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ADVANCES INSYSTEM RELIABILITY
ENGINEERING
ADVANCES INSYSTEM RELIABILITY
ENGINEERING
Editedby MANGEYRAM
J.PAULODAVIM
AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1650,SanDiego,CA92101,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom © 2019ElsevierInc.Allrightsreserved.
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Notices
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CONTRIBUTORS
MohiniAgrawal
SchoolofBusiness,GalgotiasUniversity,GreaterNoida,India
AdarshAnand
DepartmentofOperationalResearch,UniversityofDelhi,NewDelhi,India
AlessandroBarbiero
DepartmentofEconomics,ManagementandQuantitativeMethods,Università degliStudi diMilano,Milan,Italy
NavneetBhatt
DepartmentofOperationalResearch,UniversityofDelhi,NewDelhi,India
F.DeCaro
DepartmentofEngineering,UniversityofSannio,Benevento,Italy
LirongCui
SchoolofManagement&Economics,BeijingInstituteofTechnology,Beijing,China
Ant ^ onioCarlosLopesdaCosta
CentrodeDesenvolvimentodaTecnologiaNuclear—CDTN,BeloHorizonte,Brazil
VanderleydeVasconcelos
CentrodeDesenvolvimentodaTecnologiaNuclear—CDTN,BeloHorizonte,Brazil
ChenFang
SchoolofManagement&Economics,BeijingInstituteofTechnology,Beijing,China
SoufianeGasmi
Optimization,ModelingandDecisionSupport(OMAD),UniversityofTunis—Tunis NationalHigherSchoolofEngineering,Tunis,Tunisia
MiroslavKvassay
DepartmentofInformatics,UniversityofZilina,Zilina,Slovakia
DongjinLee
SchoolofComputing,Informatics,andDecisionSystemsEngineering,ArizonaState University,Tempe,AZ,UnitedStatesofAmerica
PreetiMalik
DepartmentofComputerScienceandEngineering,GraphicEraDeemedtobeUniversity, Dehradun,India
MonikaManglik
DepartmentofMathematics,UniversityofPetroleum&EnergyStudies,Dehradun,India
LataNautiyal
DepartmentofComputerScienceandEngineering,GraphicEraDeemedtobeUniversity, Dehradun,India
RongPan
SchoolofComputing,Informatics,andDecisionSystemsEngineering,ArizonaState University,Tempe,AZ,UnitedStatesofAmerica
BrianA.Polin
JerusalemCollegeofTechnology,Jerusalem,Israel
LudmilaPustylnik
DepartmentofMechanicalEngineering,AfekaTel-AvivAcademicCollegeofEngineering, TelAviv,Israel
JanRabcan
DepartmentofInformatics,UniversityofZilina,Zilina,Slovakia
MangeyRam
DepartmentofMathematics,ComputerScience&Engineering,GraphicEraUniversity, Dehradun,India
AmandaLaureanoRaso
CentrodeDesenvolvimentodaTecnologiaNuclear—CDTN,BeloHorizonte,Brazil
AlexanderRotshtein
DepartmentofIndustrialEngineering,JerusalemCollegeofTechnology,Jerusalem,Israel
PatrikRusnak
DepartmentofInformatics,UniversityofZilina,Zilina,Slovakia
LuisMejiaSanchez
CumminsInc.,Columbus,IN,UnitedStatesofAmerica
WellingtonAntonioSoares
CentrodeDesenvolvimentodaTecnologiaNuclear—CDTN,BeloHorizonte,Brazil
A.Vaccaro
DepartmentofEngineering,UniversityofSannio,Benevento,Italy
D.Villacci
DepartmentofEngineering,UniversityofSannio,Benevento,Italy
SylwiaWerbinska-Wojciechowska
DepartmentofOperationandMaintenanceofLogisticSystems,TransportationSystemsand HydraulicSystems,WroclawUniversityofScienceandTechnology,Wroclaw,Poland
PetekYontay
Intel,Inc.,Chandler,AZ,UnitedStatesofAmerica
EDITORSBIOGRAPHY
