1、BRITISH STANDARD BS ISO 5725-3:1994 Incorporating Technical Corrigendum No. 1 Implementation of ISO 5725-3:1994 Accuracy (trueness and precision) of measurement methods and results Part 3: Intermediate measures of the precision of a standard measurement method ICS 03.120.30 NO COPYING WITHOUT BSI PE
2、RMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBS ISO 5725-3:1994 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 15 March 2002 The following BSI
3、references relate to the work on this standard: Committee reference QMS/16 Draft for comment 91/89301 DC ISBN 0 580 24029 0 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
4、 following bodies were represented: 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, Fi
5、sheries and Food Ministry of Defence Royal Society of Chemistry University of London Amendments issued since publication Amd. No. Date Comments 13575 Technical Corrigendum No. 1 15 March 2002 Correction to equations and in B.2 and the first equation in Table C.2 s 2 (1) s 2 (2)BS ISO 5725-3:1994 BSI
6、 15 March 2002 i Contents Page Committees responsible Inside front cover National foreword ii Foreword iv Text of ISO 5725-3 1BS ISO 5725-3:1994 ii BSI 15 March 2002 National foreword This British Standard reproduces verbatim ISO 5725-3:1994, including technical corrigendum October 2001, and impleme
7、nts it as the UK national standard. Parts 1 to 6 of BS ISO 5725 together supersede BS 5497-1:1987 which will be withdrawn upon the publication of BS ISO 5725-5.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 Sector Board whose Technical Committee QMS/16 has the responsibili
8、ty to: NOTE International and European Standards, as well as overseas standards, are available from Customer Services, BSI, 389 Chiswick High Road, London W4 4AL. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for
9、 their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. aid enquirers to understand the text; present to the responsible international committee any enquiries on interpretation, or proposals for change, and keep UK interests informed;
10、 monitor related international and European developments and promulgate them in the UK 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 29 and a back cover. The BSI copyright notice displayed in this documen
11、t indicates when the document was last issued.Technical corrigendum2001-10-15ISO 5725-3:1994 ii BSI 15 March 2002 Contents Page Foreword iv Introduction 1 1S c o p e 2 2 Normative references 3 3 Definitions 3 4 General requirement 3 5 Important factors 3 6S t a t i s t i c a l m o d e l 4 6.1 Basic
12、model 4 6.2 General mean, m 4 6.3 Term B 5 6.4 Terms B 0 , B (1) , B (2) , etc. 5 6.5 Error term, e 6 7 Choice of measurement conditions 7 8 Within-laboratory study and analysis of intermediate precision measures 7 8.1 Simplest approach 7 8.2 An alternative method 8 8.3 Effect of the measurement con
13、ditions on the final quoted result 8 9 Interlaboratory study and analysis of intermediate precision measures 9 9.1 Underlying assumptions 9 9.2 Simplest approach 9 9.3 Nested experiments 9 9.4 Fully-nested experiment 9 9.5 Staggered-nested experiment 9 9.6 Allocation of factors in a nested experimen
14、tal design 10 9.7 Comparison of the nested design with the procedure given in ISO 5725-2 11 9.8 Comparison of fully-nested and staggered-nested experimental designs 11 Annex A (normative) Symbols and abbreviations used in ISO 5725 12 Annex B (normative) Analysis of variance for fully-nested experime
15、nts 14 B.1 Three-factor fully-nested experiment 14 B.2 Four-factor fully-nested experiment 15 Annex C (normative) Analysis of variance for staggered-nested experiments 17 C.1 Three-factor staggered-nested experiment 17 C.2 Four-factor staggered-nested experiment 18 C.3 Five-factor staggered-nested e
16、xperiment 19 C.4 Six-factor staggered-nested experiment 20 Annex D (informative) Examples of the statistical analysis of intermediate precision experiments 20 D.1 Example 1 Obtaining the time + operator-different intermediate precision standard deviation, s I(TO) , within a specific laboratory at a
17、particular level of the test 20ISO 5725-3:1994 BSI 15 March 2002 iii Page D.2 Example 2 Obtaining the time-different intermediate precision standard deviation by interlaboratory experiment 23 Annex E (informative) Bibliography 29 Figure 1 Schematic layouts for three-factor and four-factor fully-nest
18、ed experiments 10 Figure 2 Schematic layout of a four-factor staggered-nested experiment 10 Figure D.1 Carbon content in steel Deviations from the mean of the measurements on both days versus the sample number 22 Figure D.2 Vanadium content in steel Test results for day 1 and 2 at level 1 versus lab
19、oratory number 24 Figure D.3 Vanadium content in steel Repeatability standard deviation s r , time-different intermediate precision standard deviation s I(T)and reproducibility standard deviation s Ras functions of the concentration level 28 Table 1 Four important factors and their states 4 Table B.
