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1、ResamplingApproachtotheEstimationofReliabilitySystemsMaximFioshin,HelenFioshinaInstituteofTransportMachinesandTechnologies,RigaTechnicalUniversity,LomonosovaStr.1,LV1019,RigaLatviaMaksims.Fiosins@rtu.lv,Jelena.Fiosina@rtu.lvAbstractThearticleisdevoted
2、totheresamplingapproachapplicationtothereliabilityproblems.ThisapproachtoreliabilityproblemswasfirstproposedbyIvnitsky(1967).Resamplingisinten-sivestatisticalcomputermethod,whichisnon-parametrical,thatusesinitialsamplesdataindifferentcombinationstosimul
3、atetheprocessmanytimesandgetfinallytheestimatorofthecharacteristicsofinterest.Atthepresentpapersimpleresampling,hierarchicalresampling,thecaseofonesampleforseveralvariables,thecaseofpartiallyknowndistributions,anal-ysisofdegradationflow,analysisofdegrad
4、ation-renewalprocess,constructionofconfidenceintervalsaredescribed.Allthoseresamplingapplicationcasescanbeappliedsuccessfullytosolvethereliabilityproblemsasanalternativetoclassicalmethods.1IntroductionComputersplayanimportantroleinthedevelopmentofmoder
5、nstatisticalscience.Manystatisticalmethodsdevelopedinthelasttimerequireabigamountofcomputations.Suchmethodsareusuallycalledintensivestatisticalmethods.Someauthorsspeakaboutseparatedisciplinecalled”computationalstatistics”(Gentle2002).Instatisticalprob
6、lemsofreliabilityweoftenhavedifficultieswithapplicationofclassicalmethods.Inthecaseofcomplexsystems,smallsamples,unknowndistributionsofsystemcharacteristicsclassicalmethodsworknotsogood.Inthiscase,methodsofcomputationalstatisticscanbeusedasanalternative
7、.Thefieldofcomputationalstatisticsatpresenttimeincludesabignumberofmethods.Jack-knifemethodwassuggestedbyM.Quenouillein1949(Quenouille1949).Itusestheestima-tor,whichisthecombinationoftheestimator’sobtainedusingalldataandtheestimators,ob-tainedusingonly
8、partofthesamedata.In1967V.Ivnitsky(Ivnitsky1967)suggestedtousere-samplingfortheestimationofthesystems’reliabilitybysimulation.B.Efron(Efron1979)sug-gestedbootstrapmethod,whichisthegeneralizationofthejackknifemethod.Resamplingap-proachwasinvest
