1、 Collection of SANS standards in electronic format (PDF) 1. Copyright This standard is available to staff members of companies that have subscribed to the complete collection of SANS standards in accordance with a formal copyright agreement. This document may reside on a CENTRAL FILE SERVER or INTRA
2、NET SYSTEM only. Unless specific permission has been granted, this document MAY NOT be sent or given to staff members from other companies or organizations. Doing so would constitute a VIOLATION of SABS copyright rules. 2. Indemnity The South African Bureau of Standards accepts no liability for any
3、damage whatsoever than may result from the use of this material or the information contain therein, irrespective of the cause and quantum thereof. ISBN 978-0-626-22662-6 SANS 5725-4:2009Edition 1ISO 5725-4:1994Edition 1SOUTH AFRICAN NATIONAL STANDARD Accuracy (trueness and precision) of measurement
4、methods and results Part 4: Basic methods for the determination of the trueness of a standard measurement method This national standard is the identical implementation of ISO 5725-4:1994 and is adopted with the permission of the International Organization for Standardization. Published by SABS Stand
5、ards Division 1 Dr Lategan Road Groenkloof Private Bag X191 Pretoria 0001Tel: +27 12 428 7911 Fax: +27 12 344 1568 www.sabs.co.za SABS SANS 5725-4:2009 Edition 1 ISO 5725-4:1994 Edition 1 Table of changes Change No. Date Scope National foreword This South African standard was approved by National Co
6、mmittee SABS TC 169, Applications of statistical methods, in accordance with procedures of the SABS Standards Division, in compliance with annex 3 of the WTO/TBT agreement. This SANS document was published in August 2009. INTERNATIONAL STANDARD IS0 5725-4 First edition 1994-l 2-l 5 Accuracy (truenes
7、s and precision) of measurement methods and results - Part 4: Basic methods for the determination of the trueness of a standard measurement method Exactitude (justesse et fid for example, if suitable reference materials are available, or if the accepted reference value can be established by refer- e
8、nce to another measurement method or by preparation of a known sample. The trueness of the measurement method can be investigated by comparing the accepted reference value with the level of the results given by the measurement method. Trueness is normally expressed in terms of bias. Bias can arise,
9、for example, in chemical analysis if the measurement method fails to extract all of an element, or if the presence of one element interferes with the determination of another. 0.4 Two measures of trueness may be of interest and both are consid- ered in this part of IS0 5725. a) Bias of the measureme
10、nt method: where there is a possibility that the measurement method may give rise to a bias, which persists wher- ever and whenever the measurement is done, then it is of interest to investigate the “bias of the measurement method” (as defined in IS0 5725-l). This requires an experiment involving ma
11、ny laboratories, very much as described in IS0 5725-2. b) Laboratory bias: measurements within a single laboratory can reveal the “laboratory bias” (as defined in IS0 5725-l). If it is proposed to undertake an experiment to estimate laboratory bias, then it should be realized that the estimate will
12、be valid only at the time of the ex- periment. Further regular testing is required to show that the labora- tory bias does not vary; the method described in IS0 5725-6 may be used for this. SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and freemailing clients o
13、f the SABS .This page intentionally left blank SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .INTERNATIONAL STANDARD 0 IS0 IS0 5725-4: 1994(E) Accuracy (trueness and precision) of measurement methods and results - Part 4: Bas
14、ic methods for the determination of the trueness of a standard measurement method 1 Scope 1.1 This part of IS0 5725 provides basic methods for estimating the bias of a measurement method and the laboratory bias when a measurement method is applied. 1.2 It is concerned exclusively with measurement me
15、thods which yield measurements on a continuous scale and give a single value as the test result, al- though the single value may be the outcome of a calculation from a set of observations. 1.3 In order that the measurements are made in the same way, it is important that the measurement method has be
16、en standardized. All measurements are to be carried out according to that standard method. 1.4 Bias values give quantitative estimates of the ability of a measurement method to give the correct (true) result. When a value for the bias of a measure- ment method is quoted, together with a test result
17、obtained by that method, there is an implication that the same characteristic is being measured in exactly the same way. 1.5 This part of IS0 5725 can be applied only if the accepted reference value can be established as a conventional true value, for example by measurement standards or suitable ref