20、1 ANOVA table for a three-factor fully-nested experiment 14 Table B.2 ANOVA table for a four-factor fully-nested experiment 16 Table C.1 ANOVA table for a three-factor staggered-nested experiment 18 Table C.2 ANOVA table for a four-factor staggered-nested experiment 19 Table C.3 ANOVA table for a fi
21、ve-factor staggered-nested experiment 19 Table C.4 ANOVA table for a six-factor staggered-nested experiment 20 Table D.1 Original data Carbon content, % (m/m)2 1 Table D.2 Original data Vanadium content, % (m/m)2 5 Table D.3 Values of w i(1) , w i(2)and 26 Table D.4 ANOVA table Vanadium content 27 T
22、able D.5 Values of s r , s I(T)and s Rfor six levels of vanadium content in steel 27 Descriptors: Measurement, tests, test results, accuracy, reproducibility, statistical analysis. y i(2)ISO 5725-3:1994 iv BSI 15 March 2002 Foreword ISO (the International Organization for Standardization) is a world
23、wide 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 t
24、hat 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. Draft International Standards adopted
25、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 member bodies casting a vote. International Standard ISO 5725-3 was prepared by Technical Committee ISO/TC 69, Applications of statistical me
26、thods, Subcommittee SC 6, Measurement methods and results. ISO 5725 consists of the following parts, under the general title Accuracy (trueness and precision) of measurement methods and results: Part 1: General principles and definitions; Part 2: Basic method for the determination of repeatability a
27、nd reproducibility of a standard measurement method; Part 3: Intermediate measures of the precision of a standard measurement method; Part 4: Basic methods for the determination of the trueness of a standard measurement method; Part 5: Alternative methods for the determination of the precision of a
28、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 extended to cover trueness (in addition to precision) and intermediate precision conditions (in addition to repeatability conditions and reprodu
29、cibility conditions). Annex A, Annex B and Annex C form an integral part of this part of ISO 5725. Annex D and Annex E are for information only.ISO 5725-3:1994 BSI 15 March 2002 1 Introduction 0.1 ISO 5725 uses two terms “trueness” and “precision” to describe the accuracy of a measurement method. “T
30、rueness” refers to the closeness of agreement between the average value of a large number of test results and the true or accepted reference value. “Precision” refers to the closeness of agreement between test results. 0.2 General consideration of these quantities is given in ISO 5725-1 and so is no
31、t repeated here. It is stressed that ISO 5725-1 should be read in conjunction with all other parts of ISO 5725 because the underlying definitions and general principles are given there. 0.3 Many different factors (apart from variations between supposedly identical specimens) may contribute to the va
32、riability of results from a measurement method, including: a) the operator; b) the equipment used; c) the calibration of the equipment; d) the environment (temperature, humidity, air pollution, etc.); e) the batch of a reagent; f) the time elapsed between measurements. The variability between measur
33、ements performed by different operators and/or with different equipment will usually be greater than the variability between measurements carried out within a short interval of time by a single operator using the same equipment. 0.4 Two conditions of precision, termed repeatability and reproducibili
34、ty conditions, have been found necessary and, for many practical cases, useful for describing the variability of a measurement method. Under repeatability conditions, factors a) to f) in 0.3 are considered constants and do not contribute to the variability, while under reproducibility conditions the
35、y vary and do contribute to the variability of the test results. Thus repeatability and reproducibility conditions are the two extremes of precision, the first describing the minimum and the second the maximum variability in results. Intermediate conditions between these two extreme conditions of pr
