1、Weibull analysisBS EN 61649:2008raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI British StandardsNational forewordThis British Standard is the UK implementation of EN 61649:2008. It is identical to IEC 61649:2008. It supersedes BS IEC 61649:1997 w
2、hich is withdrawn.The UK participation in its preparation was entrusted by Technical CommitteeDS/1, Dependability and terotechnology, to Subcommittee DS/1/1,Dependability.A list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 represented on this committee can be obtained onrequest to its secretary.This publication does not purpor
3、t 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 cannot confer immunity fromlegal obligations.Amendments issued since publicationAmd. No. Date Text affec
4、tedBRITISH STANDARDBS EN 61649:2008This British Standard was published under the authority of the StandardsPolicy and Strategy Committee on February 2009.2 8EUROPEAN STANDARD EN 61649 NORME EUROPENNE EUROPISCHE NORM November 2008 CENELEC European Committee for Electrotechnical Standardization Comit
5、Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung Central Secretariat: 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;
6、 03.120.30 English version Weibull analysis (IEC 61649:2008) Analyse de Weibull (CEI 61649:2008) Weibull-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
7、 for giving this European Standard the status of a national standard without any alteration. Up-to-date 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 o
8、fficial versions (English, French, German). A version in any other language made by translation under 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 c
9、ommittees of Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the
10、United Kingdom. BS EN 61649:2008EN 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: lates
11、t date 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. _ Endorseme
12、nt 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 mo
13、dified). 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 a
14、s EN 61703:2002 (not modified). _ BS EN 61649:2008 3 EN 61649:2008 Annex ZA (normative) Normative references to international publications with their corresponding European publications The following referenced documents are indispensable for the application of this document. For dated references, o
15、nly 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 modifications, indicated by (mod), the relevant EN/HD applies. Publication Year Title EN/HD Year
16、 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 - Reliability test conditions and statistical test principles - - IEC 61810-2 - 1)Electromechanical el
17、ementary 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 - Vocabulary and symbols - Part 1: General statistical terms and terms used in probability - -
18、1)Undated reference. 2)Valid edition at date of issue. BS EN 61649:2008 2 61649 IEC:2008 CONTENTS INTRODUCTION.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 Weibul
19、l distribution 115.1 The two-parameter Weibull distribution115.2 The 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
20、 methods and goodness-of-fit 147.1 Overview .147.2 How to make the probability 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 probabi
21、lity plot.198.1 The bathtub curve .198.1.1 General .198.1.2 1 Implies 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
22、 Computational methods and goodness-of-fit .259.1 Introduction .259.2 Assumptions and conditions 269.3 Limitations and accuracy.269.4 Input and output data 26BS EN 61649:200861649 IEC:2008 3 9.5 Goodness-of-fit test.279.6 MLE point estimates of the distribution parameters and .279.7 Point estimate o
23、f the 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
24、 Fishers 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
25、.3211.4 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
26、3514 Other 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 probabi
27、lity paper.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
28、= 1,0 .12Figure 2 Total test time (in minutes).16Figure 3 Typical bathtub curve for an item .19BS EN 61649:2008 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 Wei
29、bull 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 .25Figure 10 New compressor design WeiBayes versus old design 35Figure A.1 Main oil pump low times38F
30、igure 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 data51Figure E.3 Cumulative hazard plot for data of Table E.4 52Figure E.4 Cumulative hazard pl
31、ots 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 rivet data .15Table 3 Adjusted ranks for suspended or censored data 16Table 4 Subgroup size to
32、 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 function47Table D.2 Fractiles of the normal distribution .47Table E.1 Practical analysis example.48Table E
33、.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.52Table E.6 A relay data provided by ISO/TC94 and Hazard analysis for failure mode 1 .53Table
34、 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 61649:200861649 IEC:2008 7 INTRODUCTION The Weibull distribution is used to model data regardless of whether the failure rate is increasing, decreasing or constan
35、t. The Weibull distribution is flexible and adaptable to a wide range of data. The time to failure, 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.
36、Guidance is given on how to perform an analysis using a spreadsheet program. Guidance is also given 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 en
37、durance in the sample. BS EN 61649:2008 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 wh
38、enever data 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 standa
39、rd is applicable 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 para
40、meters of 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 follo
41、wing referenced 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 Vocabul
42、ary Part 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 dat
43、a Techniques 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 sy
44、mbols given 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
45、 time data from such tests may be referred to as “censored data”. BS EN 61649:200861649 IEC:2008 9 3.1.2 suspended item item upon which testing has been curtailed without relevant failure NOTE 1 The item may not have failed, or it may have failed in a mode other than that under investigation. NOTE 2
46、 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 percen
47、tage of the items have failed for non-repairable items and as the time when the failure intensity has increased to a specified level for repairable items. 3.1.4 non-repairable item item that cannot, under given conditions, after a failure, be returned to a state in which it can perform as required N
48、OTE The given conditions may be technical, economic, ecological and/or others. 3.1.5 operating time time interval for which the item is in an operating state NOTE ”Operating time” is generic, and should be expressed in units appropriate to the item concerned, e.g. calendar time, operating cycles, di
49、stance run, etc. and the units should always be clearly stated. 3.1.6 relevant failure failure that should be included in interpreting test or operational results or in calculating the value of a reliability performance measure NOTE The criteria for inclusion should be stated. 3.1.7 reliability test experiment carried out in order to measure, quantify or classify a reliability measu
