Springer Series in Reliability Engineering Yu Liu Hong-Zhong Huang Tao Jiang Selective Maintenance Modelling and Optimization Basic Methods and Some Recent Advances Springer Series in Reliability Engineering SeriesEditor HoangPham,DepartmentofIndustrialandSystemsEngineering,Rutgers University,Piscataway,NJ,USA Today’s modern systems have become increasingly complex to design and build, while the demand for reliability and cost effective development continues. Reli- ability is one of the most important attributes in all these systems, including aerospace applications, real-time control, medical applications, defense systems, humandecision-making,andhome-securityproducts.Growinginternationalcompe- titionhasincreasedtheneedforalldesigners,managers,practitioners,scientistsand engineerstoensurealevelofreliabilityoftheirproductbeforereleaseatthelowest cost.Theinterestinreliabilityhasbeengrowinginrecentyearsandthistrendwill continueduringthenextdecadeandbeyond. TheSpringerSeriesinReliabilityEngineeringpublishesbooks,monographsand edited volumes in important areas of current theoretical research development in reliabilityandinareasthatattempttobridgethegapbetweentheoryandapplication inareasofinteresttopractitionersinindustry,laboratories,business,andgovernment. Nowwith100volumes! **IndexedinScopusandEICompendex** Interestedauthorsshouldcontacttheserieseditor,HoangPham,Departmentof IndustrialandSystemsEngineering,RutgersUniversity,Piscataway,NJ08854, USA. Email: [email protected], or Anthony Doyle, Executive Editor, Springer,London.Email:[email protected]. · · Yu Liu Hong-Zhong Huang Tao Jiang Selective Maintenance Modelling and Optimization Basic Methods and Some Recent Advances YuLiu Hong-ZhongHuang CenterforSystemReliabilityandSafety CenterforSystemReliabilityandSafety UniversityofElectronicScience UniversityofElectronicScience andTechnologyofChina andTechnologyofChina Chengdu,Sichuan,China Chengdu,Sichuan,China TaoJiang CenterforSystemReliabilityandSafety UniversityofElectronicScience andTechnologyofChina Chengdu,Sichuan,China ISSN 1614-7839 ISSN 2196-999X (electronic) SpringerSeriesinReliabilityEngineering ISBN 978-3-031-17322-6 ISBN 978-3-031-17323-3 (eBook) https://doi.org/10.1007/978-3-031-17323-3 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Reliability has become a crucial characteristic of advance engineered systems as systemswithpoorreliabilitysufferfromagreatamountoflifecyclecostandpoten- tialriskoffailures.Maintenance,involvingbothcorrectiveandpreventiveactions,is aneffectivewaytoretainasysteminorrestoreittoanacceptableoperatingcondi- tion,andithasbeenextensivelyimplementedinindustrialapplications.Examples ofmaintenanceactivitiesforengineeredsystemsareoilchangeofrotatingsystems, rotor balance of mechanical systems, shaft/coupling alignment, filter replacement, corroded components coating, and so forth. It is noted that inappropriate mainte- nance scheme may not guarantee the reduction of operation cost and the fulfill- ment of reliability target, and systems are over-maintained or under-maintained during its operation stage. The maintenance models and optimization have been, therefore, intensively studied in the past decade with the purpose of minimizing maintenancecostand/ormaximizingreliabilityoravailabilityofaspecificsystem. The paradigm of maintenance strategy has shifted from corrective maintenance to preventive maintenance, and then to condition-based maintenance and predictive maintenancenowadays. Selective maintenance optimization, as a specific condition-based maintenance problem, was firstlypresented by Rice, Cassady, and Nachlas in the 7th Industrial EngineeringResearchConference.Inselectivemaintenanceoptimization,asystem intendstoperformsuccessiveassignedmissionswithabreakbetweentwoadjacent missions,andmaintenanceactionscanbeexecutedinbreakstoensurethesuccessof thesubsequentmissions.However,duetothelimitedmaintenanceresources,such astimeandbudget,itisimpossibletocarryoutallthedesiredmaintenanceactions foragedandfailedcomponents.Alternatively,asubsetofmaintenanceactionshas tobeselectedfromthesetofalltheoptionalmaintenanceactions,soastomaximize thesuccessofthefuturemissions.Thepreliminarymodelforselectivemaintenance of series–parallel systems with