Principles . 7
5.1 Individual results and measurement process performance. 7
5.2 Applicability of reproducibility data. 7
5.3 Basic equations for the statistical model. 7
5.4 Repeatability data . 8
6 Evaluating uncertainty using repeatability, reproducibility and trueness estimates . 8
6.1 Procedure for evaluating measurement uncertainty. 8
6.2 Differences between expected and actual precision . 9
7 Establishing the relevance of method performance data to measurement results from a
particular measurement process . 9
7.1 General. 9
7.2 Demonstrating control of the laboratory component of bias. 9
7.3 Verification of repeatability. 11
7.4 Continued verification of performance. 12
8 Establishing relevance to the test item . 12
8.1 General. 12
8.2 Sampling . 12
8.3 Sample preparation and pre-treatment. 13
8.4 Changes in test-item type . 13
8.5 Variation of uncertainty with level of response . 13
9 Additional factors. 14
10 General expression for combined standard uncertainty. 14
11 Uncertainty budgets based on collaborative study data. 15
12 Evaluation of uncertainty for a combined result . 16
13 Expression of uncertainty information . 17
13.1 General expression. 17
13.2 Choice of coverage factor. 17
14 Comparison of method performance figures and uncertainty data . 17
14.1 Basic assumptions for comparison . 17
14.2 Comparison procedure. 18
14.3 Reasons for differences . 18
Annex A (informative) Approaches to uncertainty estimation. 19
Annex B (informative) Experimental uncertainty evaluation . 24
Annex C (informative) Examples of uncertainty calculations. 25
Bibliography . 29
© ISO 2004 – All rights reserved iii
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of normative document:
an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TS 21748 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
iv © ISO 2004 – All rights reserved
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
Introduction
Knowledge of the uncertainty associated with measurement results is essential to the interpretation of the
results. Without quantitative assessments of uncertainty, it is impossible to decide whether observed
differences between results reflect more than experimental variability, whether test items comply with
specifications, or whether laws based on limits have been broken. Without information on uncertainty, there is
a risk of misinterpretation of results. Incorrect decisions taken on such a basis may result in unnecessary
expenditure in industry, incorrect prosecution in law, or adverse health or social consequences.
Laboratories operating under ISO 17025 accreditation and related systems are accordingly required to
evaluate measurement uncertainty for measurement and test results and report the uncertainty where relevant.
The Guide to the expression of uncertainty in measurement (GUM), published by ISO, is a widely adopted
standard approach. However, it applies to situations where a model of the measurement process is available.
A very wide range of standard test methods is, however, subjected to collaborative study in accordance with
ISO 5725-2:1994. This Technical Specification provides an appropriate and economic methodology for
estimating uncertainty associated with the results of these methods, which complies fully with the relevant
principles of the GUM, whilst taking account of method performance data obtained by collaborative study.
The general approach used in this Technical Specification requires that
estimates of the repeatability, reproducibility and trueness of the method in use, obtained by collaborative
study as described in ISO 5725-2:1994, be available from published information about the test method in
use. These provide estimates of the intra- and inter-laboratory components of variance, together with an
estimate of uncertainty associated with the trueness of the method;
the laboratory confirm that its implementation of the test method is consistent with the established
performance of the test method by checking its own bias and precision. This confirms that the published
data are applicable to the results obtained by the laboratory;
any influences on the measurement results that were not adequately covered by the collaborative study
be identified and the variance associated with the results that could arise from these effects be quantified.
An uncertainty estimate is made by combining the relevant variance estimates in the manner prescribed by
the GUM.
The dispersion of results obtained in a collaborative study is often also usefully compared with measurement
uncertainty estimates obtained using GUM procedures as a test of full understanding of the method. Such
comparisons will be more effective given a consistent methodology for estimating the same parameter using
collaborative study data.
© ISO 2004 – All rights reserved v
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SIST-TS ISO/TS 21748:2006
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SIST-TS ISO/TS 21748:2006
TECHNICAL SPECIFICATION ISO/TS 21748:2004(E)
Guidance for the use of repeatability, reproducibility and
trueness estimates in measurement uncertainty estimation
1 Scope
The Technical Specification gives guidance for
evaluation of measurement uncertainties using data obtained from studies conducted in accordance with
ISO 5725-2:1994;
comparison of collaborative study results with measurement uncertainty (MU) obtained using formal
principles of uncertainty propagation (see Clause 14).
ISO 5725-3:1994 provides additional models for studies of intermediate precision. However, while the same
general approach may be applied to the use of such extended models, uncertainty evaluation using these
models is not incorporated in the present Technical Specification.
This Technical Specification is applicable in all measurement and test fields where an uncertainty associated
with a result has to be determined.
This Technical Specification does not describe the application of repeatability data in the absence of
reproducibility data.
