ISO 5725-3:2023
(Main)Accuracy (trueness and precision) of measurement methods and results — Part 3: Intermediate precision and alternative designs for collaborative studies
Accuracy (trueness and precision) of measurement methods and results — Part 3: Intermediate precision and alternative designs for collaborative studies
This document provides a) a discussion of alternative experimental designs for the determination of trueness and precision measures including reproducibility, repeatability and selected measures of intermediate precision of a standard measurement method, including a review of the circumstances in which their use is necessary or beneficial, and guidance as to the interpretation and application of the resulting estimates, and b) worked examples including specific designs and computations. Each of the alternative designs discussed in this document is intended to address one (or several) of the following issues: a) a discussion of the implications of the definitions of intermediate precision measures; b) a guidance on the interpretation and application of the estimates of intermediate precision measures in practical situations; c) determining reproducibility, repeatability and selected measures of intermediate precision; d) improved determination of reproducibility and other measures of precision; e) improving the estimate of the sample mean; f) determining the range of in-house repeatability standard deviations; g) determining other precision components such as operator variability; h) determining the level of reliability of precision estimates; i) reducing the minimum number of participating laboratories by optimizing the reliability of precision estimates; j) avoiding distorted estimations of repeatability (split-level designs); k) avoiding distorted estimations of reproducibility (taking the heterogeneity of the material into consideration). Often, the performance of the method whose precision is being evaluated in a collaborative study will have previously been assessed in a single-laboratory validation study conducted by the laboratory which developed it. Relevant factors for the determination of intermediary precision will have been identified in this prior single-laboratory study.
Exactitude (justesse et fidélité) des résultats et méthodes de mesure — Partie 3: Fidélité intermédiaire et plans alternatifs pour les études collaboratives
Le présent document fournit: a) une discussion de plans d’expérience alternatifs pour la détermination de mesures de justesse et de fidélité, y compris la reproductibilité, la répétabilité et les mesures sélectionnées de la fidélité intermédiaire d’une méthode de mesure normalisée, incluant un examen des circonstances dans lesquelles leur utilisation est nécessaire ou bénéfique, ainsi que des recommandations relatives à l’interprétation et à l’application des estimations en résultant; et b) des exemples détaillés, incluant des plans et des calculs spécifiques. Chacun des plans alternatifs abordés dans le présent document est destiné à traiter l’un (ou plusieurs) des problèmes suivants: a) une discussion des implications des définitions des mesures de fidélité intermédiaire; b) des recommandations relatives à l’interprétation et à l’application des estimations des mesures de fidélité intermédiaire dans des situations pratiques; c) la détermination de la reproductibilité, de la répétabilité et de mesures sélectionnées de la fidélité intermédiaire; d) la détermination améliorée[1] de la reproductibilité et d’autres mesures de la fidélité; e) l’amélioration de l’estimation de la moyenne de l’échantillon; f) la détermination de la plage des écarts-types de répétabilité interne; g) la détermination d’autres composantes de la fidélité, telles que la variabilité des opérateurs; h) la détermination du niveau de fiabilité des estimations de la fidélité; i) la réduction du nombre minimal de laboratoires participants en optimisant la fiabilité des estimations de la fidélité; j) l’évitement d’estimations biaisées de la répétabilité (plans à niveau fractionné); k) l’évitement d’estimations biaisées de la reproductibilité (en tenant compte de l’hétérogénéité du matériau). Il arrive souvent que la performance de la méthode dont la fidélité est soumise à évaluation dans une étude collaborative ait déjà été évaluée dans le cadre d’une étude de validation intralaboratoire menée par le laboratoire qui l’a élaborée. Des facteurs pertinents pour la détermination de la fidélité intermédiaire ont donc déjà été identifiés lors de cette étude intralaboratoire antérieure. [1] Autorisant une réduction du nombre de laboratoires.
Točnost (pravilnost in natančnost) merilnih metod in rezultatov – 3. del : Vmesne mere natančnosti in alternativni pristopi za primerjalne študije
General Information
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Standards Content (Sample)
SLOVENSKI STANDARD
01-september-2024
Točnost (pravilnost in natančnost) merilnih metod in rezultatov – 3. del : Vmesne
mere natančnosti in alternativni pristopi za primerjalne študije
Accuracy (trueness and precision) of measurement methods and results — Part 3:
Intermediate precision and alternative designs for collaborative studies
Exactitude (justesse et fidélité) des résultats et méthodes de mesure — Partie 3: Fidélité
intermédiaire et plans alternatifs pour les études collaboratives
Ta slovenski standard je istoveten z: ISO 5725-3:2023
ICS:
03.120.30 Uporaba statističnih metod Application of statistical
methods
17.020 Meroslovje in merjenje na Metrology and measurement
splošno in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 5725-3
Second edition
2023-06
Accuracy (trueness and precision) of
measurement methods and results —
Part 3:
Intermediate precision and alternative
designs for collaborative studies
Exactitude (justesse et fidélité) des résultats et méthodes de mesure —
Partie 3: Fidélité intermédiaire et plans alternatifs pour les études
collaboratives
Reference number
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols . 3
5 General requirements . 4
6 Intermediate measures of the precision of a standard measurement method .5
6.1 Factors and factor levels . 5
6.1.1 Definitions and examples . 5
6.1.2 Selection of factors of interest . 6
6.1.3 Random and fixed effects . 6
6.1.4 Statistical model . 7
6.2 Within-laboratory study and analysis of intermediate precision measures . 9
6.2.1 Simplest approach . 9
6.2.2 Alternative method . 10
6.2.3 Effect of the measurement conditions on the final quoted result . 10
7 Nested design .11
7.1 Balanced fully-nested design . 11
7.2 Staggered-nested design . 12
7.3 Balanced partially-nested design . 13