18、erence materials or by refer- ring to a reference measurement method or by prep- aration of a known sample. Reference materials could be either a) certified reference materials; b) materials manufactured for the purpose of the experiment with known properties; or c) materials whose properties have b
19、een established by measurements using an alternative measure- ment method whose bias is known to be negligi- ble . 1.6 This part of IS0 5725 considers only those cases where it is sufficient to estimate bias on one level at a time. It is not applicable if the bias in the measurement of one property
20、is affected by the level of a second property (i.e. it does not consider inter- ferences). Comparison of the trueness of two measurement methods is considered in IS0 5725-6. NOTE 1 In this part of IS0 5725, bias is considered only at one level at a time. Therefore the index j for the level has been
21、omitted throughout. 2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this part of IS0 5725. At the time of publication, the 1 SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and free
22、mailing clients of the SABS .IS0 5725-4: 1994(E) 0 IS0 ed itions indicated were valid. All standa rds are subject to revision, and parties to agreements based on this part of IS0 5725 are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below.
23、 Members of IEC and IS0 maintain reaisters of currently valid International Standards. ” IS0 3534-l : 1993, bols - Part I: terms. Statistics - Vocabulary and sym- Probability and general statistical IS0 5725-l : 1994, Accuracy (trueness and precision) of measurement methods and results - Part I: Gen
24、eral principles and definitions. IS0 5725-2: 1994, Accuracy (trueness and precision) of measurement methods and results - Part 2: Basic method for the determination of repeatability and re- producibility of a standard measurement method. 3 Definitions For the purposes of this part IS0 5725, the defi
25、nitions given in IS0 3534-l and in IS0 5725-l apply. The symbols used in IS0 5725 are given in annex A. 4 Determination of the bias of a standard measurement method by an interlaboratory experiment 4.1 The statistical model In the basic model described in subclause 5.1 of IS0 5725-l :1994, the gener
26、al mean m may be re- placed by m= P+d . . . 0 CL is the accepted reference value of the prop- erty being measured; 6 is the bias of the measurement method. The model becomes y=p+d+B+e . . . (2) Equation (2) is used when 6 is of interest. Here B is the laboratory component of bias, i.e. the component
27、 in a test result representing the between-laboratory variation. The laboratory bias, A, is given by A=d+B so the model may be written y=p+A+e . . . (3) . . . (4) Equation (4) is used when A is of interest. 42 . Reference material requirements If reference materials are used, the requirements given
28、in 4.2.1 and 4.2.2 shall be satisfied. Reference materials shall be homogeneous. 4.2.1 Choice of reference materials 4.2.1.1 The reference material shall have known properties at the level appropriate to the level at which the standard measurement method is intended to be applied, e.g. concentration
29、. In some cases it will be important to include, in the assessment exper- iment, a series of reference materials, each corre- sponding to a different level of the property, as the bias of the standard measurement method may be different at different levels. The reference material should have a matri
30、x as close as possible to the matrix of the material to be subjected to the standard measurement method, e.g. carbon in coal or carbon in steel. 4.2.1.2 The quantity of the reference material shall be sufficient for the entire experimental programme, including some in reserve if this is considered n
31、ecessary. 4.2.1.3 Wherever possible, the reference material should have stable properties throughout the exper- iment. There are three cases, as follows. a) The properties are stable: no precautions are necessary. b) The certified value of the property may be influ- enced by storage conditions: the
32、container should be stored, both before and after its opening, in the way described on the certificate. c) The properties change at a known rate: there is a certificate supplied with the reference value to define the properties at specific times. 4.2.1.4 The possible difference between the certi- fi
33、ed value and the true value expressed by the uncer- tainty of the reference material (see IS0 Guide 35) is not taken into account in the methods given here. SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .Q IS0 IS0 5725=4:1994