Dr.MangeyRam receivedaPh.D.degree,majoringinMathematicsand minoringinComputerScience,fromG.B.PantUniversityofAgriculture andTechnology,Pantnagar,India.Hehasbeenafacultymemberforaround 10yearsandhastaughtseveralcorecoursesinpureandappliedmathematics atundergraduate,postgraduate,anddoctoratelevels.HeiscurrentlyaprofessoratGraphicEraDeemedtobeUniversity,Dehradun,India.Before joiningGraphicEra,hewasadeputymanager(probationaryofficer)with SyndicateBankforashortperiod.Heiseditor-in-chiefof InternationalJournalofMathematical,EngineeringandManagementSciences andtheguesteditor andmemberoftheeditorialboardofvariousjournals.Heisaregular reviewerforinternationaljournals,includingIEEE,Elsevier,Springer, Emerald,JohnWiley,Taylor&Francis,andmanyotherpublishers.He haspublished131researchpublicationsinIEEE,Taylor&Francis,Springer, Elsevier,Emerald,WorldScientific,andmanyothernationalandinternationaljournalsofrepute,andalsopresentedhisworksatnationalandinternationalconferences.Hisfieldsofresearcharereliabilitytheoryandapplied mathematics.HeisaseniormemberoftheIEEE,lifememberofOperationalResearchSocietyofIndia,SocietyforReliabilityEngineering,QualityandOperationsManagementinIndia,IndianSocietyofIndustrialand AppliedMathematics,memberofInternationalAssociationofEngineers inHongKong,andEmeraldLiteratiNetworkintheUK.Hehasbeena memberoftheorganizingcommitteeofanumberofinternationaland nationalconferences,seminars,andworkshops.Hehasbeenconferredwith “YoungScientistAward”bytheUttarakhandStateCouncilforScienceand Technology,Dehradun,in2009.Hehasbeenawardedthe“BestFaculty Award”in2011andrecentlyResearchExcellenceAwardin2015forhis significantcontributioninacademicsandresearchatGraphicEra.
Dr.J.PauloDavim receivedaPh.D.degreeinMechanicalEngineeringin 1997,anM.Sc.degreeinMechanicalEngineering(materialsand manufacturingprocesses)in1991,aMechanicalEngineeringdegree(5years) in1986fromtheUniversityofPorto(FEUP),theAggregatetitle(Full Habilitation)fromtheUniversityofCoimbrain2005,andaD.Sc.from LondonMetropolitanUniversityin2013.HeisEurIngbyFEANI-Brussels andseniorcharteredengineerbythePortugueseInstitutionofEngineers withanMBAandSpecialisttitleinEngineeringandIndustrialManagement. Currently,heisProfessorattheDepartmentofMechanicalEngineeringof theUniversityofAveiro,Portugal.Hehasmorethan30yearsofteaching andresearchexperienceinManufacturing,MaterialsandMechanical& IndustrialEngineeringwithspecialemphasisinMachining&Tribology. HealsohasaninterestinManagement,EngineeringEducation,andHigher EducationforSustainability.Hehasguidedlargenumbersofpostdoctorate, Ph.D.,andMastersstudentsaswellascoordinatedandparticipatedinseveral researchprojects.Hehasreceivedseveralscientificawards.Hehasworkedas evaluatorofprojectsforinternationalresearchagenciesaswellasexaminer ofPh.D.thesesformanyuniversities.Heistheeditor-in-chiefofseveral internationaljournals,guesteditorofjournals,bookeditor,bookserieseditor,andscientificadvisoryformanyinternationaljournalsandconferences. Presently,heisaneditorialboardmemberof25internationaljournalsand actsasreviewerformorethan80prestigiousWebofSciencejournals.In addition,hehasalsopublishedaseditor(andcoeditor)morethan100books andasauthor(andcoauthor)morethan10books,80bookchapters,and400 articlesinjournalsandconferences(morethan200articlesinjournals indexedinWebofSciencecorecollection/h-index45+/6000+citations andSCOPUS/h-index52+/8000+citations).
