1、BRITISH 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 12603:2002 has the status of a British Standard ICS 81.040.20 BS EN 12603:2002 This British Standard, having been prepared
2、under the direction of the Building and Civil Engineering Sector Policy 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 lan
3、guage version of EN 12603:2002. The UK participation in its preparation 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
4、 obtained on request to its secretary. Cross-references The British Standards 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” faci
5、lity of the BSI Electronic Catalogue or of British Standards Online. This 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 obligation
6、s. aid enquirers to understand the text; present to the responsible international/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 pag
7、es This document comprises a front cover, an inside front cover, the EN 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 CommentsEUROPEANSTANDARD NORMEEUROPENNE
8、 EUROPISCHENORM EN12603 November2002 ICS81.040.20 Englishversion GlassinbuildingProceduresforgoodnessoffitand confidenceintervalsforWeibulldistributedglassstrengthdata VerredanslaconstructionProcduresdevaliditde lajustementetintervallesdeconfiancedesdonnesde rsistanceduverreaumoyendelaloideWeibull G
9、lasimBauwesenBestimmungderBiegefestigkeitvon GlasSchtzverfahrenundBestimmungder VertrauensbereichefrDatenmitWeibullVerteilung ThisEuropeanStandardwasapprovedbyCENon7September2002. CENmembersareboundtocomplywiththeCEN/CENELECInternalRegulationswhichstipulatetheconditionsforgivingthisEurope an Standar
10、dthestatusofanationalstandardwithoutanyalteration.Uptodatelistsandbibliographicalreferencesconcernings uchnational standardsmaybeobtainedonapplicationtotheManagementCentreortoanyCENmember. ThisEuropeanStandardexistsinthreeofficialversions(English,French,German).Aversioninanyotherlanguagemadebytra ns
11、lation undertheresponsibilityofaCENmemberintoitsownlanguageandnotifiedtotheManagementCentrehasthesamestatusasthe official versions. CENmembersarethenationalstandardsbodiesofAustria,Belgium,CzechRepublic,Denmark,Finland,France,Germany,Greece, Iceland,Ireland,Italy,Luxembourg,Malta,Netherlands,Norway,
12、Portugal,Spain,Sweden,SwitzerlandandUnitedKingdom. EUROPEANCOMMITTEEFORSTANDARDIZATION COMITEUROPENDENORMALISATION EUROPISCHESKOMITEEFRNORMUNG ManagementCentre:ruedeStassart,36B1050Brussels 2002CEN Allrightsofexploitationinanyformandbyanymeansreserved worldwideforCENnationalMembers. Ref.No.EN12603:2
13、002EEN12603:2002(E) 2 Contents page Foreword3 Introduction .4 1 Scope 5 2 Normativereferences 5 3 Termsanddefinitions. .5 4 Symbolsandabbreviatedterms. 5 5 Goodnessoffit. 6 6 Pointestimatorsfortheparameters bb and qq ofthedistribution.7 6.1 Censoredsample . 7 6.2 Uncensored(complete)sample 9 7 Asses
14、smentofdataandtests 11 7.1 TheWeibulldiagram. .11 7.2 Graphicalrepresentationoftheestimateddistributionfunction .11 7.3 PlottingofsampledataintheWeibulldiagram 11 7.3.1 Singlevalues . .11 7.3.2 Classifiedvalues. .12 7.4 Assessmentofsampledata. .12 8 Confidenceintervals 12 8.1 Confidenceintervalforth
15、eshapeparameter bb 12 8.2 Confidenceintervalforthevalueofthedistributionfunction G(x)atagivenvalueof x,ofthe attribute X .15 8.3 Confidenceintervalforthescaleparameter qq 18 8.3.1 Methodforallsamples 18 8.3.2 Methodforuncensoredsamples. .18 8.4 Confidenceintervalforthevalue xoftheattribute Xatagiven
