ISO INTERNATIONAL STANDARD 5725-2 Second edition 2019-12 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 Exactitude (justesse et fidelité) des résultats et méthodes de mesure - Partie 2: Methode de base pour la détermination de la répétabilite et de la reproductibilité d'une méthode de mesure normalisée Reference number IS0 5725-2:2019(E) ISO @ IS0 2019 IS0 5725-2:2019(E) COPYRIGHTPROTECTEDDOCUMENT @ IS0 2019 All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may below or Iso's member body in the country of the requester. ISO copyright office CP 401 : Ch. de Blandonnet 8 CH-1214 Vernier, Geneva Phone: +41 22 749 01 11 Fax: +41 22 749 09 47 Email: [email protected] Website: www.iso.org Published in Switzerland ii @ IS0 2019 - All rights reserved IS0 5725-2:2019(E) Contents Page Foreword .. Introduction. ..vi 1 Scope. 2 Normative references 3 Terms and definitions ..2 4 Symbols. ..2 5 Estimates of the parameters in the basic model 6 Requirements for a precision experiment ..5 6.1 Layoutoftheexperiment ..5 6.2 Recruitment of the laboratories .6 6.3 Preparation of the materials .6 7 Personnel involved in a precision experiment .7 7.1 Panel. .7 7.2 Statistical functions.. ..8 7.3 Executive functions.. 7.4 Supervisors. .9 7.5 Operators. .10 8 Statistical analysis of a precision experiment .10 8.1 Preliminary considerations. .10 8.2 Tabulation of the results and notation used .11 8.2.1 Cells. .11 8.2.2 Redundant data. .11 8.2.3 Missing data. ..11 8.2.4 Outliers. .11 8.2.5 Outlying laboratories. .11 8.2.6 Erroneous data .11 8.2.7 Balanced uniform-level test results .11 8.2.8 Collation of data and intermediate values .12 8.2.9 Original test results. ..12 8.2.10 Cell means (Form B of Figure 2) .12 8.2.11 Measures of cell spread (Form C of Figure 2) .12 8.2.12 Corrected or rejected data. ..13 8.3 Scrutiny of results for consistency and outliers ..13 8.3.1 Approaches for scrutiny of data ..13 8.3.2 Graphical consistency technique .13 8.3.3 Numerical outlier technique. .16 8.3.4 Cochran'stest. .16 8.3.5 Grubbs'tests .18 8.3.6 Repeated testing for outlying means or outlying data points. .20 8.3.7 Alternativeoutlierinspectionandtestmethods. 20 8.4 Calculation of the general mean and variances .20 8.4.1 Method of analysis. .20 8.4.2 Basic data. .21 8.4.3 Non-empty cells. .21 8.4.4 Calculation of the general mean, m .21 8.4.5 Calculation of variances .21 8.4.6 Alternative calculation methods for variances .22 8.4.7 Dependence of the variances upon m . .23 8.5 Establishing a functional relationship between precision values, s, and the mean level, m ..23 8.5.1 Choice of functional relationship ..23 @ IS0 2019 - All rights reserved iii IS0 5725-2:2019(E) 8.5.2 Fitting relationships I and II 24 8.5.3 Fitting relationship III 25 8.5.4 Fitting relationship IV 26 8.6 Statistical analysis as a step-by-step procedure 28 8.7 Report to the panel and decisions to be taken by the panel 30 8.7.1 Report by the statistical expert. 30 8.7.2 Decisions to be taken by the panel 32 8.7.3 Full report. 33 9 Statistical tables .33 Annex A (informative) Number of laboratories required for an estimate of precision .38 Annex B (informative) Alternative calculations of variance components. .41 Annex C (informative) Examples of the statistical analysis of precision experiments .44 AnnexD(informative)Calculationofcriticalvaluesandindicators 66 Bibliography 69 iv @ IS0 2019 - All rights reserved IS0 5725-2:2019(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 which a technical committee has been established has the right to b