PREFACE
Advancesinmodelingandsimulationisarguablyoneofthemostmultidimensionaltopicsthatonecanfaceinsystemreliabilityengineeringtoday. Thisrapiddevelopmentalsocreatesmanyopportunitiesandchallenges forbothindustrialistsandacademics,andhascompletelychangedtheglobal designandsystemengineeringenvironment.Moremodelingtaskscannow beundertakenwithinacomputerenvironmentusingsimulationandvirtual realitytechnologies.
Throughthisbook, RecentAdvancesinSystemReliabilityEngineering, engineersandacademicianswillgaintheknowledgetohelptheminsystem reliabilityengineering.Thisbookismeantforthosewhoarepursuing reliabilityengineeringasasubjectofstudy.Thematerialisintendedfor anaudienceatthelevelofpostgraduateorseniorundergraduatestudents. That’swhysystemreliabilityengineeringisnowawell-recognizedand rapidlydevelopingbranchofengineering.
Topicsoffocusinclude:
•Delay-time-basedmaintenancemodelingfortechnicalsystems
•Probabilisticanddeterministicsafetyanalysis
•Reliability-gametheory
•Integratingreliabilitymodelsandadaptivealgorithmsforwindpower forecasting
•Time-dependentanalysisofseries-parallelmultistatesystemsusingstructurefunctionandMarkovprocesses
•Modeling-correlatedcountsinreliabilityengineering
•Statisticalinferenceofanimperfectrepairmodelwithuniformdistributedrepairdegrees
•Methodoffuzzyperfectnessinhumanreliabilityanalysis;selectionof performanceconditions
•SystemreliabilityassessmentthroughBayesiannetworkmodeling
•Multistatemultifailuressystemanalysiswithreworkingstrategyand imperfectfaultcoverage
•Softwarepatchschedulingpolicyincorporatingfunctionalsafety standards
•Toolsandtechniquesinsoftwarereliabilitymodeling
Throughthisbook,theundergraduateandpostgraduatestudentsofengineering,engineers,researchscientists,andacademicianswillgaintheknowledge
tohelpthemintheirreliabilitycourses.Thisbookismeantforthosewhotake reliabilityandsafetyasasubjectofstudy.
TheeditorsacknowledgeElsevierforthisopportunityandfortheir professionalsupport.Finally,wewouldliketothankallthechapterauthors fortheiravailabilityforthiswork.
MangeyRam
ACKNOWLEDGMENTS
TheeditorsacknowledgeElsevierandtheeditorialteamfortheiradequate andprofessionalsupportduringthepreparationofthisbook.Also,wewould liketoacknowledgeallofthechapterauthorsandreviewersfortheiravailabilityforworkonthisbookproject.
GraphicEraDeemedtoUniversity,Dehradun,India
J.PauloDavim UniversityofAveiro,Aveiro,Portugal
MangeyRam
CHAPTER1
Delay-Time-BasedMaintenance ModelingforTechnicalSystems
TheoryandPractice
SylwiaWerbinska-Wojciechowska
DepartmentofOperationandMaintenanceofLogisticSystems,TransportationSystemsandHydraulic Systems,WroclawUniversityofScienceandTechnology,Wroclaw,Poland
Abstract
Thischapterwillbeavaluableresourceforunderstandingthelatestdevelopmentsin maintenancemodelingissuesinthefieldofdelay-timeapproachimplementation.This chapterpresentstheliteraturereviewondelay-timemodelingforsingle-andmultiunit systems.Themaintenancemodelsforsingle-unitsystemsassumetwo-stageorthreestagefailureprocesses.Inthecaseofcomplexsystems,thediscussedproblemsarewith regardtomodels’ parameters,estimationissues,casestudiesanalysis,orhybridmodelingapproachimplementation.Themaintenancemodelsformultiunitsystemsexamine theknownmodelsfornonseriessystems.Acasestudyformaintenancemodelingfor multiunitsystemsbasedonadelay-timeapproachisprovided.Thedirectionsforfurther researchworkaredefined.
