ISO/TS 21749:2005
(Main)Measurement uncertainty for metrological applications — Repeated measurements and nested experiments
Measurement uncertainty for metrological applications — Repeated measurements and nested experiments
ISO/TS 21749:2005 follows the approach taken in the Guide to the expression of the uncertainty of measurement (GUM) and establishes the basic structure for stating and combining components of uncertainty. To this basic structure, it adds a statistical framework using the analysis of variance (ANOVA) for estimating individual components, particularly those classified as Type A evaluations of uncertainty, i.e. based on the use of statistical methods. A short description of Type B evaluations of uncertainty (non-statistical) is included for completeness. ISO/TS 21749:2005 covers experimental situations where the components of uncertainty can be estimated from statistical analysis of repeated measurements, instruments, test items or check standards. It provides methods for obtaining uncertainties from single-, two- and three-level nested designs only. More complicated experimental situations where, for example, there is interaction between operator effects and instrument effects or a cross effect, are not covered. ISO/TS 21749:2005 is not applicable to measurements that cannot be replicated, such as destructive measurements or measurements on dynamically varying systems (such as fluid flow, electronic currents or telecommunications systems). It is not particularly directed to the certification of reference materials (particularly chemical substances) and to calibrations where artefacts are compared using a scheme known as a "weighing design". For certification of reference materials, see ISO Guide 35. When results from interlaboratory studies can be used, techniques are presented in the companion guide ISO/TS 21748. The main difference between ISO/TS 21748 and this Technical Specification is that the ISO/TS 21748 is concerned with reproducibility data (with the inevitable repeatability effects), whereas this Technical Specification concentrates on repeatability data and the use of the analysis of variance for its treatment. ISO/TS 21749:2005 is applicable to a wide variety of measurements, for example, lengths, angles, voltages, resistances, masses and densities.
Incertitude de mesure pour les applications en métrologie — Mesures répétées et expériences emboîtées
General Information
Standards Content (Sample)
TECHNICAL ISO/TS
SPECIFICATION 21749
First edition
2005-02-15
Corrected version
2005-07-15
Measurement uncertainty for
metrological applications — Repeated
measurements and nested experiments
Incertitude de mesure pour les applications en métrologie — Mesures
répétées et expériences emboîtées
Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Statistical methods of uncertainty evaluation .3
4.1 Approach of the Guide to the expression of uncertainty of measurement . 3
4.2 Check standards . 4
4.3 Steps in uncertainty evaluation. 5
4.4 Examples in this Technical Specification. 6
5 Type A evaluation of uncertainty . 6
5.1 General. 6
5.2 Role of time in Type A evaluation of uncertainty . 7
5.3 Measurement configuration. 14
5.4 Material inhomogeneity. 16
5.5 Bias due to measurement configurations . 17
6 Type B evaluation of uncertainty . 26
7 Propagation of uncertainty . 27
7.1 General. 27
7.2 Formulae for functions of a single variable .28
7.3 Formulae for functions of two variables. 28
8 Example — Type A evaluation of uncertainty from a gauge study . 30
8.1 Purpose and background. 30
8.2 Data collection and check standards. 30
8.3 Analysis of repeatability, day-to-day and long-term effects. 31
8.4 Probe bias. 31
8.5 Wiring bias. 33
8.6 Uncertainty calculation. 35
Annex A (normative) Symbols . 37
Bibliography . 38
Foreword
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(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
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established has the right to be represented on that committee. International organizations, governmental and
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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 21749 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
This corrected version of ISO/TS 21749:2005 incorporates the correction of the title.
iv © ISO 2005 – All rights reserved
Introduction
Test, calibration and other laboratories are frequently required to report the results of measurements and the
associated uncertainties. Evaluation of uncertainty is an on-going process that can consume time and
resources. In particular, there are many tests and other operations carried out by laboratories where two or
three sources of uncertainty are involved. Following the approach in the Guide to the expression of uncertainty
of measurement (GUM) to combining components of uncertainty, this document focuses on using the analysis
of variance (ANOVA) for estimating individual components, particularly those based on Type A (statistical)
evaluations.