16、value G(x)ofthedistribution function.21 8.4.1 Methodforallsamples 21 8.4.2 Methodforuncensoredsamples. .22 AnnexA (informative) Examples .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 (informat
17、ive) Weibullgraph. .32 Bibliography 33EN12603:2002(E) 3 Foreword Thisdocument(EN12603:2002)hasbeenpreparedbyTechnicalCommitteeCEN/TC129“Glassinbuilding“,the secretariatofwhichisheldbyIBN. ThisEuropeanStandardshallbegiventhestatusofanationalstandard,eitherbypublicationofanidenticaltextor byendorsemen
18、t,atthelatestbyMay2003,andconflictingnationalstandardsshallbewithdrawnatthelatestby May2003. InthisstandardtheannexesA,BandCareinformative. AccordingtotheCEN/CENELECInternalRegulations,thenationalstandardsorganizationsofthefollowing countriesareboundtoimplementthisEuropeanStandard:Austria,Belgium,Cz
19、echRepublic,Denmark,Finland, France,Germany,Greece,Iceland,Ireland,Italy,Luxembourg,Malta,Netherlands,Norway,Portugal,Spain, Sweden,SwitzerlandandtheUnitedKingdom.EN12603:2002(E) 4 Introduction ThisEuropeanStandardisbasedontheassumptionthatthestatisticaldistributionoftheattributetakeninto considerat
20、ioncanberepresentedbyonesingleWeibulldistributionfunction,evenwhereincertaincases(e.g.lifetime measurements)mixeddistributionshavefrequentlybeenobserved.Forthisreason,theuserofthestandardhasto checkbyagoodnessoffittestwhetherthemeasureddataofasamplecanberepresentedbymeansofonesingle Weibullfunction.
21、Onlyinthiscasecanthehypothesisbeacceptedandtheproceduresdescribedinthisstandardbe applied. Theuserdecidesonthisquestionalsoconsideringallpreviousrelevantdataandthegeneralstateofknowledgeinthe specialfield.Everyextrapolationintorangesoffractilesnotconfirmedbymeasuredvaluesrequiresutmostcare,the mores
22、othefarthertheextrapolationexceedstherangeofmeasurements. NOTE ThethreeparameterWeibullfunctionis: - - - = b q 0 exp 1 ) ( x x x G (1) If xo=0isassumed,thetwoparameterWeibullfunctionresults: - - = b q x x G exp 1 ) ( (2) whichcanbewrittenas: b q 1 ) ( 1 1 ln - = x G x (3) Thecalculationcanbebasedeit
23、heronanuncensoredoracensoredsample.Thereareseveralmethodsofcensoring. Inthisstandardonlythefollowingmethodofcensoringisconsidered: given a number r nofspecimensofwhichattributevalues x i weremeasured.EN12603:2002(E) 5 1Scope ThisEuropeanStandardspecifiesproceduresfortheevaluationofsampledatabymeanso
24、fatwoparameterWeibull distributionfunction. 2 Normativereferences ThisEuropeanStandardincorporatesbydatedorundatedreference,provisionsfromotherpublications.These normativereferencesarecitedattheappropriateplacesinthetext,andthepublicationsarelistedhereafter.Fordated references,subsequentamendmentsto
25、orrevisionsofanyofthesepublicationsapplytothisEuropeanStandardonly whenincorporatedinitsamendmentorrevision.Forundatedreference,thelatesteditionofthepublicationsreferredto applies(includingamendments). ISO2854:1976, StatisticalinterpretationofdataTechniquesofestimationandtestsrelatingtomeansandvaria
26、nces. ISO3534, StatisticsVocabularyandsymbols . 3 Termsanddefinitions ForthepurposesofthisEuropeanStandard,thetermsanddefinitionsgiveninISO3534apply. 4 Symbolsandabbreviatedterms X attributetakenintoconsideration; x,x i ,x r valuesof X; G(x) distributionfunctionof X=percentageoffailure; x o , b , q
