BS EN 12603-2002 Glass in building - Procedures for goodness of fit and confidence intervals for Weibull distributed glass strength data《建筑玻璃 魏布尔分布玻璃强度数据用置信区间和适配性规程》.pdf

1、Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIBRITISH STANDARD BS EN 12603:2002 Glass in building Procedures for goodness of fit and confidence intervals for Weibull distributed glass strength data The European Standard EN 12603:20

2、02 has the status of a British Standard ICS 81.040.20 Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIBS EN 12603:2002 This British Standard, having been prepared under the direction of the Building and Civil Engineering Sector Polic

3、y and Strategy Committee, was published under the authority of the Standards Policy and Strategy Committee on 9 January 2003 BSI 9 January 2003 ISBN 0 580 41104 4 National foreword This British Standard is the official English language version of EN 12603:2002. The UK participation in its preparatio

4、n was entrusted by Technical Committee B/520, Glass and glazing in building, to Subcommittee B/520/4, Properties and glazing methods, which has the responsibility to: A list of organizations represented on this subcommittee can be obtained on request to its secretary. Cross-references The British St

5、andards which implement international or European publications referred to in this document may be found in the BSI Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Search” facility of the BSI Electronic Catalogue or of British Standards Online. T

6、his publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. aid enquirers to understand the text; present to the responsible in

7、ternational/European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; monitor related international and European developments and promulgate them in the UK. Summary of pages This document comprises a front cover, an inside front cover, the E

8、N title page, pages 2 to 33 and a back cover. The BSI copyright date displayed in this document indicates when the document was last issued. Amendments issued since publication Amd. No. Date Comments Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolle

9、d Copy, (c) BSIEUROPEANSTANDARD NORMEEUROPENNE EUROPISCHENORM EN12603 November2002 ICS81.040.20 Englishversion GlassinbuildingProceduresforgoodnessoffitand confidenceintervalsforWeibulldistributedglassstrengthdata VerredanslaconstructionProcduresdevaliditde lajustementetintervallesdeconfiancedesdonn

10、esde rsistanceduverreaumoyendelaloideWeibull GlasimBauwesenBestimmungderBiegefestigkeitvon GlasSchtzverfahrenundBestimmungder VertrauensbereichefrDatenmitWeibullVerteilung ThisEuropeanStandardwasapprovedbyCENon7September2002. CENmembersareboundtocomplywiththeCEN/CENELECInternalRegulationswhichstipul

11、atetheconditionsforgivingthisEurope an Standardthestatusofanationalstandardwithoutanyalteration.Uptodatelistsandbibliographicalreferencesconcernings uchnational standardsmaybeobtainedonapplicationtotheManagementCentreortoanyCENmember. ThisEuropeanStandardexistsinthreeofficialversions(English,French,

12、German).Aversioninanyotherlanguagemadebytra nslation undertheresponsibilityofaCENmemberintoitsownlanguageandnotifiedtotheManagementCentrehasthesamestatusasthe official versions. CENmembersarethenationalstandardsbodiesofAustria,Belgium,CzechRepublic,Denmark,Finland,France,Germany,Greece, Iceland,Irel

13、and,Italy,Luxembourg,Malta,Netherlands,Norway,Portugal,Spain,Sweden,SwitzerlandandUnitedKingdom. EUROPEANCOMMITTEEFORSTANDARDIZATION COMITEUROPENDENORMALISATION EUROPISCHESKOMITEEFRNORMUNG ManagementCentre:ruedeStassart,36B1050Brussels 2002CEN Allrightsofexploitationinanyformandbyanymeansreserved wo

14、rldwideforCENnationalMembers. Ref.No.EN12603:2002E Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 2 Contents page Foreword3 Introduction .4 1 Scope 5 2 Normativereferences 5 3 Termsanddefinitions. .5 4 Symbolsandabbr

15、eviatedterms. 5 5 Goodnessoffit. 6 6 Pointestimatorsfortheparameters bb and qq ofthedistribution.7 6.1 Censoredsample . 7 6.2 Uncensored(complete)sample 9 7 Assessmentofdataandtests 11 7.1 TheWeibulldiagram. .11 7.2 Graphicalrepresentationoftheestimateddistributionfunction .11 7.3 Plottingofsampleda