This Technical Specification assumes that recognized, non-negligible systematic effects are corrected, either
by applying a numerical correction as part of the method of measurement, or by investigation and removal of
the cause of the effect.
The recommendations in this Technical Specification are primarily for guidance. It is recognized that while the
recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is
also possible to adopt other suitable approaches.
In general, references to measurement results, methods and processes in this Technical Specification are
normally understood to apply also to testing results, methods and processes.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms
ISO 5725-3:1994, Accuracy (trueness and precision) of measurement methods and results — Part 3:
Intermediate measures of the precision of a standard measurement method
© ISO 2004 – All rights reserved 1
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply. In addition, reference is made to
“intermediate precision conditions”, which are discussed in detail in ISO 5725-3:1994.
3.1
bias
difference between the expectation of the test results and an accepted reference value
NOTE Bias is the total systematic error as contrasted to random error. There may be one or more systematic error
components contributing to the bias. A larger systematic difference from the accepted reference value is reflected by a
larger bias value.
[ISO 3534-1]
3.2
combined standard uncertainty
u(y)
standard uncertainty of the result of a measurement when that result is obtained from the values of a number
of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariances of these other quantities weighted according to how the measurement result varies with changes
in these quantities
[GUM]
3.3
coverage factor
k
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty
NOTE A coverage factor, k, is typically in the range 2 to 3.
[GUM]
3.4
expanded uncertainty
U
quantity defining an interval about a result of a measurement expected to encompass a large fraction of the
distribution of values that could reasonably be attributed to the measurand
NOTE 1 The fraction may be regarded as the coverage probability or level of confidence of the interval.
NOTE 2 To associate a specific level of confidence with the interval defined by the expanded uncertainty requires
explicit or implicit assumptions regarding the probability distribution characterised by the measurement result and its
combined standard uncertainty. The level of confidence that may be attributed to this interval can be known only to the
extent to which such assumptions can be justified.
NOTE 3 Expanded uncertainty is termed overall uncertainty in Recommendation INC-1 (1980), paragraph 5.
[GUM]
3.5
precision
closeness of agreement between independent test results obtained under stipulated conditions
NOTE 1 Precision depends upon the distribution of random errors and does not relate to the true value or the specified
value.
2 © ISO 2004 – All rights reserved
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
NOTE 2 The measure of precision is usually expressed in terms of imprecision and computed as a standard deviation
of the test results. Less precision is reflected by a higher standard deviation.
NOTE 3 “Independent test results” means results obtained in a manner not influenced by any previous result on the
same or similar test object. Quantitative measures of precision depend critically on the stipulated conditions. Repeatability
and reproducibility conditions are particular examples of extreme stipulated conditions.
[ISO 3534-1]
3.6
repeatability
precision under repeatability conditions, i.e. conditions where independent test results are obtained with the
same method on identical test items in the same laboratory by the same operator using the same equipment
within short intervals of time
[ISO 3534-1]
3.7
repeatability standard deviation
standard deviation of test results obtained under repeatability conditions
NOTE This is a measure of dispersion of the distribution of test results under repeatability conditions. Similarly
“repeatability variance” and “repeatability coefficient of variation” can be defined and used as measures of the dispersion
of test results under repeatability conditions.
[ISO 3534-1]
3.8
reproducibility
precision under reproducibility conditions, i.e. conditions where test results are obtained with the same method
on identical test items in different laboratories with different operators using different equipment
NOTE A valid statement of reproducibility requires specification of the conditions changed. Reproducibility may be
expressed quantitatively in terms of the dispersion of the results.
[ISO 3534-1]
3.9
reproducibility standard deviation
standard deviation of test results obtained under reproducibility conditions
NOTE This is a measure of dispersion of the distribution of test results under reproducibility conditions. Similarly
“reproducibility variance” and “reproducibility coefficient of variation” could be defined and used as measures of the
dispersion of test results under reproducibility conditions.
[ISO 3534-1]
3.10
standard uncertainty
u(x )
i
uncertainty of the result of a measurement expressed as a standard deviation
[GUM]
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
3.11
trueness
closeness of agreement between the average value obtained from a large set of test results and an accepted
reference value
NOTE The measure of trueness is normally expressed in terms of bias. The reference to trueness as “accuracy of
the mean” is not generally recommended.
[ISO 3534-1]
3.12
uncertainty
〈measurement〉 parameter, associated with the result of a measurement, that characterizes the dispersion of
the values that could reasonably be attributed to the measurand
NOTE 1 The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an
interval having a stated level of confidence.
NOTE 2 Uncertainty of measurement comprises, in general, many components. Some of these components may be
evaluated from the statistical distribution of the results of a series of measurements and can be characterized by
experimental standard deviations. Other components, which also can be characterized by standard deviations, are
evaluated from assumed probability distributions based on experience or other information.
