1、BRITISH STANDARD BS ISO 5725-2:1994 Incorporating Technical Corrigendum No. 1 Implementation of ISO 5725-2:1994 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 ICS 03
2、.120.30 BS ISO 5725-2:1994 This British Standard, having been prepared under the direction of the Management Systems Sector Board, was published under the authority of the Standards Board and comes into effect on 15 April 1995 BSI 12 November 2002 The following BSI references relate to the work on t
3、his standard: Committee reference QMS/16 Draft for comment 90/97779 DC ISBN 0 580 24033 9 Committees responsible for this British Standard The preparation of this British Standard was entrusted to Technical Committee QMS/16, Precision of test methods, upon which the following bodies were represented
4、: British Gas plc Chemical Industries Association Consumers Association Department of Trade and Industry (Laboratory of the Government Chemist) Department of Trade and Industry (National Physical Laboratory) Institute of Quality Assurance Ministry of Agriculture, Fisheries and Food Ministry of Defen
5、ce Royal Society of Chemistry University of London Amendments issued since publication Amd. No. Date Comments 13997 Technical Corrigendum No. 1 12 November 2002 Addition of note to 7.3.4.3 and Table 5BS ISO 5725-2:1994 BSI 12 November 2002 i Contents Page Committees responsible Inside front cover Na
6、tional foreword ii Foreword iv Text of ISO 5725-2 1BS ISO 5725-2:1994 ii BSI 12 November 2002 National foreword This British Standard reproduces verbatim ISO 5725-3:1994, including technical corrigendum May 2002, and implements it as the UK national standard. Parts 1 to 6 of BS ISO 5725 together sup
7、ersede BS 5497-1:1987 which will be withdrawn upon the publication of BS ISO 5725-5. This British Standard is published under the direction of the Management Systems Sector Board whose Technical Committee QMS/16 has the responsibility to: aid enquirers to understand the text; present to the responsi
8、ble international committee any enquiries on interpretation, or proposals for change, and keep UK interests informed; monitor related international and European developments and promulgate them in the UK. Cross-references The British Standards which implement international publications referred to i
9、n this document may be found in the BSI Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Search” facility of the BSI Electronic Catalogue or of British Standards Online. This publication does not purport to include all the necessary provisions of
10、a contract. Users are responsible for its correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, the ISO title page, pages ii to iv, pages 1 to 5
11、2, an inside back cover and a back cover. The BSI copyright notice displayed in this document indicates when the document was last issued.Technical corrigendum 2002-05-15ISO 5725-2:1994 ii BSI 12 November 2002 Contents Page Foreword iv 1 Scope 3 2 Normative references 3 3 Definitions 4 4 Estimates o
12、f the parameters in the basic model 4 5 Requirements for a precision experiment 4 5.1 Layout of the experiment 4 5.2 Recruitment of the laboratories 5 5.3 Preparation of the materials 5 6 Personnel involved in a precision experiment 7 6.1 Panel 7 6.2 Statistical functions 7 6.3 Executive functions 7
13、 6.4 Supervisors 8 6.5 Operators 8 7 Statistical analysis of a precision experiment 9 7.1 Preliminary considerations 9 7.2 Tabulation of the results and notation used 9 7.3 Scrutiny of results for consistency and outliers 12 7.4 Calculation of the general mean and variances 17 7.5 Establishing a fun
14、ctional relationship between precision values and the mean level m 19 7.6 Statistical analysis as a step-by-step procedure 22 7.7 The report to, and the decisions to be taken by, the panel 26 8 Statistical tables 27 Annex A (normative) Symbols and abbreviations used in ISO 5725 31 Annex B (informati
15、ve) Examples of the statistical analysis of precision experiments 33 B.1 Example 1: Determination of the sulfur content of coal (Several levels with no missing or outlying data) 33 B.2 Example 2: Softening point of pitch (Several levels with missing data) 40 B.3 Example 3: Thermometric titration of
16、creosote oil (Several levels with outlying data) 46 Annex C (informative) Bibliography 52 Figure 1 Enlistment questionnaire for interlaboratory study 6 Figure 2 Recommended forms for the collation of results for analysis 11 Figure 3 Flow diagram of the principal steps in the statistical analysis 24
17、Figure B.1 Sulfur content of coal, sample 1 36 Figure B.2 Sulfur content of coal, sample 2 37 Figure B.3 Sulfur content of coal, sample 3 37 Figure B.4 Sulfur content of coal, sample 4 38 Figure B.5 Softening point of pitch: Cell means 44 Figure B.6 Softening point of pitch: Absolute differences wit
18、hin cells 45ISO 5725-2:1994 BSI 12 November 2002 iii Page Figure B.7 Titration of creosote oil: Mandels between-laboratory consistency statistic, h, grouped by laboratories 49 Figure B.8 Titration of creosote oil: Mandels within-laboratory consistency statistic, k, grouped by laboratories 50 Figure
19、B.9 Plot of s rjand s Rjagainst , of the data from Table B.16, showing the functional relationships fitted in 7.5 from these data 51 Table 1 Relationship I: s = bm 21 Table 2 Relationship II: s = a + bm 22 Table 3 Relationship III: lg s = c + d lg m 22 Table 4 Critical values for Cochrans test 27 Ta
20、ble 5 Critical values for Grubbs test 28 Table 6 Indicators for Mandels h and k statistics at the 1 % significance level 29 Table 7 Indicators for Mandels h and k statistics at the 5 % significance level 30 Table B.1 Original data: Sulfur content of coal 34 Table B.2 Cell means: Sulfur content of co
21、al 35 Table B.3 Standard deviations: Sulfur content of coal 35 Table B.4 Application of Grubbs test to cell means 39 Table B.5 Computed values of , s rjand s Rj,for sulfur content of coal 39 Table B.6 Original data: Softening point of pitch ( C) 41 Table B.7 Cell means: Softening point of pitch ( C)
22、 42 Table B.8 Absolute differences within cells: Softening point of pitch ( C) 42 Table B.9 Values of Cochrans test statistic, C 43 Table B.10 Application of Grubbs test to cell means 43 Table B.11 Computed values of , s Rjand s rjfor softening point of pitch 43 Table B.12 Original data: Thermometri