27、parametersofthethreeparameterWeibullfunction; identificationlabelforpointestimators(e.g. b , q ,G ); 1 a confidencelevel; i valueusedinthegoodnessoffittest; L valueusedinthegoodnessoffittest; n samplesize; r numberofspecimensofwhichattributevalues x i weremeasured; NOTE Thesampleisordered,i.e. x1 x2
28、 x3. xr r n; f,f 1 ,f 2 degreesoffreedom; k n ,k r;n factorsusedinestimating b ;EN12603:2002(E) 6 C r;n factorusedinestimating q ; s int(0,84n)=largestinteger0,84 n ; h ,x ordinateandabcissaoftheWeibulldiagram; c 2 chisquaredistributionfunction; y,v,g auxiliaryfactorsusedinestimatingtheconfidencelim
29、itsof 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 Goodnessoffit Sortthe rvaluesof xinto
30、rankascendingorder. 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 isusedtodenotethelargestintegerlessthanore
31、qualtor/2. RejectthehypothesisthatthedataisfromaWeibulldistributionatthe a significancelevelif:EN12603:2002(E) 7 () () 2 / 2 , 2 / 1 2 r r F L - a (6) Thevaluesofthefractilesofthe FdistributioncanbefoundforexampleinTableIVofISO2854:1976. 6 Pointestimatorsfortheparameters b and q ofthedistribution 6.
32、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.EN12603:2002(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
33、 1,202 20 0,0513 0,1583 0,2721 0,3944 0,5277 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
34、 0,7202 0,8949 1,108 1,400 70 0,0879 0,1961 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 0,21
35、129 0,32723 0,45234 0,58937 0,74274 0,92026 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 2EN12603:2002(E) 9 Table2Coefficient C r,n nr /n 0,1 0,2 0
36、,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 1,578 1,089 0,7202 0,4106 0,1301 0,1415 0,4262 0,7664 50 2,365 1,562 1,077
37、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 0,7998 90 2,313 1,534 1,056 0,6932 0,3861 0,1064 0,1660 0,4537 0,8035 100 2,
38、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 0,091 0,111 0,369 0,891 2,825 Asymptoticestimateforlarge n: C r,n = c p +
39、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.EN12603:2002(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 1,26
40、74 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 5
41、0 1,5411 21 1,4408 51 1,5046 22 1,4609 52 1,5126 23 1,4797 53 1,5204 24 1,4975 54 1,5279 25 1,5142 55 1,5352 26 1,4479 56 1,5424 27 1,4642 57 1,5096EN12603:2002(E) 11 Table3 (continued) 28 1,4796 58 1,5167 29 1,4943 59 1,5236 30 1,5083 60 1,5304 31 1,5216 1,5692 7 Assessmentofdataandtests 7.1 TheWei
42、bulldiagram TheprobabilitydiagramfortheWeibulldistributionisdrawnupinsuchawaythatthedistributionfunctionofatwo parameterWeibulldistributionisrepresentedbyastraightline. Theordinateaxisisgraduatedaccordingtothefunction G(x) = 1 1 ln ln h (12) andtheabscissaaxisaccordingtothefunction x = ln x or x = l
43、og x (13) NOTE Suchformsareavailable.Asarule,diagramsshouldbeusedwitharangeof Gvaluesfrom G=1 10 3 =0,1%to G=0,999=99,9%.Thenecessaryrangeof xvaluesdependsonthevalue b oftheshapeparameter. 7.2 Graphicalrepresentationoftheestimateddistributionfunction Thepointestimatorsoftheshapeparameter b andthesca
44、leparameter q defineastraightlineintheWeibulldiagram;it isappropriatetodefinethisstraightlinethoughthefollowingtwopoints: q = x % 21 , 63 6321 , 0 ) ( = = x G (14) b q 1 01005 , 0 = x % 1 01 , 0 ) ( = = x G (15) Thisstraightlineshallbeplottedintothediagram. 7.3 PlottingofsampledataintheWeibulldiagram 7.3.1 Singlevalues Measurementsofacensore