NOTE 3 It is understood that the result of the measurement is the best estimate of the value of the measurand, and
that all components of uncertainty, including those arising from systematic effects such as components associated with
corrections and reference standards, contribute to the dispersion.
[GUM]
3.13
uncertainty budget
list of sources of uncertainty and their associated standard uncertainties, compiled with a view to evaluating a
combined standard uncertainty associated with a measurement result
NOTE The list often includes additional information such as sensitivity coefficients (rate of change of result with
change in a quantity affecting the result), degrees of freedom for each standard uncertainty, and an identification of the
means of evaluating each standard uncertainty in terms of a Type A or Type B evaluation.
4 Symbols
a coefficient indicating an intercept in the empirical relationship sˆ =+abm
R
B laboratory component of bias
b coefficient indicating a slope in the empirical relationship sˆ =+abm
R
d
c coefficient in the empirical relationship sˆ = cm
R
c sensitivity coefficient ∂∂yx/
i i
d
d coefficient indicating an exponent in the empirical relationship sˆ = cm
R
e random residual error
e random residual error under repeatability conditions
r
k numerical factor used as a multiplier of the combined standard uncertainty u in order to obtain an
expanded uncertainty U
l laboratory number
4 © ISO 2004 – All rights reserved
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
m mean value of the measurements
N number of contributions included in combined uncertainty calculations
′
n number of contributions incorporated in combined uncertainty calculations in addition to collaborative
study data
n number of replicates at one level by laboratory l
l
n number of replicate measurements
r
p number of laboratories
Q number of test items from a larger batch
q number of assigned values by consensus during a collaborative study
r correlation coefficient between x and x , in the range −1 to +1
ij i j
s between-group component of variance expressed as a standard deviation
b
2
s between-group component of variance
b
s estimated, or experimental, standard deviation of results obtained by repeated measurement on a
D
reference material used for checking control of bias
s repeatability standard deviation with ν degrees of freedom
i i
s uncertainty associated with the inhomogeneity of the sample
inh
2
s component of variance associated with the inhomogeneity of the sample
inh
s experimental or estimated inter-laboratory standard deviation
L
ˆ
s adjusted uncertainty associated with B where the contribution is dependent on the response
L
2
s the estimated variance of B
L
s intra-laboratory standard deviation
r
ˆ
s adjusted estimate of inter-laboratory standard deviation, where the contribution is dependent on the
r
response
2
s estimated variance of e
r
r
s estimated reproducibility standard deviation
R
′
s adjusted estimate of the reproducibility standard deviation
R
ˆ
s adjusted reproducibility standard deviation calculated from an empirical model, where the contributions
R
are dependent on the response
s intra-laboratory standard deviation derived from replicates or other repeatability studies
w
2
s intra-group component of variance (often an intra-laboratory component of variance)
w
s(∆ ) laboratory standard deviation of differences during a comparison of a routine method with a definitive
y
method
x value of the ith input value in the determination of a result
i
'
x deviation of the ith input value from the nominal value of x
i
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
x the jth input value in the determination of a result
j
ˆ
u()δ uncertainty associated with δ due to the uncertainty of estimating δ by measuring a reference
ˆ
measurement standard or reference material with certified value µ
ˆ ˆ
u( µ ) uncertainty associated with the certified value µ
22
u(y) combined standard uncertainty associated with y where uy() = c u (x )
∑ii
in=1,
2
u(Y) combined uncertainty for the result Y = f(y , y , .) where uY() = c u(y )
1 2 ∑ ii
i
2
u (y) combined standard uncertainty associated with y, expressed as a variance
u uncertainty associated with sample inhomogeneity
inh
U expanded uncertainty, equal to k times the standard uncertainty u
U(y) expanded uncertainty in y where U(y) = ku(y), where k is a coverage factor
y result for test item i from the definitive method during a comparison of methods
i
ˆ
y result for test item i from the routine test method during a comparison of methods
i
y assigned value for proficiency testing
0
∆ laboratory bias
ˆ
∆ estimate of bias of laboratory l, equal to the laboratory mean, m, minus the certified value, µ
l
∆ mean laboratory bias during a comparison of a routine method with a definitive method
y
δ bias intrinsic to the measurement method in use
ˆ
δ estimated or measured bias
µ unknown expectation of the ideal result
ˆ
µ certified value of a reference material
σ standard deviation for proficiency testing
0
σ true value of the standard deviation of results obtained by repeated measurement on a reference
D
material used for checking control of bias
σ inter-laboratory standard deviation; standard deviation of B
L
2
σ variance of B; inter-laboratory variance
L
σ intra-laboratory standard deviation; standard deviation of e
r r
2
σ variance of e ; intra-laboratory variance
r
r
σ within-group standard deviation
w
σ standard deviation required for adequate performance (ISO Guide 33)
w0
ν effective degrees of freedom for the standard deviation of, or uncertainty associated with input value x
eff i
6 © ISO 2004 – All rights reserved
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SIST-TS ISO/TS 21748:2006
ISO/TS 21748:2004(E)
ν number of degrees of freedom
i
5 Principles
5.1 Individual results and measurement process performance
5.1.1 Measurement uncertainty relates to individual results. Repeatability, reproducibility, and bias, by
contrast, relate to the performance of a measurement or testing process. For studies under all parts of
ISO 5725, the measurement or testing process will be a single measurement method, used by all laboratories
taking part in the study. Note that for the purposes of this Technical Specification, the measurement method is
assumed to be implemented in the form of a single detailed procedure (as defined in the International
Vocabulary of Basic and General Terms in Metrology). It is implicit in this Technical Specification that process-
performance figures derived from method-performance studies are relevant to all individual measurement
results produced by the process. It will be seen that this ass
...