An experiment is designed by the laboratory to enable an adequate number of measurements to be made, the
analysis of which will permit the separation of the uncertainty components. The experiment, in terms of design
and execution, and the subsequent analysis and uncertainty evaluation, require familiarity with data analysis
techniques, particularly statistical analysis. Therefore, it is important for laboratory personnel to be aware of
the resources required and to plan the necessary data collection and analysis.
In this Technical Specification, the uncertainty components based on Type A evaluations can be estimated
from statistical analysis of repeated measurements, from instruments, test items or check standards.
A purpose of this Technical Specification is to provide guidance on the evaluation of the uncertainties
associated with the measurement of test items, for instance as part of ongoing manufacturing inspection.
Such uncertainties contain contributions from the measurement process itself and from the variability of the
manufacturing process. Both types of contribution include those from operators, environmental conditions and
other effects. In order to assist in separating the effects of the measurement process and manufacturing
variability, measurements of check standards are used to provide data on the measurement process itself.
Such measurements are nominally identical to those made on the test items. In particular, measurements on
check standards are used to help identify time-dependent effects, so that such effects can be evaluated and
contrasted with a database of check standard measurements. These standards are also useful in helping to
control the bias and long-term drift of the process once a baseline for these quantities has been established
from historical data.
Clause 4 briefly describes the statistical methods of uncertainty evaluation including the approach
recommended in the GUM, the use of check standards, the steps in uncertainty evaluation and the examples
in this Technical Specification. Clause 5, the main part of this Technical Specification, discusses the Type A
evaluations. Nested designs in ANOVA are used in dealing with time-dependent sources of uncertainty. Other
sources such as those from the measurement configuration, material inhomogeneity, and the bias due to
measurement configurations and related uncertainty analyses are discussed. Type B (non-statistical)
evaluations of uncertainty are discussed for completeness in Clause 6. The law of propagation of uncertainty
described in the GUM has been widely used. Clause 7 provides formulae obtained by applying this law to
certain functions of one and two variables. In Clause 8, as an example, a Type A evaluation of uncertainty for
a gauge study is discussed, where uncertainty components from various sources are obtained. Annex A lists
the statistical symbols used in this Technical Specification.
TECHNICAL SPECIFICATION ISO/TS 21749:2005(E)
Measurement uncertainty for metrological applications —
Repeated measurements and nested experiments
1 Scope
This Technical Specification follows the approach taken in the Guide to the expression of the uncertainty of
measurement (GUM) and establishes the basic structure for stating and combining components of
uncertainty. To this basic structure, it adds a statistical framework using the analysis of variance (ANOVA) for
estimating individual components, particularly those classified as Type A evaluations of uncertainty, i.e. based
on the use of statistical methods. A short description of Type B evaluations of uncertainty (non-statistical) is
included for completeness.
This Technical Specification covers experimental situations where the components of uncertainty can be
estimated from statistical analysis of repeated measurements, instruments, test items or check standards.
It provides methods for obtaining uncertainties from single-, two- and three-level nested designs only. More
complicated experimental situations where, for example, there is interaction between operator effects and
instrument effects or a cross effect, are not covered.
This Technical Specification is not applicable to measurements that cannot be replicated, such as destructive
measurements or measurements on dynamically varying systems (such as fluid flow, electronic currents or
telecommunications systems). It is not particularly directed to the certification of reference materials
(particularly chemical substances) and to calibrations where artefacts are compared using a scheme known
[14]
as a “weighing design”. For certification of reference materials, see ISO Guide 35 .
When results from interlaboratory studies can be used, techniques are presented in the companion guide
[15]
ISO/TS 21748 . The main difference between ISO/TS 21748 and this Technical Specification is that the
ISO/TS 21748 is concerned with reproducibility data (with the inevitable repeatability effects), whereas this
Technical Specification concentrates on repeatabil
...
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