ISO/TR 21074:2016

TECHNICAL ISO/TR
REPORT 21074
First edition
2016-10-15
Application of ISO 5725 for the
determination of repeatability and
reproducibility of precision tests
performed in standardization work
for chemical analysis of steel
Application de la norme ISO 5725 pour la détermination de la
répétabilité et la reproductibilité des essais de précision réalisés en
travaux de normalisation pour l’analyse chimique de l’acier
Reference number
©
ISO 2016
© ISO 2016, Published in Switzerland
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ii © ISO 2016 – All rights reserved

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Precision test . 1
4.1 Structure of the precision test . 1
4.2 Homogeneity of samples . 2
4.3 Number of laboratories and number of levels . 2
5 Representation of the experimental results . 2
5.1 General . 2
5.2 Table of results and number of decimal places . 2
5.3 Graphical representation of the data . 3
5.3.1 General. 3
5.3.2 Data plot . 3
6 Statistical evaluation . 4
6.1 Cochran’s test . 5
6.2 Grubbs’ test . 6
6.2.1 General. 6
6.2.2 Grubbs’ test for one outlier observation . 7
6.2.3 Grubbs’ test for two outlier observations . 7
6.3 Treatment of outlier observations . 8
6.4 Calculation of precision . 8
6.5 Representation of the results of the statistical evaluations . 9
6.6 Functions linking the level and the precision parameters .13
7 Determining smoothed precision and scope .15
Bibliography .16
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 documents 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).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
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constitute an endorsement.
For an explanation on 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 the following URL: www.iso.org/iso/foreword.html.
The committee responsible for this document is ISO/TC 17, Steel, Subcommittee SC 1, Methods of
determination of chemical composition.
iv © ISO 2016 – All rights reserved

TECHNICAL REPORT ISO/TR 21074:2016(E)
Application of ISO 5725 for the determination of
repeatability and reproducibility of precision tests
performed in standardization work for chemical analysis
of steel
1 Scope
This document describes how to determine the repeatability and reproducibility of precision tests
performed within standardization work using the chemical analysis method. Specifically, this document
explains the procedure for calculating precision, using precision test data of ISO 5725-3:1994, Table D.2
for the precision test in ISO 9647:1989 as an example.
The procedure of the international test for determining precision is described in ISO 5725-2 and
ISO 5725-3.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
4 Precision test
4.1 Structure of the precision test
The structure of the precision test normally used within standardization work using chemical analysis
is a 3-factor, staggered-nested structure, as shown in Figure 1.
Day 1 Day 2
A B C
Figure 1 — Structure of the precision test
a) Both A and B (Day 1) are obtained under repeatability where independent test results are obtained
with the same method on identical items in the same laboratory by the same operator using the
same equipment within short intervals of time.
b) C (Day 2) is obtained under time-different intermediate precision conditions, except for the time
factor. The measurement is performed by the same operator and, in addition, the measurements at
a given level are performed using the same sample and equipment throughout.
4.2 Homogeneity of samples
For a precision test it is important to use homogeneous samples. Therefore, it is necessary to control the
homogeneity of the samples selected for each precision test, if the samples are not certified reference
materials, before starting a test in order to be sure that the heterogeneity level of the sample can be
included in the expected precision values.
4.3 Number of laboratories and number of levels
In principle, the number of laboratories that participate in an international cooperative test is decided
on the basis of the required precision. As this approach is often difficult to implement, the practical rule
typically followed is the selection of 8 to 15 (or more) laboratories see ISO 5725-1:1994, 6.3.4, preferably
in 5 countries. The number of levels depends on the range and scope of the method to be tested. A
minimum of two levels by decade with the scheme (for example, 1–10) is required, and in the case of
limited application ranges, three or more levels by decade (for example, 1–2–5–10) can be selected.
NOTE Fully-nested experiments offer higher reliability of repeatability than staggered-nested experiments.
However, it will not improve the reliability of reproducibility significantly. From the standpoint of improving
reliability, it is effective to increase the number of participating laboratories.
5 Representation of the experimental results
5.1 General
First, on the basis of precision test results, prepare the following tables and graphs.
5.2 Table of results and number of decimal places
Prepare a list of precision data.
In the list of data, the number of decimal places is the number required in the experiment plus one
according to the convenor’s requirement.
Table 1 shows an example of a list of data.
The data obtained by laboratory i are indicated by y ( j = 1, 2, 3).
ij
The symbol p represents the number of laboratories participating in the experiment. (It should be
noted that the number changes if outliers are deleted.)
2 © ISO 2016 – All rights reserved

Table 1 — Original results
Lab. no. Day 1 Day 2
A B C
1 y11 y12 y13
— — — —
i yi1 yi2 yi3
— — — —
p yp1 yp2 yp3
5.3 Graphical representation of the data
5.3.1 General
All data can be evaluated by graphical representation just to get an overview of the data population
distribution. If there are laboratories which have obviously erroneous values for several levels,
eliminating those laboratories as an outlier may be considered if deemed necessary.
5.3.2 Data plot
Draw a graph for each of the levels by plotting the data as follows.
a) For each of the laboratories in Table 1, plot Day 1 to 1 (= yi1), Day 1 to 2 (= yi2) and Day 2 (= yi3)
using different symbols.
b) Indicate the average mx for each level.
An example of the graph for the original results is shown in Figure 2.
Y
0,015
0,014
0,013
yi1
0,012
0,011
yi2
0,010
yi3
0,009
0,008 m
x
0,007
0,006
X
012345678 9101112131415161718192021
Key
X laboratory no.
Y contents % (mass fraction)
Figure 2 — Original results
6 Statistical evaluation
The general flow chart of the statistical evaluation is shown in Figure 3.
Perform Cochran’s test and Grubbs’ test following the procedure shown below to detected the outliers
and delete them. The flow chart diagram of the tests is shown in Figure 4.
Input results
1) List of raw data
2) Plot of raw data
Cochran's test Grubbs' test
Remove the outliers
Calculate the precisions for
Table 2
List of statistical values in
Table 2
Prepare the equation of
precision data in Table 2
Validate the statistical values
Vr < VRw < VR" (where V=variance)
CVR, AIMCVR, MAXCVR, trueness
Determine the precision of
smoothed values in Table 3
Determine the scope
Figure 3 — Flow for determining the precision
4 © ISO 2016 – All rights reserved

Cochran's test START Grubbs' test START
One outlying observation for
G-value MAX (or G-value MIN)
NO
Are outliers
NO
present?
Are outliers present?
YES
YES
Delete outliers
Two outlier observations for the
Delete outliers
two largest and two smallest
Print out the outlier lab. numbers
One outlier observation for
with a double asterisk **
G-value MIN (or G-value MAX) NO
Are outliers present?
Delete outliers NO
Are outliers present?
YES
YES
Dele
...