16、taintheWeibulldiagram 11 7.3.1 Singlevalues . .11 7.3.2 Classifiedvalues. .12 7.4 Assessmentofsampledata. .12 8 Confidenceintervals 12 8.1 Confidenceintervalfortheshapeparameter bb 12 8.2 Confidenceintervalforthevalueofthedistributionfunction G(x)atagivenvalueof x,ofthe attribute X .15 8.3 Confidenc

17、eintervalforthescaleparameter qq 18 8.3.1 Methodforallsamples 18 8.3.2 Methodforuncensoredsamples. .18 8.4 Confidenceintervalforthevalue xoftheattribute Xatagivenvalue G(x)ofthedistribution function.21 8.4.1 Methodforallsamples 21 8.4.2 Methodforuncensoredsamples. .22 AnnexA (informative) Examples .

18、23 A.1 Uncensoredsample. 23 A.1.1 Data .23 A.1.2 Statisticalevaluation .24 A.2 Censoredsample . 27 A.2.1 Data .27 A.2.2 Statisticalevaluation .29 AnnexB (informative) Weibullgraph. .32 Bibliography 33 Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontroll

19、ed Copy, (c) BSIEN12603:2002(E) 3 Foreword Thisdocument(EN12603:2002)hasbeenpreparedbyTechnicalCommitteeCEN/TC129“Glassinbuilding“,the secretariatofwhichisheldbyIBN. ThisEuropeanStandardshallbegiventhestatusofanationalstandard,eitherbypublicationofanidenticaltextor byendorsement,atthelatestbyMay2003

20、,andconflictingnationalstandardsshallbewithdrawnatthelatestby May2003. InthisstandardtheannexesA,BandCareinformative. AccordingtotheCEN/CENELECInternalRegulations,thenationalstandardsorganizationsofthefollowing countriesareboundtoimplementthisEuropeanStandard:Austria,Belgium,CzechRepublic,Denmark,Fi

21、nland, France,Germany,Greece,Iceland,Ireland,Italy,Luxembourg,Malta,Netherlands,Norway,Portugal,Spain, Sweden,SwitzerlandandtheUnitedKingdom. Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 4 Introduction ThisEuropean

22、Standardisbasedontheassumptionthatthestatisticaldistributionoftheattributetakeninto considerationcanberepresentedbyonesingleWeibulldistributionfunction,evenwhereincertaincases(e.g.lifetime measurements)mixeddistributionshavefrequentlybeenobserved.Forthisreason,theuserofthestandardhasto checkbyagoodn

23、essoffittestwhetherthemeasureddataofasamplecanberepresentedbymeansofonesingle Weibullfunction.Onlyinthiscasecanthehypothesisbeacceptedandtheproceduresdescribedinthisstandardbe applied. Theuserdecidesonthisquestionalsoconsideringallpreviousrelevantdataandthegeneralstateofknowledgeinthe specialfield.E

24、veryextrapolationintorangesoffractilesnotconfirmedbymeasuredvaluesrequiresutmostcare,the moresothefarthertheextrapolationexceedstherangeofmeasurements. NOTE ThethreeparameterWeibullfunctionis: - - - = b q 0 exp 1 ) ( x x x G (1) If xo=0isassumed,thetwoparameterWeibullfunctionresults: - - = b q x x G

25、 exp 1 ) ( (2) whichcanbewrittenas: b q 1 ) ( 1 1 ln - = x G x (3) Thecalculationcanbebasedeitheronanuncensoredoracensoredsample.Thereareseveralmethodsofcensoring. Inthisstandardonlythefollowingmethodofcensoringisconsidered: given a number r nofspecimensofwhichattributevalues x i weremeasured. Licen

26、sed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 5 1Scope ThisEuropeanStandardspecifiesproceduresfortheevaluationofsampledatabymeansofatwoparameterWeibull distributionfunction. 2 Normativereferences ThisEuropeanStandardinco

