Table Of ContentSpringer Series in Reliability Engineering
Yu Liu
Hong-Zhong Huang
Tao Jiang
Selective
Maintenance
Modelling and
Optimization
Basic Methods and Some Recent
Advances
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· ·
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
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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