independent and identical copies of a component wasgeneralized toabasicframeworkbyCassadyandco-authors inthefollow-up researchworks.Asselectivemaintenanceoptimizationexactlymatchesupwiththe manyindustrialandmilitaryscenarioswhereonlyalimitedamountofmaintenance v vi Preface resources have to be allocated among components of a system, it has been exten- sivelystudiedinthepastdecadefromvariousanglesandimplementedinadiversity of industrial applications. Research articles on this subject are continuously being published in journals and conference proceedings. Nevertheless, to the best of our knowledge,thesubjecthasneverbeenadequatelyorsystematicallyreportedinreli- abilitybook.Theincreasedandsustainedinterestinthissubjectdrivesustopublish thisbook. Thisbooksystematicallyintroducesthebasicselectivemaintenanceoptimization model.Itis,toalargeextent,acollectionofourrecentresearchadvancesonselective maintenanceoptimizationfromtheCenterforSystemReliabilityandSafetyatthe UniversityofElectronicScienceandTechnologyofChina.Thelayoutofthisbook isasfollowing: Chapter1introducestheroleofmaintenanceoptimizationinlifecyclemanage- mentofengineeringassetsandgivesanoverviewpictureofresearchtopicsinmain- tenanceoptimization.Itisfollowedbyasystematicalliteraturereviewontheexisting researcheffortsonselectivemaintenanceoptimization. Chapter 2 offers an introduction to the basic mathematical model of selective maintenanceproblem,inwhichbothasystemanditscomponentsareassumedtobe binary-state.Threeselectivemaintenancemodelswithdistinctobjectivesfunctions andconstraintsareformulated. Chapter3discussestheselectivemaintenanceoptimizationformulti-statesystems withbinary-capacitatedcomponents.TheKijimatypeIIagereductionmodel,serving asaspecificimperfectmaintenancemodel,isincorporatedintheselectivemainte- nanceoptimization.Theuniversalgeneratingfunctionisutilizedtoevaluatetheprob- abilityofasystemsuccessfullycompletingthenextmission.Thegeneticalgorithm isintroducedtoresolvetheresultingoptimizationmodel. Chapter 4 focuses on the selective maintenance optimization for multi-state systems with the load sharing mechanism. A joint optimization model is formu- latedtosimultaneouslyoptimizetheloaddistributionandtheallocationofthelimited maintenancebudgetamongcomponents.Thegeneticalgorithmisemployedtosolve theoptimizationproblem. Chapter 5 discusses selective maintenance optimization under stochastic time durations of breaks and maintenance actions. The distribution of the number of completedmaintenanceactionsinabreakwithtimedurationuncertaintyisevaluated byusingthesaddlepointapproximation.Atailoredantcolonyoptimizationalgorithm isdevelopedtosolvetheresultingcombinationaloptimizationprobleminthecases oflarge-scalesystems. Chapter 6 presents a robust selective maintenance optimization model to treat theuncertaintyproducedbyimperfectobservations.Amulti-objectiveoptimization modelisformulatedwiththeaimsofmaximizingtheexpectationandsimultaneously minimizingthevarianceofasystemsuccessfullycompletingthenextmission. Chapter7takesaccountofuncertaintiesfrombothmaintenanceandinspectionand introducesajointselectivemaintenanceandinspectionoptimizationmodel.Afinite- horizonmixedobservabilityMarkovdecisionprocessisformulatedastheremaining resourceisfullyobservableandthecomponentstatesarepartiallyobservable.The Preface vii dynamicprogramingandthedeepreinforcementlearningalgorithmareimplemented toresolvesmall-scaleproblemsandlarge-scaleproblems,respectively. Chapter 8 discusses selective maintenance optimization for systems executing multipleconsecutivemissions.Theuncertaintiesassociatedwiththetimeduration of each future mission and the working time of each component in each future missionareaddressed.Theselectivemaintenanceproblemisformulatedasamax- min optimization model, and it is resolved by a customized simulated annealing- basedgeneticalgorithm. Chapter 9 introduces a dynamic selective maintenance for multi-state systems operatingmultipleconsecutivemissions.Theresultingsequentialdecisionproblem isformulatedasaMarkovdecisionprocesswithamixedinteger-discrete-continuous statespace.Adeepreinforcementlearningmethodiscustomizedbasedontheactor- criticframework,andapostprocessisutilizedtosearchfortheoptimalmaintenance