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1、ANoteontheOptimalReplacementProblemAuthor(s):LamYehSource:AdvancesinAppliedProbability,Vol.20,No.2(Jun.,1988),pp.479-482Publishedby:AppliedProbabilityTrustStableURL:http://www.jstor.org/stable/1427402.Accessed:07/04/201306:54YouruseoftheJSTORarchiveindicatesyouracceptanc
2、eoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolsto
3、increaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..AppliedProbabilityTrustiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoAdvancesinAppliedProbability.http://www.jstor.orgThiscontentdownloadedfr
4、om114.83.186.199onSun,7Apr201306:54:34AMAllusesubjecttoJSTORTermsandConditionsAdv.Appl.Prob.20,479-482(1988)PrintedinN.Ireland(AppliedProbabilityTrust1988ANOTEONTHEOPTIMALREPLACEMENTPROBLEMLAMYEH,*TheChineseUniversityofHongKongAbstractInthisnote,westudyanewrepairreplacem
5、entmodelforadeterioratingsystem,inwhichthesuccessivesurvivaltimesofthesystemformageometricprocessandarestochasticallynon-increasing,whereastheconsecutiverepairtimesafterfailurealsoconstituteageometricprocessbutarestochasticallynon-decreasing.Twokindsofreplacementpolicyar
6、econsidered,onebasedontheworkingageofthesystemandtheotheronedeterminedbythenumberoffailures.Theexplicitexpressionsofthelong-runaveragecostsperunittimeunderthesetwokindsofpolicyarecalculated.REPLACEMENTPROBLEM;STOCHASTICMONOTONICITY;RENEWALPROCESSES1.IntroductionMostrepai
7、rreplacementmodelsassumethatafailuresystemafterrepairwillyieldafunctioningsystemwhichis'asgoodasnew'i.e.,thesystemisrenewedaftereachfailure.Analternativeassumptionistoassumethatafailuresystemafterrepairwillfunctionagain,buthasthesamefailurerateandthesameeffectiveageatthe
8、timeoffailure:thisleadstotheminimalrepairmodel.Inbothcases,therepairtimesareoftennegligible(seee.g.Barl
