ISO INTERNATIONAL STANDARD 5168 Second edition 2005-06-15 Measurement of fluid flow Procedures for the evaluation of uncertainties Mesure de débit des fluides - Procédures pour le calcul de I'incertitude Reference number ISO 5168:2005(E) ISO @ ISO 2005 ISO5168:2005(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 ?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 @ISO2005-All rights reserved ISO5168:2005(E) Contents Page Foreword Introduction 1 Scope 2 Normative references .. 3 Terms and definitions.. 4 Symbols and abbreviated terms 4.1 Symbols 4.2 Subscripts 5 Evaluation of the uncertainty in a measurement process 6 Type A evaluations of uncertainty 6.1 General considerations. 6.2 Calculation procedure 7 Type B evaluation of uncertainties 0 7.1 General considerations 10 7.2 Calculation procedur 10 7.3 Rectangularprobabilitydistribution 7.4 Normalprobabilitydistribution. 7.5 Triangular probability distribution 7.6 Bimodal probability distribution 7.7 Assigning a probability distribution. 7.8 Asymmetric probability distributions 8 Sensitivity coefficients. 12 8.1 General.... 12 8.2 Analytical solution 12 8.3 Numerical solution... 12 9 Combination of uncertainties 13 10 Expression of results. 10.1 Expandeduncertainty. 14 10.2 Uncertainty budget ... 15 Annex A (normative) Step-by-step procedure for calculating uncertainty Annex B (normative) Probability distributions ... .20 Annex C (normative) Coverage factors. .22 Annex D (informative) Basic statistical concepts for use in Type A assessments of uncertainty .... 24 AnnexE(informative)Measurementuncertainty sources 36 Annex F (informative) Correlated input variables 38 Annex G (informative) Examples .. .40 Annex H (informative) The calibration of a flow meter on a calibration rig... Annex I (informative) Type A and Type B uncertainties in relation to contributions to uncertainty from“random" and "systematic" sources of uncertainty.... 61 Annex J (informative) Special situations using two or more meters in parallel... .62 Annex K (informative)Alternative technique for uncertainty analysis. Bibliography alion'ghts reserved ili ISO 5168:2005(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 sO established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with isO, also take part in the work. isO 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/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. Publi