actionsinaconstrainedlarge-scaleactionspace. The target audience of this book is undergraduate and graduate students, relia- bility practitioners, and researchers. The readers should have background in basic probabilitytheory,stochasticmodels,andoptimizationalgorithms.Thebookoffers agreatmountofknowledgeandinsightsonsystemmaintenancemodellingmethods and optimization algorithms, with which readers can deal with many real-world engineeringcases. This book is a collection of materials developed in the dissertations and journal/conferencepapersofseveralformerandcurrentgraduatestudentsfromthe CenterforSystemReliabilityandSafetyattheUniversityofElectronicScienceand TechnologyofChina.Themajorityofthechaptershavebeendevelopedbasedonthe dissertationsandresearchworksofDr.TaoJiang(M.Sc.studentfrom2014–2017and Ph.D.studentfrom2017–2022),Dr.YimingChen(Ph.D.studentfrom2015–2022), Mr. Jian Gao (M.Sc. student from 2019–2022), Mr. Chujie Chen (M.Sc. student from2012–2015),andMr.QinZhang(M.Sc.studentfrom2020–2022).Thebook waseditedwiththeadditionalassistanceofDr.TangfanXiahou(Ph.D.studentfrom 2018–2022)andDr.MingangYin(Post-doctoralresearchfellowfrom2021–2023). Wewouldliketoexpressoursinceregratitudeandappreciationtoresearchersand friendswhohavediscussedwiththeconceptsandmodelsofthisbook,orhaveco- authoredwithusonsometopicsofthisbook.Tonameafew,Prof.MingJ.Zuoat UniversityofAlberta,Prof.WeiChenatNorthwesternUniversity,Prof.MinXieat CityUniversityofHongKong,Prof.LirongCuiatQingdaoUniversity,Prof.Liudong XingatUniversityofMassachusetts-Dartmouth,Dr.GregoryLevitinatIsraelElec- tricCorporation,Prof.Yi-KueiLinatTaiwanYangMingChiaoTung,Prof.Tongdan Jin at Texas State University, Prof. Haitao Liao at University of Arkansas, Prof. Zhisheng Ye at National University of Singapore, Prof. Zhiguo Zeng at Centrale- Supélec—UniversitéParis-Saclay,Prof.YishaXiangatTexasTechUniversity,Prof. YuchangMoatHuaqiaoUniversity,andProf.HuiXiaoatSouthwesternUniversity ofFinanceandEconomics. Lastbutnotleast,wewouldliketothankProf.HoangPhamatRutgersUniversity, whogaveagreatsupporttothepublicationofthisbook.Itisalsoindeedourpleasure workingwithMr.KavithaSathishandtheSpringereditorialteam. viii Preface The research works in this book received financial support from the National Natural Science Foundation of China under contact numbers 71922006 and 71771039. Chengdu,Sichuan,China YuLiu June2022 Hong-ZhongHuang TaoJiang Contents 1 Introduction ................................................... 1 1.1 OverviewofMaintenanceOptimization ....................... 1 1.1.1 ParadigmsofMaintenanceOptimization ................ 3 1.1.2 SystemDegradationCharacteristics ..................... 5 1.1.3 MaintenanceEfficiencies .............................. 6 1.1.4 InspectionStrategies ................................. 8 1.1.5 Multi-componentSystems ............................. 9 1.1.6 MaintenanceObjectives ............................... 11 1.1.7 OptimizationAlgorithms .............................. 12 1.2 SelectiveMaintenance ...................................... 13 1.2.1 SystemModelling .................................... 14 1.2.2 EfficiencyofMaintenanceActions ..................... 17 1.2.3 ConstraintsofMaintenanceResources .................. 19 1.2.4 MissionCharacteristicsandOperatingEnvironment ....... 20 1.2.5 SolutionAlgorithms .................................. 22 References ..................................................... 23 2 BasicSelectiveMaintenanceModel .............................. 31 2.1 Introduction ............................................... 31 2.2 ProblemStatementsandModelAssumptions ................... 33 2.2.1 ProblemStatements .................................. 33 2.2.2 ModelAssumptions .................................. 33 2.3 DecisionVariables .......................................... 34 2.4 ProbabilityofaSystemSuccessfullyCompletingaMission ...... 35 2.4.1 SurvivalProbabilityofaComponent .................... 35 2.4.2 TypicalLifetimeDistribution .......................... 36 2.4.3 ProbabilityofaSystemSuccessfullyCompleting theNextMission ..................................... 36 2.5 SelectiveMaintenanceModelling ............................. 38 2.5.1 ConstraintsofSelectiveMaintenanceProblems ........... 38 ix