Keywords: Delay-timeconcept,Multiunitsystems,Literaturereview,Maintenance modeling,Optimization
Abbreviations
AIC
Akaikeinformationcriterion
BI BlockInspection
CM correctivemaintenance
DT delaytime
DTA delay-timeapproach
DTM delay-timemodels
ELECTRE eliminationandchoiceexpressingthereality
HPP homogeneousPoissonprocess
MAUT multiattributeutilitytheory
MC MonteCarlo
MLE maximumlikelihoodestimation
MRT meanrepairtime
MTBF meantimebetweenfailures
NHPP nonhomogeneousPoissonprocess
PAR proportionalagereduction
PM preventivemaintenance
PROMETHEE preferencerankingorganizationmethodforenrichmentevaluations
AdvancesinSystemReliabilityEngineering © 2019ElsevierInc. https://doi.org/10.1016/B978-0-12-815906-4.00001-4 Allrightsreserved.
ImportantNotations
c(Tin) expectedcostovereachinspectioncycle
c(Tini) expectedcostover ithinspectioncycle
C(Tin) totalcostsresultingfromchosenmaintenancepolicy
ccs clean-upcostconnectedwithcleaningupanyspillagethatmayresultina failure
cin costofinspectionactionperformance
cp costofpreventivereplacementofaunit
cr costoffailedunitreplacement
din timeofsingleinspectionactionperformance
dp thetimeofpreventivereplacementofasystem
dr timeofcorrectivereplacementofasystem(afterafailure)
E[x] expectedvalueofrandomvariable x
Ed(Tin) expecteddowntimeinaninspectioncycleoflength Tin
F(t) probabilitydistributionfunctionofsystem/unitlifetime; F(t)¼1 F(t)
Fh(h) probabilitydistributionfunctionofsystemdelaytime
fh(h) probabilitydensityfunctionofsystemdelaytime
Fhi(h) probabilitydistributionfunctionof ithelementdelaytime
fhi(h) probabilitydensityfunctionof ithelementdelaytime
Gh(t) probabilitydistributionfunctionoftheinitialtime u,whichelapsesfrom thebeginningofoperationby“asgoodasnew”elementsofasystemuntil themomentoffirstsymptomsoffailureoccurrence
gh(t) probabilitydensityfunctionoftheinitialtime u,whichelapsesfromthe beginningofoperationby“asgoodasnew”elementsofasystemuntil themomentoffirstsymptomsoffailureoccurrence
Ghi(t) probabilitydistributionfunctionofinitialtime u of ithelementinasystem
ghi(t) probabilitydensityfunctionofinitialtime u of ithelementinasystem
h delaytimeofadefect,denotingtheperiodbetweenthemomentofappearanceofthefirstsymptomsofpotentialfailureandthemomentofan object’sfailureoccurrence
ku constantrateforfault’sarrivalinatechnicalsystemforany inspectionperiod
Mcs measureofpossibleimpactofafailureofapieceofequipmentonan environment
Menv(Tin) environmentalmodelofatechnicalobject
m numberoffailuresuntilelementreplacement
n numberofelementsinasystem
nk minimumnumberofoperatingcomponentstomakeasystemfunction (performancein nk-out-of-n reliabilitystructure)
Nrin(ti–1 in, tiin) expectednumberoffailuresoverinspectioninterval(ti–1 in, tiin)
pcs probabilityofafailureresultinginaspillagerequiringcleanup pin probabilityofimperfectinspectionoccurrence
PuF(Tin) probabilityofafaultarisingasabreakdowninasystem
pw probabilitythat,duringsysteminspection,performancesymptomsof forthcomingfailures(iftheyoccurinasystem)areidentified
R(t) reliabilityfunctionofasystem
RTin(t) componentreliabilityattime t
RTinic acubicapproximationofaveragereliabilityoveran ithinspection
RTiniL alinearapproximationofaveragereliabilityoveran ithinspection
rmr repaircostrate
rTin (i ) (t) reliabilityfunctionforacomponentattime t
r˙(k)
Tin(kTin) left-handderivativeofreliabilityfunctionat t ¼ kTin
tf randommomentoffailureoccurrenceinasystem
Tin timebetweeninspectionactions’performance
Tini timeof ithinspectioncycleperformance(betweentwoconsecutiveinspectionactions’performance)
