1、 IEC 61649Edition 2.0 2008-08INTERNATIONAL STANDARD NORME INTERNATIONALEWeibull analysis Analyse de Weibull IEC61649:2008THIS PUBLICATION IS COPYRIGHT PROTECTED Copyright 2008 IEC, Geneva, Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or u
2、tilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either IEC or IECs member National Committee in the country of the requester. If you have any questions about IEC copyright or have an enquiry about obtaining addit
3、ional rights to this publication, please contact the address below or your local IEC member National Committee for further information. Droits de reproduction rservs. Sauf indication contraire, aucune partie de cette publication ne peut tre reproduite ni utilise sous quelque forme que ce soit et par
4、 aucun procd, lectronique ou mcanique, y compris la photocopie et les microfilms, sans laccord crit de la CEI ou du Comit national de la CEI du pays du demandeur. Si vous avez des questions sur le copyright de la CEI ou si vous dsirez obtenir des droits supplmentaires sur cette publication, utilisez
5、 les coordonnes ci-aprs ou contactez le Comit national de la CEI de votre pays de rsidence. IEC Central Office 3, rue de Varemb CH-1211 Geneva 20 Switzerland Email: inmailiec.ch Web: www.iec.ch About the IEC The International Electrotechnical Commission (IEC) is the leading global organization that
6、prepares and publishes International Standards for all electrical, electronic and related technologies. About IEC publications The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the latest edition, a corrigenda or an amendment might hav
7、e been published. Catalogue of IEC publications: www.iec.ch/searchpub The IEC on-line Catalogue enables you to search by a variety of criteria (reference number, text, technical committee,). It also gives information on projects, withdrawn and replaced publications. IEC Just Published: www.iec.ch/on
8、line_news/justpub Stay up to date on all new IEC publications. Just Published details twice a month all new publications released. Available on-line and also by email. Electropedia: www.electropedia.org The worlds leading online dictionary of electronic and electrical terms containing more than 20 0
9、00 terms and definitions in English and French, with equivalent terms in additional languages. Also known as the International Electrotechnical Vocabulary online. Customer Service Centre: www.iec.ch/webstore/custserv If you wish to give us your feedback on this publication or need further assistance
10、, please visit the Customer Service Centre FAQ or contact us: Email: csciec.ch Tel.: +41 22 919 02 11 Fax: +41 22 919 03 00 A propos de la CEI La Commission Electrotechnique Internationale (CEI) est la premire organisation mondiale qui labore et publie des normes internationales pour tout ce qui a t
11、rait llectricit, llectronique et aux technologies apparentes. A propos des publications CEI Le contenu technique des publications de la CEI est constamment revu. Veuillez vous assurer que vous possdez ldition la plus rcente, un corrigendum ou amendement peut avoir t publi. Catalogue des publications
12、 de la CEI: www.iec.ch/searchpub/cur_fut-f.htm Le Catalogue en-ligne de la CEI vous permet deffectuer des recherches en utilisant diffrents critres (numro de rfrence, texte, comit dtudes,). Il donne aussi des informations sur les projets et les publications retires ou remplaces. Just Published CEI:
13、www.iec.ch/online_news/justpub Restez inform sur les nouvelles publications de la CEI. Just Published dtaille deux fois par mois les nouvelles publications parues. Disponible en-ligne et aussi par email. Electropedia: www.electropedia.org Le premier dictionnaire en ligne au monde de termes lectroniq
14、ues et lectriques. Il contient plus de 20 000 termes et dfinitions en anglais et en franais, ainsi que les termes quivalents dans les langues additionnelles. Egalement appel Vocabulaire Electrotechnique International en ligne. Service Clients: www.iec.ch/webstore/custserv/custserv_entry-f.htm Si vou
15、s dsirez nous donner des commentaires sur cette publication ou si vous avez des questions, visitez le FAQ du Service clients ou contactez-nous: Email: csciec.ch Tl.: +41 22 919 02 11 Fax: +41 22 919 03 00 IEC 61649Edition 2.0 2008-08INTERNATIONAL STANDARD NORME INTERNATIONALEWeibull analysis Analyse