SPÉCIFICATION ISO/TS
TECHNIQUE 21748
Première édition
2004-03-15
Lignes directrices relatives à l'utilisation
d'estimations de la répétabilité, de la
reproductibilité et de la justesse dans
l'évaluation de l'incertitude de mesure
Guidance for the use of repeatability, reproducibility and trueness
estimates in measurement uncertainty estimation
Numéro de référence
ISO/TS 21748:2004(F)
©
ISO 2004
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ISO/TS 21748:2004(F)
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Publié en Suisse
ii © ISO 2004 – Tous droits réservés
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ISO/TS 21748:2004(F)
Sommaire Page
Avant-propos. iv
Introduction . v
1 Domaine d'application. 1
2 Références normatives. 1
3 Termes et définitions . 2
4 Symboles. 4
5 Principes. 7
5.1 Résultats individuels et performance du processus de mesure . 7
5.2 Utilisation des données de reproductibilité . 7
5.3 Équations fondamentales pour le modèle statistique . 7
5.4 Données de répétabilité. 8
6 Évaluation de l’incertitude de mesure à l’aide des estimations de la répétabilité, de la
reproductibilité et de la justesse . 9
6.1 Procédure pour l’évaluation de l’incertitude de mesure. 9
6.2 Différences entre fidélité attendue et fidélité réelle. 9
7 Établissement de la pertinence des données de performance de la méthode aux résultats
de mesure à partir d’un processus de mesure particulier. 9
7.1 Généralités. 9
7.2 Démonstration du contrôle du composant de biais du laboratoire. 9
7.3 Vérification de la répétabilité . 12
7.4 Vérification continue de la performance . 12
8 Établissement de la pertinence de l’individu d’essai. 13
8.1 Généralités. 13
8.2 Échantillonnage. 13
8.3 Préparation et traitement préalable des échantillons . 13
8.4 Changements du type d’individu d’essai . 13
8.5 Variation de l’incertitude avec le niveau de réponse . 14
9 Facteurs supplémentaires. 14
10 Expression générale pour l’estimation de l’incertitude-type composée . 15
11 Budgets d’incertitude fondés sur des données d’études collaboratives . 15
12 Évaluation de l’incertitude pour un résultat composé. 17
13 Expression des données d’incertitude . 17
13.1 Expression générale. 17
13.2 Choix du facteur d’élargissement . 17
14 Comparaison des valeurs de performance d’une méthode et des données d’incertitude . 18
14.1 Hypothèses de base . 18
14.2 Procédure d’essai. 18
14.3 Raisons des différences. 19
Annexe A (informative) Méthodes d’estimation de l’incertitude. 20
Annexe B (informative) Évaluation expérimentale de l'incertitude . 25
Annexe C (informative) Exemples de calcul de l’incertitude de mesure . 26
Bibliographie . 31
© ISO 2004 – Tous droits réservés iii
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ISO/TS 21748:2004(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée
aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du
comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur
publication comme Normes internationales requiert l'approbation de 75 % au moins des comités membres
votants.
Dans d'autres circonstances, en particulier lorsqu'il existe une demande urgente du marché, un comité
technique peut décider de publier d'autres types de documents normatifs:
une Spécification publiquement disponible ISO (ISO/PAS) représente un accord entre les experts dans
un groupe de travail ISO et est acceptée pour publication si elle est approuvée par plus de 50 % des
membres votants du comité dont relève le groupe de travail;
une Spécification technique ISO (ISO/TS) représente un accord entre les membres d'un comité technique
et est acceptée pour publication si elle est approuvée par 2/3 des membres votants du comité.
Une ISO/PAS ou ISO/TS fait l'objet d'un examen après trois ans afin de décider si elle est confirmée pour trois
nouvelles années, révisée pour devenir une Norme internationale, ou annulée. Lorsqu'une ISO/PAS ou
ISO/TS a été confirmée, elle fait l'objet d'un nouvel examen après trois ans qui décidera soit de sa
transformation en Norme internationale soit de son annulation.