27、rporatesbydatedorundatedreference,provisionsfromotherpublications.These normativereferencesarecitedattheappropriateplacesinthetext,andthepublicationsarelistedhereafter.Fordated references,subsequentamendmentstoorrevisionsofanyofthesepublicationsapplytothisEuropeanStandardonly whenincorporatedinitsam

28、endmentorrevision.Forundatedreference,thelatesteditionofthepublicationsreferredto applies(includingamendments). ISO2854:1976, StatisticalinterpretationofdataTechniquesofestimationandtestsrelatingtomeansandvariances. ISO3534, StatisticsVocabularyandsymbols . 3 Termsanddefinitions Forthepurposesofthis

29、EuropeanStandard,thetermsanddefinitionsgiveninISO3534apply. 4 Symbolsandabbreviatedterms X attributetakenintoconsideration; x,x i ,x r valuesof X; G(x) distributionfunctionof X=percentageoffailure; x o , b , q parametersofthethreeparameterWeibullfunction; identificationlabelforpointestimators(e.g. b

30、 , q ,G ); 1 a confidencelevel; i valueusedinthegoodnessoffittest; L valueusedinthegoodnessoffittest; n samplesize; r numberofspecimensofwhichattributevalues x i weremeasured; NOTE Thesampleisordered,i.e. x1 x2 x3. xr r n; f,f 1 ,f 2 degreesoffreedom; k n ,k r;n factorsusedinestimating b ; Licensed

31、Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 6 C r;n factorusedinestimating q ; s int(0,84n)=largestinteger0,84 n ; h ,x ordinateandabcissaoftheWeibulldiagram; c 2 chisquaredistributionfunction; y,v,g auxiliaryfactorsusedin

32、estimatingtheconfidencelimitsof G(x); A,B,C constantsusedinevaluating v ; H(f 2 ) variableusedinevaluating g ; T n;a /2 ,T n;1 a /2 coefficientsusedinestimatingtheconfidencelimitsof q ; Subscripts: un lowerconfidencelimit; ob upperconfidencelimit; z confidenceintervallimitedontwosides. 5 Goodnessoff

33、it Sortthe rvaluesof xintorankascendingorder. Computeforeachvaluefrom i =1to i = r 1: () + + - + + - - - = + 1 4 3 4 ln 1 4 3 ) 1 ( 4 ln ln ) ln( ) ln( 1 n i n n i n x x i i i (4) Computethequantity: () = - + = - = 2 / 1 1 1 2 / 2 / 2 / 1 r i i r r i i r r L (5) wherethesymbol 2 / r isusedtodenoteth

34、elargestintegerlessthanorequaltor/2. RejectthehypothesisthatthedataisfromaWeibulldistributionatthe a significancelevelif: Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 7 () () 2 / 2 , 2 / 1 2 r r F L - a (6) Thevalu

35、esofthefractilesofthe FdistributioncanbefoundforexampleinTableIVofISO2854:1976. 6 Pointestimatorsfortheparameters b and q ofthedistribution 6.1 Censoredsample x x r n = i r = i r r;n ln ln 1 k b (7) b q 1 ln exp C x = n r; r (8) Thefactors k r;n and C r;n arelistedinTable1andTable2. Licensed Copy: W

36、ang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 8 Table1Coefficient kk r;n nr /n 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 5 0,2231 0,4813 0,8018 10 0,1054 0,2172 0,3369 0,4667 0,6098 0,7715 0,9616 1,202 20 0,0513 0,1583 0,2721 0,3944 0,52

37、77 0,6756 0,8448 1,048 1,316 30 0,0684 0,1759 0,2904 0,4137 0,5482 0,6979 0,8697 1,077 1,357 40 0,0770 0,1848 0,2996 0,4233 0,5584 0,7090 0,8822 1,092 1,378 50 0,0821 0,1901 0,3051 0,4291 0,5646 0,7158 0,8898 1,101 1,391 60 0,0855 0,1936 0,3088 0,4330 0,5687 0,7202 0,8949 1,108 1,400 70 0,0879 0,196