16、 de Weibull INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE XBICS 03.120.01; 03.120.30 PRICE CODECODE PRIXISBN 2-8318-9954-0 Registered trademark of the International Electrotechnical Commission Marque dpose de la Commission Electrotechnique Internationale 2 6164
17、9 IEC:2008 CONTENTS FOREWORD.5INTRODUCTION.71 Scope.82 Normative references .83 Terms, definitions, abbreviations and symbols83.1 Terms and definitions 83.2 Abbreviations 103.3 Symbols 104 Application of the techniques115 The Weibull distribution 115.1 The two-parameter Weibull distribution115.2 The
18、 three-parameter Weibull distribution .136 Data considerations136.1 Data types.136.2 Time to first failure 136.3 Material characteristics and the Weibull distribution 136.4 Sample size 136.5 Censored and suspended data 147 Graphical methods and goodness-of-fit 147.1 Overview .147.2 How to make the p
19、robability plot147.2.1 Ranking.157.2.2 The Weibull probability plot .157.2.3 Dealing with suspensions or censored data .157.2.4 Probability plotting.177.2.5 Checking the fit .177.3 Hazard plotting188 Interpreting the Weibull probability plot.198.1 The bathtub curve .198.1.1 General .198.1.2 1 Implie
20、s wear-out.208.2 Unknown Weibull modes may be “masked“208.3 Small samples.218.4 Outliers .228.5 Interpretation of non-linear plots228.5.1 Distributions other than the Weibull .258.5.2 Data inconsistencies and multimode failures .259 Computational methods and goodness-of-fit .259.1 Introduction .259.
21、2 Assumptions and conditions 269.3 Limitations and accuracy.269.4 Input and output data 2661649 IEC:2008 3 9.5 Goodness-of-fit test.279.6 MLE point estimates of the distribution parameters and .279.7 Point estimate of the mean time to failure289.8 Point estimate of the fractile (10 %) of the time to
22、 failure.289.9 Point estimate of the reliability at time t (t T).289.10 Software programs 2810 Confidence intervals.2810.1 Interval estimation of 2810.2 Interval estimation of .2910.3 MRR Beta-binomial bounds .3010.4 Fishers Matrix bounds 3010.5 Lower confidence limit for B10.3110.6 Lower confidence
23、 limit for R 3111 Comparison of median rank regression (MRR) and maximum likelihood (MLE) estimation methods 3111.1 Graphical display.3111.2 B life estimates sometimes known as B or L percentiles 3111.3 Small samples.3211.4 Shape parameter 3211.5 Confidence intervals3211.6 Single failure .3211.7 Mat
24、hematical rigor.3211.8 Presentation of results 3212 WeiBayes approach3312.1 Description3312.2 Method3312.3 WeiBayes without failures .3312.4 WeiBayes with failures 3312.5 WeiBayes case study 3413 Sudden death method 3514 Other distributions 37Annex A (informative) Examples and case studies .38Annex
25、B (informative) Example of computations 40Annex C (informative) Median rank tables42Annex D (normative) Statistical Tables 47Annex E (informative) Spreadsheet example48Annex F (informative) Example of Weibull probability paper.55Annex G (informative) Mixtures of several failure modes56Annex H (infor
26、mative) Three-parameter Weibull example.59Annex I (informative) Constructing Weibull paper.61Annex J (informative) Technical background and references64Bibliography67Figure 1 The PDF shapes of the Weibull family for = 1,0 .12Figure 2 Total test time (in minutes).16Figure 3 Typical bathtub curve for
27、an item .19 4 61649 IEC:2008 Figure 4 Weibull failure modes may be “masked” .21Figure 5 Sample size: 10 .21Figure 6 Sample size: 100 .22Figure 7 An example showing lack of fit with a two-parameter Weibull distribution .23Figure 8 The same data plotted with a three-parameter Weibull distribution show
28、s a good fit with 3 months offset (location 2,99 months).24Figure 9 Example of estimating t0by eye .25Figure 10 New compressor design WeiBayes versus old design 35Figure A.1 Main oil pump low times38Figure A.2 Augmenter pump bearing failure .39Figure A.3 Steep values hide problems .39Figure B.1 Plot
29、 of computations .41Figure E.1 Weibull plot for graphical analysis.49Figure E.2 Weibull plot of censored data51Figure E.3 Cumulative hazard plot for data of Table E.4 52Figure E.4 Cumulative hazard plots for Table E.6 54Figure H.1 Steel-fracture toughness Curved data59Figure H.2 t0improves the fit o
30、f Figure H.1 data 60Table 1 Guidance for using this International Standard 11Table 2 Ranked flare failure rivet data .15Table 3 Adjusted ranks for suspended or censored data 16Table 4 Subgroup size to estimate time to X % failures using the sudden death method .36Table 5 Chain data: cycles to failur
