1、Weibull analysisBS EN 61649:2008raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI British StandardsLicensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSINational forewordThis British Standard is the UK im
2、plementation of EN 61649:2008. It is identical to IEC 61649:2008. It supersedes BS IEC 61649:1997 which is withdrawn.The UK participation in its preparation was entrusted by Technical CommitteeDS/1, Dependability and terotechnology, to Subcommittee DS/1/1,Dependability.A list of organizations repres
3、ented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisions of acontract. Users are responsible for its correct application. BSI 2009ISBN 978 0 580 54368 5ICS 03.120.01; 03.120.30Compliance with a British Standard canno
4、t confer immunity fromlegal obligations.Amendments issued since publicationAmd. No. Date Text affectedBRITISH STANDARDBS EN 61649:2008This British Standard was published under the authority of the StandardsPolicy and Strategy Committee on February 2009.2 8Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA
5、STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSIEUROPEAN STANDARD EN 61649 NORME EUROPENNE EUROPISCHE NORM November 2008 CENELEC European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung Central Sec
6、retariat: rue de Stassart 35, B - 1050 Brussels 2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members. Ref. No. EN 61649:2008 E ICS 03.120.01; 03.120.30 English version Weibull analysis (IEC 61649:2008) Analyse de Weibull (CEI 61649:2008) Weibu
7、ll-Analyse (IEC 61649:2008) This European Standard was approved by CENELEC on 2008-10-01. CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-dat
8、e lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CENELEC member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under
9、the responsibility of a CENELEC member into its own language and notified to the Central Secretariat has the same status as the official versions. CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France
10、, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom. BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:1
11、0, Uncontrolled Copy, (c) BSIEN 61649:2008 2 Foreword The text of document 56/1269/FDIS, future edition 2 of IEC 61649, prepared by IEC TC 56, Dependability, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as EN 61649 on 2008-10-01. The following dates were fixed: latest d
12、ate by which the EN has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2009-07-01 latest date by which the national standards conflicting with the EN have to be withdrawn (dow) 2011-10-01 Annex ZA has been added by CENELEC. _ Endorsement
13、notice The text of the International Standard IEC 61649:2008 was approved by CENELEC as a European Standard without any modification. In the official version, for Bibliography, the following notes have to be added for the standards indicated: IEC 60300-1 NOTE Harmonized as EN 60300-1:2003 (not modif
14、ied). IEC 60300-2 NOTE Harmonized as EN 60300-2:2004 (not modified). IEC 60300-3-1 NOTE Harmonized as EN 60300-3-1:2004 (not modified). IEC 60300-3-2 NOTE Harmonized as EN 60300-3-2:2005 (not modified). IEC 60300-3-4 NOTE Harmonized as EN 60300-3-4:2008 (not modified). IEC 61703 NOTE Harmonized as E
15、N 61703:2002 (not modified). _ BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSI 3 EN 61649:2008 Annex ZA (normative) Normative references to international publications with their corresponding European publications The following refe
16、renced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. NOTE When an international publication has been modified by common
17、modifications, indicated by (mod), the relevant EN/HD applies. Publication Year Title EN/HD Year IEC 60050-191 1990 International Electrotechnical Vocabulary (IEV) - Chapter 191: Dependability and quality of service - - IEC 60300-3-5 2001 Dependability management - Part 3-5: Application guide - Reli
18、ability test conditions and statistical test principles - - IEC 61810-2 - 1)Electromechanical elementary relays - Part 2: Reliability EN 61810-2 2005 2)ISO 2854 1976 Statistical interpretation of data - Techniques of estimation and tests relating to means and variances - - ISO 3534-1 2006 Statistics
19、 - Vocabulary and symbols - Part 1: General statistical terms and terms used in probability - - 1)Undated reference. 2)Valid edition at date of issue. BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSI 2 61649 IEC:2008 CONTENTS INTRODU
20、CTION.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 three-parameter Weibull distribution
21、 .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 probability plot147.2.1 Ranking.157.2.
