ISO/TS TECHNICAL SPECIFICATION 21749 First edition 2005-02-15 Measurement and uncertainty for metrological applications Repeated measurements and nested experiments Incertitude de mesure pourles applications en metrologie-Mesures répetées et expériences emboitées Reference number ISO/TS 21749:2005(E) @ ISO 2005 yIHSunder Inc /5909636100 ISO/TS 21749:2005(E) PDF disclaimer 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 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. ?ISO2005 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 Copyihtinteratinal organization for Standardization @ ISo 2005 - All rights reserved es Inc /5909636100 I without license from IHS ISO/TS 21749:2005(E) Contents Page Foreword .iv Introduction. 1 Scope 2 Normative references... 3 Terms and definitions 4 Statistical methods of uncertainty evaluation.... 4.1 Approach of the Guide to the expression of uncertainty of measurement. 4.2 Check standards ......... 4.3 Steps in uncertainty evaluation ..... 4.4 Examples in this Technical Specification. 5 Type A evaluation of uncertainty.. 6 5.1 General... 6 5.2 Role of time in Type A evaluation of uncertainty.. 5.3 Measurement configuration .... 14 5.4 Material inhomogeneity .. .16 5.5 Bias due to measurement configurations . 17 6 Type B evaluation of uncertainty. .26 7 Propagation of uncertainty. .27 7.1 27 7.2 Formulae for functions of a single variable... .28 7.3 Formulae for functions of two variables.. 28 8 Example Type A evaluation of uncertainty from a gauge study. .30 8.1 .30 8.2 8.3 Analysis of repeatability, day-to-day and long-term effects... .31 8.4 Probe bias. 31 8.5 33 8.6 Uncertainty calculation.. .35 Annex A (normative) Symbols.. Bibliography ii 5909636100 se from IHS ISO/TS21749:2005(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 technicalcommittees.Eachmemberbodyinterestedinasubjectforwhichatechnicalcommitteehasbeen non-governmental, in liaison with isO, also take part in the work. isoO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the IsO/lE Directives, Part 2. adopted by the technical committees are circulated to the member bodies for voting. Publication as an technical committee may decide to publish other types of normative document: an ISO Publicly Available Specification (IsO/PAs) represents an agreement between technical experts in an isO working group and is accepted for publication if it is approved by more than 50 % of the members of the parent committee casting a vote; a vote. An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a further three