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1、SequentialEstimationbyMalayGhosh,NitisMukhopadhyayandPranabK.SenCopyright©1997JohnWiley&Sons,Inc.Chapter13SequentialEstimationinReliabilityModels13.1INTRODUCTIONTime-sequentialestimationproblemsarisinginavarietyoflife-testingmodelsweretreatedintheprecedi
2、ngchapter.Althoughsuchlife-testingmodelsconstituteanimportantclassofreliabilitymodels,thereareothernotablemembersofthisclassthatdeserveacarefulstudy.Thecurrentchapterisdevotedtosuchmodelsandisaimedatdisseminatingtheroleofsequentialestimationtheoryinthisc
3、ontext.Reliabilityandsurvivabilitytheoryarebothrelatedtomeasurementoflengthoflife,althoughthecontextmayvaryfromapureengineeringsetuptoaclinicalone,andthisspectrumofvariationhascalledforattentiontomoreflexibleandrobuststatisticaltheory.Sequentialmodelsint
4、hisframeworkmaynotnecessarilyrelatetoatime-sequentialsetup.Ontheotherhand,thereliabilityofasystemwithmorethanonecomponentcanbemodeledbyprobabilitylawsforthecomponentunitsandthestructuralsetupofthecomponents,andhenceusefulstatisticalconclusionscanbedrawnb
5、yexaminingsuchstructuresandtheassociatedprobabilitylaws.Oftensuchanexaminationmayleadtoasomewhatdifferentformulationofthemodel,leadingtomorecomprehensivesolutionsaswell.Admittedlyinthisframeworkthereisagreateremphasisonthetestingofstatisticalhypothesespr
6、oblems.Newbetterthanused,IFRA,DFRA,andrelatedterminologieshaveallinvadedstatisticalmethodologyprimarilyfromthetestingpointofview.Sincesuchtestingproblemsdonotproperlybelongtothecontemplateddomainofsequentialestimation,wewillconcentrateonsomereliabilitymo
7、delswherethereisconsiderablescopeforrobustsequentialestimation.Fourimportantstatisticalproblemsarisinginreliabilitytheoryarecon-sideredhere.Bundlestrengthofparallelfilaments(Daniels1945)isanin-terestingmixtureofsomeparametricswithnonparametrics,whiletheo
8、therthree—system¿-componentsinseries,system¿-componentsinparallel,and36736813.SEQUENTIALESTIMATIONINRELIABILITYMODELSsystemavailabilityunderprovisionofaspareandrepair—liemoreinthecoreofreliabilitytheory(BarlowandProschan,1