22、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 Implies wear-out.208.2 Unknown Weibull mode
23、s 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 .259.2 Assumptions and conditions 269.3 Li
24、mitations and accuracy.269.4 Input and output data 26BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSI61649 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
25、mean time to failure289.8 Point estimate of the fractile (10 %) of the time to 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 Fishe
26、rs Matrix bounds 3010.5 Lower confidence limit for B10.3110.6 Lower confidence 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.
27、4 Shape parameter 3211.5 Confidence intervals3211.6 Single failure .3211.7 Mathematical 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 O
28、ther distributions 37Annex A (informative) Examples and case studies .38Annex 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 p
29、aper.55Annex G (informative) Mixtures of several failure modes56Annex H (informative) 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
30、.12Figure 2 Total test time (in minutes).16Figure 3 Typical bathtub curve for an item .19BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSI 4 61649 IEC:2008 Figure 4 Weibull failure modes may be “masked” .21Figure 5 Sample size: 10 .21
31、Figure 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 shows a good fit with 3 months offset (location 2,99 months).24Figure 9 Example of estimating t0by eye .25Figur
32、e 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 of computations .41Figure E.1 Weibull plot for graphical analysis.49Figure E.2 Weibull plot of censored da
33、ta51Figure 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 of Figure H.1 data 60Table 1 Guidance for using this International Standard 11Table 2 Ranked flare failure r
34、ivet 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 failure 36Table B.1 Times to failure 40Table B.2 Summary of results 41Table D.1 Values of the gamma function47Tab
35、le 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 suspended data50Table E.4 Example of Spreadsheet application for censored data 51Table E.5 Example spreadsheet.
36、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 data entered into a spreadsheet.62BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/0
37、6/2009 02:10, Uncontrolled Copy, (c) BSI61649 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, cycles t
38、o 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 on how t
39、o 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. BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:
40、10, Uncontrolled Copy, (c) BSI 8 61649 IEC:2008 WEIBULL ANALYSIS 1 Scope This International Standard provides methods for analysing data from a Weibull distribution using continuous parameters such as time to failure, cycles to failure, mechanical stress, etc. This standard is applicable whenever da
41、ta on strength parameters, e.g. times to failure, cycles, stress, etc. are available for a random sample of items operating under test conditions or in-service, for the purpose of estimating measures of reliability performance of the population from which these items were drawn. This standard is app
42、licable when the data being analysed are independently, identically distributed. This should either be tested or assumed to be true (see IEC 60300-3-5). In this standard, numerical methods and graphical methods are described to plot data, to make a goodness-of-fit test, to estimate the parameters of
43、 the two- or three-parameter Weibull distribution and to plot confidence limits. Guidance is given on how to interpret the plot in terms of risk as a function of time, failure modes and possible weak population and time to first failure or minimum endurance. 2 Normative references The following refe
44、renced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. IEC 60050-191:1990, International Electrotechnical Vocabulary Part
45、191: Dependability and quality of service IEC 60300-3-5:2001, Dependability management Part 3-5: Application guide Reliability test conditions and statistical test principles IEC 61810-2, Electromechanical elementary relays Part 2: ReliabilityISO 2854:1976, Statistical interpretation of data Techniq
46、ues of estimations and tests relating to means and variances ISO 3534-1:2006, Statistics Vocabulary and symbols Part 1: General statistical terms and terms in probability 3 Terms, definitions, abbreviations and symbols For the purposes of this document, the definitions, abbreviations and symbols giv
47、en inIEC 60050-191 and ISO 3534-1 apply, together with the following. 3.1 Terms and definitions 3.1.1 censoring terminating a test after either a given duration or a given number of failures NOTE A test terminated when there are still unfailed items may be called a “censored test“, and test time dat
48、a from such tests may be referred to as “censored data”. BS EN 61649:2008Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 19/06/2009 02:10, Uncontrolled Copy, (c) BSI61649 IEC:2008 9 3.1.2 suspended item item upon which testing has been curtailed without relevant failure NOTE 1 The item may no
49、t have failed, or it may have failed in a mode other than that under investigation. NOTE 2 An “early suspension” is one that was suspended before the first failure. A “late suspension” is suspended after the last failure. 3.1.3 life test test conducted to estimate or verify the durability of a product NOTE The end of the useful life will often be defined as the time when a certain p