38、1 0,3114 0,4357 0,5717 0,7235 0,8985 1,112 1,406 80 0,0898 0,1980 0,3134 0,4378 0,5739 0,7259 0,9012 1,115 1,410 90 0,0912 0,1995 0,3149 0,4394 0,5756 0,7277 0,9033 1,118 1,414 100 0,0924 0,2007 0,3162 0,4407 0,5770 0,7292 0,9050 1,120 1,417 k p 0,10265 0,21129 0,32723 0,45234 0,58937 0,74274 0,9202

39、6 1,1382 1,4436 d 1 1,0271 1,0622 1,1060 1,1634 1,2415 1,3540 1,5313 1,8567 2,6929 d 2 0,000 0,030 0,054 0,089 0,145 0,242 0,433 0,906 2,796 Asymptoticestimateforlarge n: k r,n = k p + d 1 /n+ d 2 /n 2 Licensed Copy: Wang Bin, ISO/Exchange China Standards Information Centre, 08 April 2003, Uncontrol

40、led Copy, (c) BSIEN12603:2002(E) 9 Table2Coefficient C r,n nr /n 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 10 2,880 1,826 1,267 0,8681 0,5436 0,2574 0,0120 0,2837 0,5846 20 2,547 1,658 1,147 0,7691 0,4548 0,1727 0,0979 0,3776 0,7022 30 2,444 1,605 1,108 0,7364 0,4253 0,1443 0,1269 0,4098 0,7446 40 2,394 1

41、,578 1,089 0,7202 0,4106 0,1301 0,1415 0,4262 0,7664 50 2,365 1,562 1,077 0,7105 0,4018 0,1216 0,1503 0,4360 0,7796 60 2,345 1,522 1,069 0,7040 0,3959 0,1159 0,1562 0,4426 0,7885 70 2,331 1,544 1,064 0,6994 0,3917 0,1118 0,1604 0,4473 0,7949 80 2,321 1,539 1,060 0,6959 0,3886 0,1088 0,1635 0,4509 0,

42、7998 90 2,313 1,534 1,056 0,6932 0,3861 0,1064 0,1660 0,4537 0,8035 100 2,307 1,531 1,054 0,6911 0,3841 0,1045 0,1679 0,4559 0,8065 c p 2,2504 1,4999 1,0309 0,67173 0,36651 0,08742 0,18563 0,47589 0,83403 a 1 5,5743 3,0740 2,2859 1,9301 1,7619 1,7114 1,7727 2,0110 2,7773 a 2 7,201 1,886 0,767 0,335

43、0,091 0,111 0,369 0,891 2,825 Asymptoticestimateforlarge n: C r,n = c p + a 1 /n+ a 2 /n 2 6.2 Uncensored(complete)sample x x s n s n = i s = i i n + s = i n ln ln 1 1 k b (10) + = n i i x n = 1 1 5772 , 0 ln 1 exp b q (11) Thefactors k n arelistedinTable3. Licensed Copy: Wang Bin, ISO/Exchange Chin

44、a Standards Information Centre, 08 April 2003, Uncontrolled Copy, (c) BSIEN12603:2002(E) 10 Table3Coefficient kk n n k n n k n 2 0,6931 32 1,4665 3 0,9808 33 1,4795 4 1,1507 34 1,4920 5 1,2674 35 1,5040 6 1,3545 36 1,5156 7 1,1828 37 1,5266 8 1,2547 38 1,4795 9 1,3141 39 1,4904 10 1,3644 40 1,5009 11 1,4079 41 1,5110 12 1,4461 42 1,5208 13 1,3332 43 1,5303 14 1,3686 44 1,4891 15 1,4004 45 1,4984 16 1,4293 46 1,5075 17 1,4556 47 1,5163 18 1,4799 48 1,5248 19 1,3960 49 1,5331 20 1,4192 50 1,5411 21 1,4408 51 1,5046 22 1,4609 52 1,5126 23 1,4797 53 1