L'attention est appelée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable de ne
pas avoir identifié de tels droits de propriété et averti de leur existence.
L'ISO/TS 21748 a été élaborée par le comité technique ISO/TC 69, Application des méthodes statistiques,
sous-comité SC 6, Méthodes et résultats de mesure.
iv © ISO 2004 – Tous droits réservés
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ISO/TS 21748:2004(F)
Introduction
Pour pouvoir interpréter des résultats, il est essentiel de connaître l’incertitude associée aux résultats des
mesures. Sans évaluation quantitative de l’incertitude, il est impossible de décider si les différences
observées entre des résultats sont supérieures à la variabilité expérimentale, si les individus d’essai sont
conformes aux spécifications ou si des lois basées sur des limites ont été enfreintes. Sans information sur
l’incertitude, il existe un risque de mal estimer les résultats. Des décisions incorrectes prises sur ces bases
peuvent entraîner des dépenses inutiles pour l’industrie, des poursuites judiciaires inappropriées ou bien des
conséquences néfastes sur la santé ou pour la société.
Par conséquent, les laboratoires accrédités selon l’ISO 17025 et les systèmes connexes sont tenus d’évaluer
l’incertitude de mesure pour leurs résultats d’essai et de mesure et, le cas échéant, de rapporter cette
incertitude. Le Guide pour l’expression de l’incertitude de mesure (GUM), publié par l’ISO, constitue une
méthode normalisée largement adoptée. Néanmoins, il s’applique à des situations où un modèle complet du
processus de mesure est disponible. Un très vaste ensemble de méthodes d’essai normalisées est toutefois
l'objet d'études collaboratives selon l’ISO 5725-2:1994. La présente Spécification technique fournit une
méthodologie appropriée et économique d’estimation de l’incertitude associée aux résultats de ces méthodes,
en totale conformité avec les principes correspondants du GUM, tout en tenant compte des données de
performances des méthodes, obtenues par une étude collaborative.
L’approche générale utilisée dans la présente Spécification technique nécessite que
les estimations de la répétabilité, de la reproductibilité et de la justesse de la méthode utilisée, obtenues
par des études collaboratives telles que décrites dans l’ISO 5725-2, soient disponibles dans les
informations publiées sur la méthode d’essai utilisée; ces études collaboratives fournissent des
estimations de la composante de variance intralaboratoire et interlaboratoires, accompagnées d’une
estimation de l’incertitude associée à la justesse de la méthode;
le laboratoire confirme que la mise en œuvre de la méthode d’essai est cohérente avec la performance
définie de la méthode d’essai, en vérifiant son propre biais et sa propre fidélité; cela confirme que les
données publiées sont applicables aux résultats obtenus par le laboratoire;
toutes les influences sur les résultats de mesure qui ne sont pas correctement couvertes pour l’étude
collaborative soient identifiées et la variance associée aux résultats qui peut découler de ces effets soit
quantifiée.
Une estimation de l’incertitude est effectuée en combinant les estimations pertinentes de la variance telles
que prescrites dans le GUM.
À titre d’essai de compréhension globale de la méthode, il peut aussi être utile de comparer la dispersion des
résultats, obtenue dans une étude collaborative, aux estimations de l’incertitude de mesure obtenues en
utilisant les procédures du GUM. Ces comparaisons seront plus efficaces s'il est donné une méthodologie
cohérente d’estimation du même paramètre à partir de données d’une étude collaborative.
© ISO 2004 – Tous droits réservés v
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SPÉCIFICATION TECHNIQUE ISO/TS 21748:2004(F)
Lignes directrices relatives à l'utilisation d'estimations de la
répétabilité, de la reproductibilité et de la justesse dans
l'évaluation de l'incertitude de mesure
1 Domaine d'application
La présente Spécification technique donne des lignes directrices en vue
d’évaluer l’incertitude de mesure à partir de données obtenues lors d’études menées conformément à
l’ISO 5725-2:1994, et
de comparer les résultats d’une étude collaborative à l’incertitude de mesure obtenue en appliquant des
principes formels de propagation de l’incertitude (voir Article 14).
L’ISO 5725-3:1994 fournit des modèles supplémentaires d’études de la fidélité intermédiaire. Cependant, bien
que la même méthode générale puisse s’appliquer à l’utilisation de ces modèles étendus, l’évaluation de
l’incertitude à partir de ces modèles n’est pas traitée dans la présente Spécification technique.
La présente Spécification technique est applicable dans tous les domaines de mesure et d’essai nécessitant
la détermination d’une incertitude associée à un résultat.
La présente Spécification technique ne décrit pas l'utilisation de données de répétabilité en l’absence de
données de reproductibilité.
