ISO INTERNATIONAL STANDARD 20988 First edition 2007-06-15 Air quality - Guidelines for estimating measurement uncertainty Qualite de I'air- Lignes directrices pour estimer I'incertitude de mesure Reference number ISO 20988:2007(E) @ ISO 2007 IHS under ISO 20988:2007(E) PDFdisclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISo Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by IsO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT @ISO2007 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 2007 - All rights reserved I without license from IHS ISO 20988:2007(E) Contents Page Foreword. iv Introduction 1 Scope 2 Normative references .. 3 Terms and definitions. 4 Symbols and abbreviated terms . 5 5 Basic concepts. 6 5.1 Outline... 5.2 Measurement uncertainty 9 5.3 Correction for systematic effects........... 10 5.4 Provision of input data. 11 6 Problem specification. 13 6.1 Objectives... 13 6.2 13 6.3 Uncertainty parameters 15 6.4 Input data... 15 6.4.1 General. 15 6.4.2 Assessment of representativeness 16 6.5 Effects not described by series of observations. 17 7 Statistical analysis. .18 7.1 Objectives.. 18 7.2 Indirect approach. 19 7.3 7.4 Statistical validity.. 22 8 Estimation of variances and covariances ... .23 8.1 23 8.2 Variance estimates of Type A... 23 8.3 Variance estimates of Type B.... 8.4 Estimation of covariances . 24 9 Evaluation of uncertainty parameters 25 9.1 25 9.2 Combined standard uncertainty.... 25 9.3 Expanded uncertainty .... 26 9.3.1 26 9.3.2 Expanded uncertainty of results exhibiting a Gaussian distribution...... 27 10 Reporting .. .28 Annex A (informative) Testing a coverage probability . 30 Annex B (informative) Type A evaluation methods for experimental designs A1 to A8.... ..34 Annex C (informative) Examples .. .49 Bibliography 81 Copyrght InternationalOrganizaisandardizaoghtsreserved ili Nioense nse from IHS ISO 20988:2007(E) Foreword IsO (the International Organization for Standardization) is a worldwide federation of national standards bodies technicalcommittees.Eachmemberbodyinterestedinasubjectforwhichatechnicalcommitteehasbeen established has the right to be represented on that committee. International organizations, governmental and InternationalElectrotechnicalCommission(lEC)onallmattersofelectrotechnicalstandardization. International Standards are drafted in accordance with the rules given in the ISO/lEC Directives, Part 2. The main task of technical committees is to prepare International Standards. 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 member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the s