7.4 Orthogonal array design . 14
8 Design for heterogeneous material .16
8.1 Applications of the design for a heterogeneous material . 16
8.2 Layout of the design for a heterogeneous material . 17
8.3 Statistical analysis . 17
9 Split-level design .17
9.1 Applications of the split-level design . 17
9.2 Layout of the split-level design . 19
9.3 Statistical analysis . 19
10 Design across levels .19
10.1 Applications of the design across levels . 19
10.2 Layout of the design across levels . 20
10.3 Statistical analysis . 20
11 Reliability of interlaboratory parameters .20
11.1 Reliability of precision estimates . 20
11.2 Reliability of estimates of the overall mean . 21
11.2.1 General . 21
11.2.2 Balanced fully-nested design (2 factors) . 21
11.2.3 Staggered nested design (2 factors) . 21
11.2.4 Balanced partially-nested design . 21
11.2.5 Orthogonal array design . 21
11.2.6 Split-level design . 22
Annex A (informative) Fully- and partially-nested designs .23
Annex B (informative) Analysis of variance for balanced fully-nested design .25
Annex C (informative) Analysis of variance for staggered design .30
Annex D (informative) Analysis of variance for the balanced partially-nested design (three
factors) .38
iii
Annex E (informative) Statistical model for an experiment with heterogeneous material .41
Annex F (informative) Analysis of variance for split-level design .42
Annex G (informative) Example for split-level design . 44
Annex H (informative) Design across levels .47
Annex I (informative) Restricted maximum likelihood (REML) .48
Annex J (informative) Examples of the statistical analysis of intermediate precision
experiment .49
Annex K (informative) Example for an analysis across levels .55
Bibliography .57
iv
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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO document should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use
of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
patent rights in respect thereof. As of the date of publication of this document, ISO had not received
notice of (a) patent(s) which may be required to implement this document. However, implementers are
cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all
such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
This second ed
...
INTERNATIONAL ISO
STANDARD 5725-3
Second edition
2023-06
Accuracy (trueness and precision) of
measurement methods and results —
Part 3:
Intermediate precision and alternative
designs for collaborative studies
Exactitude (justesse et fidélité) des résultats et méthodes de mesure —
Partie 3: Fidélité intermédiaire et plans alternatifs pour les études
collaboratives
Reference number
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .v
Introduction . vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols . 3
5 General requirements . 4
6 Intermediate measures of the precision of a standard measurement method .5
6.1 Factors and factor levels . 5
6.1.1 Definitions and examples . 5
6.1.2 Selection of factors of interest . 6
6.1.3 Random and fixed effects . 6
6.1.4 Statistical model . 7
6.2 Within-laboratory study and analysis of intermediate precision measures . 9
6.2.1 Simplest approach . 9
6.2.2 Alternative method . 10
6.2.3 Effect of the measurement conditions on the final quoted result . 10
7 Nested design .11
7.1 Balanced fully-nested design . 11
7.2 Staggered-nested design . 12
7.3 Balanced partially-nested design . 13
7.4 Orthogonal array design . 14
8 Design for heterogeneous material .16
8.1 Applications of the design for a heterogeneous material . 16
8.2 Layout of the design for a heterogeneous material . 17
8.3 Statistical analysis . 17
9 Split-level design .17
9.1 Applications of the split-level design . 17
9.2 Layout of the split-level design . 19
9.3 Statistical analysis . 19
10 Design across levels .19
10.1 Applications of the design across levels . 19
10.2 Layout of the design across levels . 20
10.3 Statistical analysis . 20
11 Reliability of interlaboratory parameters .20
11.1 Reliability of precision estimates . 20
11.2 Reliability of estimates of the overall mean . 21
11.2.1 General . 21
11.2.2 Balanced fully-nested design (2 factors) . 21
11.2.3 Staggered nested design (2 factors) . 21
11.2.4 Balanced partially-nested design . 21
11.2.5 Orthogonal array design . 21
11.2.6 Split-level design . 22
Annex A (informative) Fully- and partially-nested designs .23
Annex B (informative) Analysis of variance for balanced fully-nested design .25
Annex C (informative) Analysis of variance for staggered design .30
Annex D (informative) Analysis of variance for the balanced partially-nested design (three
factors) .38
iii
Annex E (informative) Statistical model for an experiment with heterogeneous material .41
Annex F (informative) Analysis of variance for split-level design .42
Annex G (informative) Example for split-level design . 44
Annex H (informative) Design across levels .47
Annex I (informative) Restricted maximum likelihood (REML) .48
Annex J (informative) Examples of the statistical analysis of intermediate precision
experiment .49
Annex K (informative) Example for an analysis across levels .55
Bibliography .57
iv
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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO document should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use
of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
patent rights in respect thereof. As of the date of publication of this document, ISO had not received
notice of (a) patent(s) which may be required to implement this document. However, implementers are
cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all
such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
This second edition cancels and replaces the first edition (ISO 5725-3:1994), which has been technically
revised. It also incorporates the Technical Corrigendum ISO 5725-3:1994/Cor.1:2001.
The main changes are as follows:
— Several additional experimental designs have been added to this version compared to the previous
version, some of them from ISO 5725-5. These are orthogonal array designs, split level designs,
designs for heterogeneous sample material as well as designs across levels.
— Furthermore, the standard was supplemented by considerations on the selection of factors and
modelling of the factorial effects, as well as by a section in which the reliability of the various
interlaboratory test parameters (mean and precision parameters) are considered.
A list of all parts in the ISO 5725 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
v
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