La présente Spécification technique suppose que les effets systématiques non négligeables reconnus sont
corrigés, soit en appliquant une correction numérique dans le cadre de la méthode de mesure, soit en
recherchant et en éliminant l’origine de ces effets.
Les recommandations de la présente Spécification technique sont avant tout indicatives. Il est reconnu que,
même si les recommandations présentées constituent une méthode valable d’évaluation de l’incertitude à de
nombreux égards, d’autres méthodes appropriées peuvent aussi être adoptées.
En général, il convient de comprendre que les références faites dans la présente Spécification technique à
des résultats, méthodes et processus de mesure s’appliquent également à des résultats, méthodes et
processus d’essai.
2 Références normatives
Les documents de référence suivants sont indispensables pour l'application du présent document. Pour les
références datées, seule l'édition citée s'applique. Pour les références non datées, la dernière édition du
document de référence s'applique (y compris les éventuels amendements).
ISO 3534-1, Statistique — Vocabulaire et symboles — Partie 1: Probabilité et termes statistiques généraux
ISO 5725-3:1994, Exactitude (justesse et fidélité) des résultats et méthodes de mesure — Partie 3: Mesures
intermédiaires de la fidélité d’une méthode de mesure normalisée
© ISO 2004 – Tous droits réservés 1
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ISO/TS 21748:2004(F)
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions suivants s'appliquent. En plus, il est fait
référence aux «conditions intermédiaires de fidélité», décrites en détail dans l’ISO 5725-3:1994.
3.1
biais
différence entre l’espérance mathématique des résultats d’essais et la valeur de référence acceptée
NOTE Le biais est une erreur systématique totale par opposition à l’erreur aléatoire. Il peut y avoir une ou plusieurs
composantes d’erreurs systématiques qui contribuent au biais. Une différence systématique importante par rapport à la
valeur de référence acceptée est reflétée par une grande valeur du biais.
[ISO 3534-1]
3.2
incertitude-type composée
u(y)
incertitude-type du résultat d’un mesurage, lorsque ce résultat est obtenu à partir des valeurs d’autres
grandeurs, égale à la racine carrée d’une somme de termes, ces termes étant les variances ou covariances
de ces autres grandeurs, pondérées selon la variation du résultat de mesure en fonction de celle de ces
grandeurs
[Guide pour l’expression de l’incertitude de mesure]
3.3
facteur d’élargissement
k
facteur numérique utilisé comme multiplicateur de l’incertitude-type composée pour obtenir l’incertitude élargie
NOTE Un facteur d’élargissement, k, a sa valeur typiquement comprise entre 2 et 3.
[Guide pour l’expression de l’incertitude de mesure]
3.4
incertitude élargie
U
grandeur définissant un intervalle autour du résultat d’un mesurage, dont on puisse s’attendre à ce qu’il
comprenne une fraction élevée de la distribution des valeurs qui pourraient être attribuées raisonnablement
au mesurande
NOTE 1 La fraction peut être considérée comme la probabilité ou le niveau de confiance de l’intervalle.
NOTE 2 L’association d’un niveau de confiance spécifique à l’intervalle défini par l’incertitude élargie nécessite des
hypothèses explicites ou implicites sur la loi de probabilité caractérisée par le résultat de mesure et son incertitude-type
composée. Le niveau de confiance qui peut être attribué à cet intervalle ne peut être connu qu’avec la même validité que
celle qui se rattache à ces hypothèses.
NOTE 3 L’incertitude élargie est appelée «incertitude globale» au Paragraphe 5 de la Recommandation INC-1 (1980).
[Guide pour l’expression de l’incertitude de mesure]
3.5
fidélité
étroitesse d’accord entre des résultats d’essais indépendants obtenus sous des conditions stipulées
NOTE 1 La fidélité dépend uniquement de la distribution des erreurs aléatoires et n’a aucune relation avec la valeur
vraie ou la valeur spécifiée.
NOTE 2 La mesure de la fidélité est exprimée en termes d’infidélité et est calculée à partir de l’écart-type des résultats
d’essais. Une fidélité faible est reflétée par un grand écart-type.
2 © ISO 2004 – Tous droits réservés
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ISO/TS 21748:2004(F)
NOTE 3 Des résultats d’essais indépendants signifient des résultats obtenus d’une façon non influencée par un
résultat précédent sur le même matériel ou similaire. Les mesures quantitatives de la fidélité dépendent de façon critique
des conditions stipulées. Les conditions de répétabilité et de reproductibilité sont des ensembles particuliers de conditions
extrêmes stipulées.