23、c titration of creosote oil 46 Table B.13 Cell means: Thermometric titration of creosote oil 47 Table B.14 Cell ranges: Thermometric titration of creosote oil 48 Table B.15 Application of Grubbs test to cell means 48 Table B.16 Computed values of , s rjand s Rjfor thermometric titration of creosote
24、oil 51 m j m j m j m jISO 5725-2:1994 iv BSI 12 November 2002 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 comm
25、ittees. 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
26、International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. 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 mem
27、ber bodies casting a vote. International Standard ISO 5725-2 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 6, Measurement methods and results. ISO 5725 consists of the following parts, under the general title Accuracy (trueness and precision) of
28、measurement methods and results: Part 1: General principles and definitions; Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method; Part 3: Intermediate measures of the precision of a standard measurement method; Part 4: Basic methods for th
29、e determination of the trueness of a standard measurement method; Part 5: Alternative methods for the determination of the precision of a standard measurement method; Part 6: Use in practice of accuracy values. Parts 1 to 6 of ISO 5725 together cancel and replace ISO 5725:1986, which has been extend
30、ed to cover trueness (in addition to precision) and intermediate precision conditions (in addition to repeatability and reproducibility conditions). Annex A forms an integral part of this part of ISO 5725. Annex B and Annex C are for information only. Descriptors: measurement, tests, test results, a
31、ccuracy, reproducibility, statistical analysis.ISO 5725-2:1994 BSI 12 November 2002 1 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 tes
32、t 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 part of ISO 5725. ISO 5725-1 should be read in conjunction with all other parts o
33、f ISO 5725, including this part, because it gives the underlying definitions and general principles. This part of ISO 5725 is concerned solely with estimating by means of the repeatability standard deviation and reproducibility standard deviation. Although other types of experiment (such as the spli
34、t-level experiment) are used in certain circumstances for the estimation of precision, they are not dealt with in this part of ISO 5725 but rather are the subject of ISO 5725-5. Nor does this part of ISO 5725 consider any other measures of precision intermediate between the two principal measures; t
35、hose 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. The estimation of trueness is not considered in this part of ISO 5725; all aspects of the estimation of trueness are the subject of
36、 ISO 5725-4.2 blankISO 5725-2:1994 BSI 12 November 2002 3 1 Scope 1.1 This part of ISO 5725 amplifies the general principles to be observed in designing experiments for the numerical estimation of the precision of measurement methods by means of a collaborative interlaboratory experiment; provides a
37、 detailed practical description of the basic method for routine use in estimating the precision of measurement methods; provides guidance to all personnel concerned with designing, performing or analysing the results of the tests for estimating precision. NOTE 1 Modifications to this basic method fo
38、r particular purposes are given in other parts of ISO 5725. Annex B provides practical examples of estimating the precision of measurement methods by experiment. 1.2 This part of ISO 5725 is concerned exclusively with measurement methods which yield measurements on a continuous scale and give a sing
39、le value as the test result, although this single value may be the outcome of a calculation from a set of observations. 1.3 It assumes that in the design and performance of the precision experiment, all the principles as laid down in ISO 5725-1 have been observed. The basic method uses the same numb
40、er 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. NOTE 2 Worked examples are given to d
41、emonstrate 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
42、 also considered. 1.4 The statistical model of clause 5 of ISO 5725-1:1994 is accepted as a suitable basis for the interpretation and analysis of the test results, the distribution of which is approximately normal. 1.5 The basic method, as described in this part of ISO 5725, will (usually) estimate
43、the precision of a measurement method: a) when it is required to determine the repeatability and reproducibility standard deviations as defined in ISO 5725-1; b) when the materials to be used are homogeneous, or when the effects of heterogeneity can be included in the precision values; and c) when t
44、he use of a balanced uniform-level layout is acceptable. 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 standards contain provisions which, th
45、rough reference in this text, constitute provisions of this part of ISO 5725. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this part of ISO 5725 are encouraged to investigate the possibility of applying the m
46、ost recent editions of the standards indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. ISO 3534-1:1993, Statistics Vocabulary and symbols Part 1: Probability and general statistical terms. ISO 5725-1:1994, Accuracy (trueness and precision) of meas
47、urement methods and results Part 1: General principles and definitions.ISO 5725-2:1994 4 BSI 12 November 2002 3 Definitions For the purposes of this part of ISO 5725, the definitions given in ISO 3534-1 and in ISO 5725-1 apply. The symbols used in ISO 5725 are given in Annex A. 4 Estimates of the pa
48、rameters in the basic model 4.1 The procedures given in this part of ISO 5725 are based on the statistical model given in clause 5 of ISO 5725-1:1994 and elaborated upon in subclause 1.2 of ISO 5725-1:1994. In particular, these procedures are based on equations (2) to (6) of clause 5 of ISO 5725-1:1
49、994. The model is y = m + B + e where, for the particular material tested, 4.2 Equations (2) to (6) of ISO 5725-1:1994, clause 5 are expressed in terms of the true standard deviations of the populations considered. In practice, the exact values of these standard deviations are not known, and estimates of precision values must be made from a relatively small sample of all the possible l