34、(E) 4.2.2 Check and distribution of the reference material Where sub-division of the unit of the reference ma- terial occurs prior to distribution, it shall be performed with care to avoid the introduction of any additional error. Relevant International Standards on sample division should be consult
35、ed. The units should be selected on a random basis for distribution. If the measurement process is non-destructive, it is poss- ible to give all the laboratories in the interlaboratory experiment the same unit of reference material, but this will extend the time-frame of the experiment. 4.3 Experime
36、ntal design considerations when estimating the bias of a measurement method 4.3.1 The objective of the experiment is to estimate the magnitude of the bias of the measurement method and to determine if it is statistically signif- icant. If the bias is found to be statistically insignif- icant, then t
37、he objective is to determine the magnitude of the maximum bias that would, with a certain probability, remain undetected by the results of the experiment. number of laboratories to be used is discussed in subclause 6.3 of IS0 5725-l :I 994. A guide to decid- ing how many is given below. In order for
38、 the results of an experiment to be able to detect with a high probability (see annex C) a prede- termined magnitude of bias, the minimum number of laboratories, p, and test results, n, shall satisfy the following equation: s AaR I v 2 2 where xc1 _ .,(v) is the (1 - Number of factors considered in
39、precision conditions Number of iterations Mandels within-laboratory consistency test statistic intermediate Number of test results obtained in one labora- tory at one level (i.e. per cell) Number of laboratories participating in the inter- laboratory experiment Probability Number of levels of the te
40、st property in the interlaboratory experiment Repeatability limit Reproducibility limit Reference material Estimate of a standard deviation Predicted standard deviation Total or sum of some expression Number of test objects or groups Upper control limit (either action limit or warning limit) Weighti
41、ng factor used in calculating a weighted regression Range of a set of test results Datum used for Grubbs test Test result SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .63 IS0 IS0 5725-4: 1994(E) Arithmetic mean of test resul
42、ts Symbols used as subscripts Grand mean of test results Significance level Type II error probability Ratio of the reproducibility standard deviation to the repeatability standard deviation (Q/O,) C E i I( Laboratory bias j Calibration-different Equipment-different Identifier for a particular labora
43、tory Identifier for intermediate measures of precision; in brackets, identification of the type of intermediate situation Identifier for (IS0 5725-2) a particular level . Estimate of A Bias of the measurement method k Estimate of d Detectable difference between two laboratory biases or the biases of
44、 two measurement methods True value or accepted reference value of a test property Number of degrees of freedom Detectable ratio between the repeatability stan- dard deviations of method B and method A Identifier for a group of tests or for a factor (IS0 5725-3) Identifier for a particular test resu
45、lt in a laboratory i at level j Between-laboratory (interlaboratory) Identifier for detectable bias Between-test-sample Operator-different Probability Repeatability True value of a standard deviation Component in a test result representing the variation due to time since last calibration L m M 0 P r
46、 R T W Detectable ratio between the square roots of the between-laboratory mean squares of method B and method A 1, 2, 3. Reproducibility Time-different Within-laboratory (intralaboratory) For test results, numbering in the order of obtaining them X,(V) p-quantile of the X*-distribution with v degre
47、es of freedom (11, (21, (310 F or es results, numbering in the order t t of increasing magnitude SANS 5725-4:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .IS0 5725-4: 1994(E) Annex B (informative) Example of an accuracy experiment B.l D
48、escription of the experiment An accuracy experiment on the determination of manganese content in iron ores by an atomic absorp- tion method was conducted by lSO/TC 102, iron ores, using five test materials with the accepted ref- erence values (p) given in table B.l (which were not disclosed to the l
49、aboratories). Each laboratory re- ceived two randomly selected bottles of test sample for each level and performed duplicate analyses on each bottle. The purpose of the two-bottle system was to confirm the absence of the between-bottle variation. The analysis was performed such that in the case where the absence of between-bottle variation is confirmed, the four analytical results can be con- sidered as replicates under repeatability conditions. Analysis of the results showed that the between- bottle variation was indeed insignificant; the sample was considered to be homogeneous. Thus re