[ISO 3534-1]
3.6
répétabilité
fidélité sous des conditions de répétabilité, c’est-à-dire des conditions où des résultats d’essais indépendants
sont obtenus par la même méthode sur des individus d’essai identiques dans le même laboratoire, par le
même opérateur, utilisant le même équipement et pendant un court intervalle de temps
[ISO 3534-1]
3.7
écart-type de répétabilité
écart-type des résultats d'essais obtenus sous des conditions de répétabilité
NOTE C’est une mesure de la dispersion de la loi des résultats d’essais sous des conditions de répétabilité. On peut
définir de façon similaire la «variance de répétabilité» et le «coefficient de variation de répétabilité» et les utiliser comme
mesures de la dispersion des résultats d’essais sous des conditions de répétabilité.
[ISO 3534-1]
3.8
reproductibilité
fidélité sous des conditions de reproductibilité, c’est-à-dire des conditions où les résultats d’essais sont
obtenus par la même méthode sur des individus d’essai identiques dans différents laboratoires, avec
différents opérateurs et utilisant des équipements différents
NOTE Une déclaration valide de la reproductibilité nécessite de spécifier les conditions modifiées. La reproductibilité
peut être exprimée de manière quantitative en termes de dispersion des résultats.
[ISO 3534-1]
3.9
écart-type de reproductibilité
écart-type des résultats d'essais obtenus sous des conditions de reproductibilité
NOTE C’est une mesure de la dispersion de la loi des résultats d’essais sous des conditions de reproductibilité. On
peut définir de façon similaire la «variance de reproductibilité» et le «coefficient de variation de reproductibilité» et les
utiliser comme mesures de la dispersion des résultats d’essais sous des conditions de reproductibilité.
[ISO 3534-1]
3.10
incertitude-type
u(x )
i
incertitude du résultat d’un mesurage exprimée sous la forme d’un écart-type
[Guide pour l’expression de l’incertitude de mesure]
© ISO 2004 – Tous droits réservés 3
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ISO/TS 21748:2004(F)
3.11
justesse
étroitesse de l’accord entre la valeur moyenne obtenue à partir d’une large série de résultats d’essai et une
valeur de référence acceptée
NOTE La mesure de la justesse est généralement exprimée en termes de biais. La justesse a également été
appelée «exactitude de la moyenne». Cet usage n’est pas recommandé.
[ISO 3534-1]
3.12
incertitude de mesure
paramètre, associé au résultat d’un mesurage, qui caractérise la dispersion des valeurs qui pourraient
raisonnablement être attribuées au mesurande
NOTE 1 Le paramètre peut être, par exemple, un écart-type (ou un multiple de celui-ci) ou la demi-largeur d’un
intervalle de niveau de confiance déterminé.
NOTE 2 L’incertitude de mesure comprend, en général, plusieurs composantes. Certaines peuvent être évaluées à
partir de la distribution statistique des résultats de séries de mesurages et peuvent être caractérisées par des écarts-types
expérimentaux. Les autres composantes, qui peuvent aussi être caractérisées par des écarts-types, sont évaluées en
admettant des lois de probabilité, d’après l’expérience acquise ou d’après d’autres informations.
NOTE 3 Il est entendu que le résultat du mesurage est la meilleure estimation de la valeur du mesurande, et que
toutes les composantes de l’incertitude, y compris celles qui proviennent d’effets systématiques, telles que les
composantes associées aux corrections et aux étalons de référence, contribuent à la dispersion.
[Guide pour l’expression de l’incertitude de mesure]
3.13
budget d’incertitude
liste de sources d’incertitude et de leurs incertitudes-types associées, établie en vue d’évaluer l’incertitude-
type composée associée à un résultat de mesure
NOTE Cette liste peut comprendre en outre des informations telles que les coefficients de sensibilité, les degrés de
liberté pour chaque incertitude-type et une identification des moyens d’évaluer chaque incertitude-type en des termes
d’évaluation de type A ou de type B.
