ISO/TR TECHNICAL REPORT 13587 First edition 2012-07-15 Three statistical approaches for the assessment and interpretation of measurement uncertainty Trois approches statistiques pour I'évaluation et I'interpretation de Iincertitude de mesure Reference number ISO/TR 13587:2012(E) @ ISO 2012 by IHS under lic itted without license from IHS Not for Resale ISO/TR 13587:2012(E) COPYRIGHTPROTECTEDDOCUMENT @ISO2012 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either isO at the address below or Iso's member body in the country of the requester. ISO copyright office Case postale 56. CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail [email protected] Web www.iso.org Published in Switzerland @ ISO 2012 - All rights reserved Tby IHS under itted without license from IHS Not for Resale ISO/TR 13587:2012(E) Contents Page Foreword. Introduction. .. vi 1 Scope. 2 Normative references.. 3 Terms and definitions 4 Symbols (and abbreviated terms).... .2 5 The problem addressed 6 Statistical approaches .. 6.1 Frequentist approach... 6.2 Bayesian approach... 6.3 Fiducial approach. 6.4 Discussion.. 7 Examples .6 7.1 General , .6 7.2 Example 1a. .6 7.3 Example 1b. 7.4 Example 1c.. 8 Frequentist approach to uncertainty evaluation... 8.1 Basic method.. 8.2 Bootstrap uncertainty intervals 10 8.3 Example1 13 8.3.1 General , 13 8.3.2 Example 1a. 14 8.3.3 Example 1b.... 8.3.4 Example 1c.. 15 9 Bayesian approach for uncertainty evaluation .... .16 9.1 Basic method.... 16 9.2 Example 1.. .18 9.2.1 General. 18 9.2.2 Example1a 18 9.2.3 Example 1b. 20 9.2.4 9.2.5 Summary of example , 21 10 Fiducial inference for uncertainty evaluation... 21 10.1 Basic method .... 21 10.2 Example 1.... 23 10.2.1 Example 1a.... 23 10.2.2 Example 1b... 25 10.2.3 Example1c.. 26 11 Example 2: calibration of a gauge block. .26 11.1 11.2 Frequentist approach. .28 11.3 Bayesian approach.... 30 11.4 Fiducial approach.... 33 12 35 12.1 Comparison of uncertainty evaluations using the three statistical approaches.. ili Copyright International Organization for Standardizalon ghts reserved Not for Resale