TM(Tin) totalexpectedlengthofarenewalcycle
TM(Tini) expectedlengthof ithinspectioncycle
TOP randomvariabledenotingsystem’slifetime
TOP(Tin) expectedlengthofelement/system’slifetime
tu momentofthefirstsymptomsofpotentialfailureoccurrence u initialtimeofadefect
δh standarddeviationfornormaldistributionofadelaytime h
δr standarddeviationfornormaldistributionofatimetofailure
λh(t) intensityfunctionofasystemdelaytime
λu(u) randomrateforfault’sarrivalinatechnicalsystemforanyinspectionperiod
1INTRODUCTION
Manyreal-lifesystemsmaydisplaysomesymptomsofforthcomingfailure. Oneexamplemaybeaproductionprocess,whichmaystartproducing defectiveitemsaftersomerandomamountoftime.Ifthesituationisnot corrected,productqualitygraduallydeterioratestoalevelwhereitisselfevidenttoanoperatorthatthesystemhasfailed.Byinspectingtheproduct qualityatsomeintervals,theoperatormaybeabletoreducethecost incurredwiththesystemlifetime [1].Thesetypesofcomponentsmaybenefitfromaninspectionpolicywherebyacomponentisinspectedforadefect andconsequentlyreplacedatinspectiontopreventfailure [2].Recent reviewsoninspectionmaintenancemodelingissuesarepresentedintheliterature [3–9].
Thebasicinspectionmodelsareextendedbyusingatechniquecalled delay-timeanalysis(DTA),whichwasdevelopedformodelingtheconsequencesofaninspectionpolicyforanysystem [10].Thisapproachwasfirst describedandinvestigatedbyChristeretal. [10–16]
Thismaintenanceconceptisbasedontheassumptionthatbeforeasystembreaksdown,therewillbesomesignsofitsreducedperformance.The timebetweenthefirstidentificationofabnormalities(calledinitialpoint)
Initial time — during this time interval the defect cannot be visible
Delay time — during this time interval the defect can be identified by an inspection
Time point when a fault could be first identified
Time point when a component fails if no maintenance intervention during time h is conducted
andtheactualfailuretime(calledfailurepoint)iscalledadelaytimeand determinesthebestopportunitytocarryoutmaintenanceoraninspection (Fig.1).Asaresult,thedelay-timeconceptdefinesatwo-stageprocessfor three-statedsystems(beingeitherinupstate,partiallyupstate,orindownstate).Formoreinformation,theauthorrecommendsreadingWang etal. [17]
Theinspectionschemesindelay-timemodelsmaybeperiodicorbased oncondition-basedmaintenanceimplementation [18].Inthischapter,the authorfocusesonperiodicinspectionmaintenancemodelingissues.More informationaboutcondition-baseddelay-timemodelsmaybefoundin theliterature [19–25].
TheinterestinDTmodelingissueshasincreasedsignificantlyinrecent years.Literaturereviews,inwhichdelay-timemodelsareinvestigatedalong withotherpreventivemaintenancemodels,aregiveninseveralstudies [26–32].Thestatesofartworks,dedicatedtoDTmodeling,weremostly developedinthe1990s.Oneofthefirstliteraturereviewswasgivenby Christeretal. [19],wheretheauthorsdiscussedabasicDTmodelfora single-unitcasetakingintoaccountmodelparametersestimationproblems. Later,thestateofartwasupdatedinChristeretal. [33].Inthiswork,mathematicalmethodsforupdatingdelay-timemodelsofindustrialinspection practiceareproposed.Theypresentedalineardelay-timeupdatemethod andmodelparametervariation.Moreover,theauthorsalsoprovideacombinationofthesemethodsinthemaintenanceareaanddefinesthecriteriafor choosinganupdatingmethod.
Christerlaterpresentedabasicdelay-timemodel [34] anddiscussedthe maindevelopmentdirections,includingperfect/nonperfectinspection
Fig.1 Time-delay-modelingconcept.
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