36、ecision are also conceivable, when one or more of factors a) to f) are allowed to vary, and are used in certain specified circumstances. Precision is normally expressed in terms of standard deviations. 0.5 This part of ISO 5725 focuses on intermediate precision measures of a measurement method. Such
37、 measures are called intermediate as their magnitude lies between the two extreme measures of the precision of a measurement method: repeatability and reproducibility standard deviations. To illustrate the need for such intermediate precision measures, consider the operation of a present-day laborat
38、ory connected with a production plant involving, for example, a three-shift working system where measurements are made by different operators on different equipment. Operators and equipment are then some of the factors that contribute to the variability in the test results. These factors need to be
39、taken into account when assessing the precision of the measurement method. 0.6 The intermediate precision measures defined in this part of ISO 5725 are primarily useful when their estimation is part of a procedure that aims at developing, standardizing, or controlling a measurement method within a l
40、aboratory. These measures can also be estimated in a specially designed interlaboratory study, but their interpretation and application then requires caution for reasons explained in 1.3 and 9.1. 0.7 The four factors most likely to influence the precision of a measurement method are the following. a
41、) Time: whether the time interval between successive measurements is short or long. b) Calibration: whether the same equipment is or is not recalibrated between successive groups of measurements. c) Operator: whether the same or different operators carry out the successive measurements. d) Equipment
42、: whether the same or different equipment (or the same or different batches of reagents) is used in the measurements.ISO 5725-3:1994 2 BSI 15 March 2002 0.8 It is, therefore, advantageous to introduce the following M-factor-different intermediate precision conditions (M = 1, 2, 3 or 4) to take accou
43、nt of changes in measurement conditions (time, calibration, operator and equipment) within a laboratory. a) M = 1: only one of the four factors is different; b) M = 2: two of the four factors are different; c) M = 3: three of the four factors are different; d) M = 4: all four factors are different.
44、Different intermediate precision conditions lead to different intermediate precision standard deviations denoted by s I( ) , where the specific conditions are listed within the parentheses. For example, s I(TO)is the intermediate precision standard deviation with different times (T) and operators (O
45、). 0.9 For measurements under intermediate precision conditions, one or more of the factors listed in 0.7 is or are different. Under repeatability conditions, those factors are assumed to be constant. The standard deviation of test results obtained under repeatability conditions is generally less th
46、an that obtained under the conditions for intermediate precision conditions. Generally in chemical analysis, the standard deviation under intermediate precision conditions may be two or three times as large as that under repeatability conditions. It should not, of course, exceed the reproducibility
47、standard deviation. As an example, in the determination of copper in copper ore, a collaborative experiment among 35 laboratories revealed that the standard deviation under one-factor-different intermediate precision conditions (operator and equipment the same but time different) was 1,5 times large
48、r than that under repeatability conditions, both for the electrolytic gravimetry and Na 2 S 2 O 3titration methods. 1 Scope 1.1 This part of ISO 5725 specifies four intermediate precision measures due to changes in observation conditions (time, calibration, operator and equipment) within a laborator
49、y. These intermediate measures can be established by an experiment within a specific laboratory or by an interlaboratory experiment. Furthermore, this part of ISO 5725 a) discusses the implications of the definitions of intermediate precision measures; b) presents guidance on the interpretation and application of the estimates of intermediate precision measures in practical situations; c) does not provide any measure of the errors in estimating intermediate precision measures; d) does not concern its