31、e 36Table B.1 Times to failure 40Table B.2 Summary of results 41Table D.1 Values of the gamma function47Table D.2 Fractiles of the normal distribution .47Table E.1 Practical analysis example.48Table E.2 Spreadsheet set-up for analysis of censored data 50Table E.3 Example of Weibull analysis for susp
32、ended data50Table E.4 Example of Spreadsheet application for censored data 51Table E.5 Example spreadsheet.52Table E.6 A relay data provided by ISO/TC94 and Hazard analysis for failure mode 1 .53Table I.1 Construction of ordinate (Y).62Table I.2 Construction of abscissa (t).62Table I.3 Content of da
33、ta entered into a spreadsheet.6261649 IEC:2008 5 INTERNATIONAL ELECTROTECHNICAL COMMISSION _ WEIBULL ANALYSIS FOREWORD 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees).
34、 The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, and Guides (hereafter
35、referred to as “IEC Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participat
36、e in this preparation. IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations. 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an inte
37、rnational consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees. 3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense. While all reaso
38、nable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user. 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC
39、 Publications transparently to the maximum extent possible in their national and regional publications. Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter. 5) IEC provides no marking procedure to indicate its app
40、roval and cannot be rendered responsible for any equipment declared to be in conformity with an IEC Publication. 6) All users should ensure that they have the latest edition of this publication. 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual
41、experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) andexpenses arising out of the publication, use of, or reliance upon, this IE
42、C Publication or any other IEC Publications. 8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is indispensable for the correct application of this publication. 9) Attention is drawn to the possibility that some of the elements of this IE
43、C Publication may be the subject of patent rights. IEC shall not be held responsible for identifying any or all such patent rights. International Standard IEC 61649 has been prepared by IEC technical committee 56: Dependability. This second edition cancels and replaces the first edition, published i
44、n 1997, and constitutes a technical revision. The main changes with respect to the previous edition are as follows: the title has been shortened and simplified to read “Weibull analysis”; provision of methods for both analytical and graphical solutions have been added. The text of this standard is b
45、ased on the following documents: FDIS Report on voting 56/1269/FDIS 56/1281/RVD Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. 6 6
46、1649 IEC:2008 The committee has decided that the contents of this publication will remain unchanged until the maintenance result date indicated on the IEC web site under “http:/webstore.iec.ch“ in the data related to the specific publication. At this date, the publication will be reconfirmed, withdr
47、awn, replaced by a revised edition, or amended. 61649 IEC:2008 7 INTRODUCTION The Weibull distribution is used to model data regardless of whether the failure rate is increasing, decreasing or constant. The Weibull distribution is flexible and adaptable to a wide range of data. The time to failure,
48、cycles to failure, mileage to failure, mechanical stress or similar continuous parameters need to be recorded for all items. A life distribution can be modelled even if not all the items have failed. Guidance is given on how to perform an analysis using a spreadsheet program. Guidance is also given
49、on how to analyse different failure modes separately and identify a possible weak population. Using the three-parameter Weibull distribution can give information on time to first failure or minimum endurance in the sample. 8 61649 IEC:2008 WEIBULL ANALYSIS 1 Scope This International Standard provides methods for analysing data from a W