4 Symboles
a coefficient indiquant une constante de la relation empirique sˆ =+abm
R
B composante laboratoire du biais
b coefficient indiquant une pente de la relation empirique sˆ =+abm
R
d
c coefficient dans la relation empirique sˆ = cm
R
c coefficient de sensibilité ∂yx/ ∂
i i
d
ˆ
d coefficient indiquant un exposant dans la relation empirique s = cm
R
e erreur résiduelle aléatoire
e erreur résiduelle aléatoire dans des conditions de répétabilité
r
k facteur numérique utilisé comme multiplicateur de l’incertitude-type composée u pour obtenir
l’incertitude élargie U
l numéro de laboratoire
m valeur moyenne des mesures
4 © ISO 2004 – Tous droits réservés
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ISO/TS 21748:2004(F)
N nombre de contributions comprises dans le calcul d’une incertitude composée
n′ nombre de contributions incorporées dans le calcul d’une incertitude composée, en plus des données
d’un essai interlaboratoires
n nombre de répliques à 1 niveau par le laboratoire l
l
n nombre de mesurages répétés
r
p nombre de laboratoires
Q nombre d’individus d’essai provenant d’un plus grand lot
q nombre de valeurs assignées par consensus dans le cadre d’une étude collaborative
r coefficient de corrélation entre x et x , compris entre −1 et +1
ij i j
s composante intergroupes de la variance, exprimée comme un écart-type
b
2
s composante intergroupes de la variance
b
s écart-type, estimé ou expérimental, de résultats obtenus par mesurages répétés sur un matériau de
D
référence utilisé pour vérifier le biais
s écart-type de répétabilité avec ν degrés de liberté
i i
s incertitude associée à l’inhomogénéité de l’échantillon
inh
2
s composante de la variance associée à l’inhomogénéité de l’échantillon
inh
s écart-type interlaboratoires estimé ou expérimental
L
ˆ
s estimation ajustée de l'écart-type interlaboratoires, dans le cas où la contribution à l’incertitude dépend
L
de la réponse
2
s variance estimée de B
L
s écart-type intralaboratoire
r
ˆ
s estimation ajustée de l'écart-type intralaboratoire, dans le cas où la contribution à l’incertitude dépend
r
de la réponse
2
s variance estimée de e
r
r
s écart-type de reproductibilité
R
′
s estimation ajustée de l’écart-type de reproductibilité
R
sˆ écart-type de reproductibilité ajusté, calculé à partir d'un modèle empirique, dans le cas où les
R
contributions dépendent de la réponse
s écart-type intralaboratoire issu de répliques ou d’autres études de répétabilité
w
2
s composante intragroupe ou intralaboratoire de la variance
w
s(∆ ) écart-type des différences dans le cadre d’une comparaison d’une méthode de routine à une méthode
y
d’essai définitive
ème
x la i valeur d'entrée dans la détermination d'un résultat
i
ème
′
x écart de la i valeur d'entrée par rapport à la valeur nominale de x
i
ème
x la j valeur d'entrée dans la détermination d'un résultat
j
© ISO 2004 – Tous droits réservés 5
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ISO/TS 21748:2004(F)
ˆ
u()δ incertitude associée à δ due à l’incertitude de l’estimation de δ en mesurant un étalon de mesure de
ˆ
référence ou un matériau de référence de valeur certifiée µ
u( µˆ ) incertitude associée à la valeur certifiée µˆ
22
u(y) incertitude-type composée, associée à y, où uy() = c u (x )
ii
∑
in=1,
2
u(Y) incertitude composée pour le résultat Y = f(y , y , .), où uY() = c u(y )
∑ ii
1 2
i
2
u (y) incertitude-type composée, associée à y, exprimée comme une variance
u incertitude associée à l’inhomogénéité de l’échantillon
inh
U incertitude élargie, égale à k fois l’incertitude-type u
U(y) incertitude élargie de y, où U(y) = ku(y), où k est un facteur d’élargissement
y résultat de la méthode définitive pour l’individu d’essai i dans le cadre d’une comparaison de méthodes
i
d’essai
yˆ résultat de la méthode de routine pour l’individu d’essai i dans le cadre d’une comparaison de
i
méthodes d’essai
y valeur assignée dans le cadre d’un essai d’aptitude
0
∆ biais de laboratoire
∆ estimation du biais du laboratoire l, égale à la moyenne de laboratoire, m, moins la valeur certifiée, µˆ
l
∆ biais moyen de laboratoire dans le cadre d’une comparaison d’une méthode de routine à une méthode
y
d’essai définitive
δ biais intrinsèque de la méthode de mesure utilisée
ˆ
δ biais estimé ou mesuré
µ espérance mathématique inconnue de résultats idéaux
µˆ valeur certifiée d’un matériau de référence
σ écart-type dans le cadre d’un essai d’aptitude
0
σ valeur vraie de l’écart-type de résultats obtenus par mesurages répétés sur un matériau de référence
D
utilisé pour la vérification du biais
σ écart-type interlaboratoires; écart-type de B
L
2
σ variance de B; variance interlaboratoires
L
σ écart-type intralaboratoire; écart-type de e
r r
2
σ variance de e ; variance intralaboratoire
r r
σ écart-type intragroupe
w
σ écart-type intralaboratoire requis pour une performance adéquate
w0
ν nombre réel de degrés de liberté pour l'écart-type de la valeur d'entrée x , ou pour l'incertitude associée
eff i
à x
i
6 © ISO 2004 – Tous droits réservés
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ISO/TS 21748:2004(F)
ν nombre de degrés de liberté
i
5 Principes
5.1 Résultats individuels et performance du processus de mesure
5.1.1 L’incertitude de mesure réfère aux résultats individuels. En revanche, la répétabilité, la reproductibilité
et le biais se rapportent à la performance d’un processus de mesure ou d’essai. Pour les études selon
l’ISO 5725 (toutes les parties), le processus de mesure ou d’essai
...
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