ISO/FDIS 5725-2

2025-07-26
ISO/TC 69/SC 6
Secretariat: JISC
Date: 2025-xx
Accuracy (trueness and precision) of measurement methods and
results — —
Part 2:
Basic method for the determination of repeatability and
reproducibility of a standard measurement method
Exactitude (justesse et fidélité) des résultats et méthodes de mesure — —
Partie 2: Méthode de base pour la détermination de la répétabilité et de la reproductibilité d'une méthode de
mesure normalisée
FDIS stage
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'sISO’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:
E-mail: copyright@iso.org
Website: www.iso.org
Published in Switzerland.
ii
Contents
Foreword . iv
Introduction . v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and subscripts . 2
4.1 Symbols . 2
4.2 Subscripts . 3
5 Estimates of the parameters in the basic model . 4
6 Requirements for a precision experiment . 5
6.1 Layout of the experiment . 5
6.2 Recruitment of the laboratories . 6
6.3 Preparation of the materials . 6
7 Personnel involved in a precision experiment . 7
7.1 Panel . 7
7.2 Statistical functions . 8
7.3 Executive functions . 8
7.4 Supervisors . 9
7.5 Operators . 9
8 Statistical analysis of a precision experiment . 10
8.1 Preliminary considerations . 10
8.2 Tabulation of the results and notation used . 11
8.3 Scrutiny of results for consistency and outliers . 13
8.4 Calculation of the general mean and variances . 21
8.5 Establishing a functional relationship between precision values, s, and the mean level, m23
8.6 Statistical analysis as a step-by-step procedure . 30
8.7 Report to the panel and decisions to be taken by the panel . 32
9 Statistical tables . 35
Annex A (informative) Number of laboratories required for an estimate of precision . 40
Annex B (informative) Alternative calculations of variance components . 44
Annex C (informative) Examples of the statistical analysis of precision experiments . 46
Annex D (informative) Calculation of critical values and indicators . 69
Bibliography . 72

iii
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 third edition cancels and replaces the second edition (ISO 5725-2:2019), which has been technically
revised.
The main changes are as follows:
— — several typos have been corrected;
— — subscripts have been made consistent;
— — references have been updated
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.
iv
Introduction
ISO 5725 uses two terms, “trueness” and “precision”, to describe the accuracy of a measurement method.
“Trueness” refers to the closeness of agreement between the arithmetic mean of a large number of test results
and the true or accepted reference value. “Precision” refers to the closeness of agreement between test results.
General consideration of these quantities is given in ISO 5725-1 and so is not repeated in this document.
ISO 5725-1 should be read in conjunction with all other parts of ISO 5725, including this document, because
it gives the underlying definitions and general principles.
This document is concerned solely with estimating the repeatability standard deviation and reproducibility
standard deviation based on an interlaboratory design in which each laboratory conducts a number of
independent measurements of the same sample under repeatability conditions. There are other designs (such
as nested, factorial or split-level experiments) which can be used for the estimation of precision: these are not
dealt with in this document but rather are the subject of other parts of ISO 5725. Nor does this document
consider any other measures of precision intermediate between the two principal measures; those are the
subject of ISO 5725-3.
In certain circumstances, the data obtained from an experiment carried out to estimate precision are used also
to estimate trueness and can be used to evaluate measurement uncertainty. The estimation of trueness is not
considered in this document; all aspects of the estimation of trueness are the subject of ISO 5725-4. The
evaluation of measurement uncertainty, using inter-laboratory estimates of trueness and precision, is the
subject of ISO 21748.
Annex CAnnex C provides practical examples of estimating the precision of measurement methods by
experiment. Worked examples are given to demonstrate balanced uniform sets of test results, although in one
example a variable number of replicates per cell were reported (unbalanced design) and in another some data
were missing. This is because an experiment designed to be balanced can turn out to be unbalanced. Stragglers
and outliers are also considered.
v
Accuracy (trueness and precision) of measurement methods and
results — —
Part 2:
Basic method for the determination of repeatability and
reproducibility of a standard measurement method
1 Scope
1.1 1.1 This document
— — amplifies the general principles for designing experiments for the numerical estimation of the
precision of measurement methods by means of a collaborative interlaboratory experiment,
— — provides a detailed practical description of the basic method for routine use in estimating the precision
of measurement methods, and
— — provides guidance to all personnel concerned with designing, performing or analysing the results of
the tests for estimating precision.
NOTE Modifications to this basic method for particular purposes are given in other parts of ISO 5725.
1.2 1.2 It is concerned exclusively with measurement methods which yield measurements on a
continuous scale and give a single value as the test result, although this single value can be the outcome of a
calculation from a set of observations.
1.3 1.3 It assumes that in the design and performance of the precision experiment, all the principles
as laid down in ISO 5725-1 are observed. The basic method uses the same number of test results in each
laboratory, with each laboratory analysing the same levels of test sample; i.e. a balanced uniform-level
experiment. The basic method applies to procedures that have been standardized and are in regular use in a
number of laboratories.
1.4 1.4 The statistical model of ISO 5725-1:2023, Clause 5, is accepted as a suitable basis for the
interpretation and analysis of the test results, the distribution of which is approximately normal.
1.5 1.5 The basic method, as described in this document, (usually) estimates the precision of a
measurement method:
a) a) when it is required to determine the repeatability and reproducibility standard deviations as
defined in ISO 5725-1;
b) b) when the materials to be used are homogeneous, or when the effects of heterogeneity can be
included in the precision values;
c) c) when the use of a balanced uniform-level layout is acceptable.
1.6 1.6 The same approach can be used to make a preliminary estimate of precision for measurement
methods which have not reached standardization or are not in routine use.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements 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: General statistical terms and terms used in
probability
ISO 3534--2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534--3, Statistics — Vocabulary and symbols — Part 3: Design of experiments
ISO 5725--1, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principles and definitions
3 Terms and definitions
For the purposes of this document, the definitions given in ISO 3534-1, ISO 3534-2, ISO 3534-3, an
...