1、Application of ISO 5725 for the determination of repeatability and reproducibility of precision tests performed in standardization work for chemical analysis of steel PD ISO/TR 21074:2016 BSI Standards Publication WB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06National foreword This Publish
2、ed Document is the UK implementation of ISO/TR 21074:2016. The UK participation in its preparation was entrusted to Technical Committee ISE/102, Methods of Chemical Analysis for Iron and Steel. A list of organizations represented on this committee can be obtained on request to its secretary. This pu
3、blication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2016. Published by BSI Standards Limited 2016 ISBN 978 0 580 92003 5 ICS 17.020; 77.080.01 Compliance with a British Standard cannot
4、confer immunity from legal obligations. This Published Document was published under the authority of the Standards Policy and Strategy Committee on 30 November 2016. Amendments/corrigenda issued since publication Date Text affected PUBLISHED DOCUMENT PD ISO/TR 21074:2016 ISO 2016 Application of ISO
5、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 dtermination de la rptabilit et la reproductibilit des essais de prcision raliss en travaux de normalisation po
6、ur lanalyse chimique de lacier TECHNICAL REPORT ISO/TR 21074 Reference number ISO/TR 21074:2016(E) First edition 2016-10-15 PD ISO/TR 21074:2016 ISO/TR 21074:2016(E)ii ISO 2016 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO 2016, Published in Switzerland All rights reserved. Unless otherwise s
7、pecified, 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 o
8、r ISOs member body in the country of the requester. ISO copyright office Ch. de Blandonnet 8 CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 copyrightiso.org www.iso.org PD ISO/TR 21074:2016 ISO/TR 21074:2016(E)Foreword iv 1 Scope . 1 2 Normative references 1 3
9、 T erms 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 rep
10、resentation of the data . 3 5.3.1 General 3 5.3.2 Data plot 3 6 Statistical evaluation 4 6.1 Cochrans 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 Calculatio
11、n 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 ISO 2016 All rights reserved iii Contents Page PD ISO/TR 21074:2016 ISO/TR 21074:20
12、16(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 whi
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14、atters 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
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18、RL: 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 PD ISO/TR 21074:2016 TECHNICAL REPORT ISO/TR 21074:2016(E) Application of ISO 5725 for the determina
19、tion 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 me
20、thod. 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
21、-3. 2 Normative references There are no normative references in this document. 3 T erms a nd definiti ons 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:/ /
22、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 F
23、igure 1.A B C Day 2 Day 1 Figure 1 Structure of the precision test ISO 2016 All rights reserved 1 PD ISO/TR 21074:2016 ISO/TR 21074:2016(E) 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 laborat
24、ory 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 per
25、formed 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 materia
26、ls, 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
27、 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
28、tested. A minimum of two levels by decade with the scheme (for example, 110) is required, and in the case of limited application ranges, three or more levels by decade (for example, 12510) can be selected. NOTE Fully-nested experiments offer higher reliability of repeatability than staggered-nested
29、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 te
30、st 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 convenors requirement. Table 1 shows an exampl
31、e of a list of data. The data obtained by laboratory i are indicated by ( j = 1, 2, 3). 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 PD ISO/TR 21074:2016 ISO/TR
32、21074:2016(E) 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 laborator
33、ies 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),
34、Day 1 to 2 (= yi2) and Day 2 (= yi3) using different symbols. b) Indicate the average for each level. An example of the graph for the original results is shown in Figure 2. 0,006 0,007 0,008 0,009 0,010 0,011 0,012 0,013 0,014 0,015 01234567891 01112131415161718192021 X yi1 yi2 yi3 m x Y Key X labor
35、atory no. Y contents % (mass fraction) Figure 2 Original results ISO 2016 All rights reserved 3 PD ISO/TR 21074:2016 ISO/TR 21074:2016(E) 6 Statistical evaluation The general flow chart of the statistical evaluation is shown in Figure 3. Perform Cochrans test and Grubbs test following the procedure
36、shown below to detected the outliers and delete them. The flow chart diagram of the tests is shown in Figure 4. Input results Cochrans test Grubbs test Remove the outliers Calculate the precisions for Table 2 Table 2 List of statistical values in precision data in Table 2 Prepare the equation of Val
37、idate 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 1) List of raw data 2) Plot of raw data Figure 3 Flow for determining the precision4 ISO 2016 All rights reserved PD ISO/TR 21074:2016 IS
38、O/TR 21074:2016(E) Are outliers present? Delete outliers Are outliers present? Delete outliers YES NO YES NO Grubbs test START One outlying observation for G-value MAX (or G-value MIN) Are outliers present? YES NO One outlier observation for G-value MIN (or G-value MAX) Two outlier observations for
39、the two largest and two smallest STOP YES NO NO YES Delete outliers Delete outliers Cochrans test START Print out the outlier lab. numbers with a double asterisk * STOP 90 % of original Are outliers present? Delete outliers Print out the outlier lab. numbers with a double asterisk * Remaining data i
40、s Figure 4 Flow diagram of the Cochrans test and Grubbs test 6.1 Cochrans test See ISO 5725-2:1994, 7.3.3. The purpose of the Cochrans test is to evaluate the interlaboratory repeatability variance. For that purpose, the intralaboratory repeatability variance is calculated and compared with those of
41、 other laboratories. For each level j , perform the following calculations on each test data set. The test data sets are (A, B) and (A+B)/2, C. a) Obtain the standard deviation: b) Calculate the C-value: ISO 2016 All rights reserved 5 PD ISO/TR 21074:2016 ISO/TR 21074:2016(E) wherei is the identifie
42、r for a certain lab;j is the identifier for a certain level;p is the number of laboratories of level j (note that the number, p , changes if outliers are deleted);S is the highest standard deviation in the set of level j . c) Compare the calculated value with the value for n = 2 in the critical valu
43、es table (see ISO 5725-2:1994, Table 4). d) If the calculated value is larger than 1 % critical value, assume it is an outlier and delete the corresponding data. Then, repeat steps a) to c) for the remaining data. e) Finish the test either when no outliers are detected or the remaining data are equa
44、l to or not less than 90 % of the original data. NOTE A piece of statistical data greater than 1 % or 5 % of the critical value is called an “outlier” and “straggler”, respectively. 6.2 Grubbs test 6.2.1 General See ISO 5725-2:1994, 7.3.4. The purpose of the Grubbs test is to evaluate the between-la
45、boratory consistency. For that purpose, the cell average for each laboratory is obtained and evaluated in terms of the deviation from the overall average. Using (A+B+C)/3 as the test data, perform the following calculations for each level j . NOTE The symbols used in this clause are the same as thos
46、e in 6.1 a) Obtain the average value = of A-B-C. b) Arrange the average values = in ascending order. NOTE The number, p , changes if outliers are removed. d) Obtain the unbiased variance for = : 1 1 6 ISO 2016 All rights reserved PD ISO/TR 21074:2016 ISO/TR 21074:2016(E) 6.2.2 Grubbs test for one ou
47、tlier observation See ISO 5725-2:1994, 7.3.4.1. a) Calculate the following G-values and compare them with the appropriate value in the table of critical values (see ISO 5725-2:1994, Table 5). If the calculated value is larger than 1 % critical value, assume it is an outlier. 1) Test of the maximum v
48、alue: 2) Test of the minimum value: 11 b) If in a) above the maximum value (minimum value) is an outlier, remove it and apply the Grubbs test to the minimum value (maximum value). c) Finish the test when no outliers are detected in steps a) and/or b). When no outliers are detected, conduct a further test for two outlier observations (6.2.2). 6.2.3 Grubbs test for two outlier observations See ISO 5725-2:1994, 7.3.4.2. If in the above Grubbs test a) to c) neither the maximum value nor the minimum value is an outlier, calculate the following G-values and compare them with the appropriate va
