Optimal Inspection Models with Their Applications

266 Pages·2023·3.056 MB·English

by  Kodo Ito, Toshio Nakagawa

Springer Series in Reliability Engineering
Kodo Ito
Toshio Nakagawa
Optimal Inspection
Models with Their
Applications
Springer Series in Reliability Engineering
SeriesEditor
HoangPham,DepartmentofIndustrialandSystemsEngineering
RutgersUniversity,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].
·
Kodo Ito Toshio Nakagawa
Optimal Inspection Models
with Their Applications
KodoIto ToshioNakagawa
FacultyofEngineering,SocialSystems DepartmentofBusinessAdministration
andCivilEngineering AichiInstituteofTechnology
TottoriUniversity Toyota,Japan
Tottori,Japan
ISSN 1614-7839 ISSN 2196-999X (electronic)
SpringerSeriesinReliabilityEngineering
ISBN 978-3-031-22020-3 ISBN 978-3-031-22021-0 (eBook)
https://doi.org/10.1007/978-3-031-22021-0
©SpringerNatureSwitzerlandAG2023
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Preface
Inspectionsareneededgreatlyforeverythingwithhighreliability.Today,hard-time
maintenances rarely apply to new products to avoid high operation cost. On the
otherhand,conditionmonitoringmaintenancesarewidelyappliedtomostsystems,
andtheirsystemstatuscanbejudgedfrominspectionresultsandminimumneces-
sarymaintenancescanbeperformed.Mostpeopleknowstheimportanceofinspec-
tions, however, we do not feel its necessary on daily life because relaibilities of
productsaresohigh.Occasionalcatastrophessuchastunnelcollapseaccidentand
reactorpipedeteriorationruptureaccident,tellustheimportanceofinspectionfor
oursocialinfrastructures.Reliabilitiesofvariousdevicesaroundushaveimproved,
however,systemswithhighreliabilitystillcannotsatisfytheexpectationsofsociety.
When a space rocket is launched, inspections before launching are indispensable
for successful launch, but such complicated and time-consuming works should be
eliminatedwithadvancesinautomationtechnologies.
The purpose of this book is to bridge theory and practice by providing various
theories and application examples of inspection. Many books have already been
publishedconcerningtheories,sothat,principalinspectionmodelsareoutlined,and
new themes such as inspection fast, last and overtime are described in this book.
One special topic is the problem of failure detections: When failures occur, there
existtwotypesoffailures.Onecanbedetectedimmediatelyandanothercannotbe
detectedunlessinspectionisundergone.Inspectionpoliciesfortwotypesoffailures
are taken up. Another topic is the problem of hierarchical structure reliabilities,
andtheoreticalstudiesontheirreliabilitiesareimportant.Applicationexamplesof
storagesystem,phasedarrayradar,gasturbine,thermalpowerplantandairframeare
introduced.Eachsystemhasitsownuniquecharacteristicsandrequiresappropriate
modificationsforapplications.
The logical dependence of chapters is shown in Fig. 1: Chap. 1 is devoted to
explainingtheimportanceofreliabilityengineering,thegapbetweenmathematical
models and their applications, problems of inspection, and briefly reviewing the
following 9 chapters. Chapter 2 summarizes the results of past inspection models.
v
vi Preface
Fig.1 Logicaldependence
ofchapters
Chapter 3 is devoted to inspection first, last and overtime which are new models.
Chapter 4 summarizes the extension of inspection firstand lasttogeneral models.
Chapter5isdevotedtoinspectionmodelsoftwotypesoffailures.Chapter6summa-
rizes a hierarchical structure reliability. Chapters 7–10 are devoted to application
examplesofstoragesystem,phasedarrayradar,powergenerator,andairframe.
This book provides readers with inspiration for theoretical extensions based on
practicalideas.Thesystemhasvariousuniquecharacteristicsfromtheviewpointof
peopleinvolvedinitsdesignandoperation.Whenconventionalinspectionmethods
areimprovedbyautomationtechnologies,itisnecessarytoestimatequantitatively
howmuchithasimprovedcomparedtoconventionalones,andatthattime,extended
modelsthatreflectcharacteristicsofactualsystemsareneeded.
WewishtothankMr.K.D.A.TruongforChaps.6,8,10,andMr.S.Kawakami
for Chap. 3. We wish to thank all members of Nagoya Computer and Reliability
ResearchGroupfortheircooperationandvaluablediscussions.Especially,wewish
toexpressourspecialthanktoProf.S.MizutaniandProf.X.Zhaowithcooperation
ofourworks.Finally,IwouldliketoexpressoursincereappreciationtoProf.Hoang
Pham,RutgersUniversity,andEditorKavithaSathish,Springer-Verlag,London,for
providingustheopportunitytowritethisbook.
Tottori,Japan KodoIto
Toyota,Japan ToshioNakagawa
Contents
1 Introduction .................................................. 1
1.1 ImportanceofReliabilityEngineering ....................... 1
1.2 StochasticModelsandPracticalApplications ................ 3
1.3 TwoProblemsofInspection ............................... 5
1.4 StandardandRandomInspections .......................... 7
1.5 GeneralInspection ....................................... 8
1.6 InspectionModelwithMinimalRepair ...................... 8
1.7 HierarchicalStructureReliability ........................... 9
1.8 ApplicationExamples ..................................... 11
1.9 Problems ................................................ 16
References .................................................... 16
2 StandardInspectionModels .................................... 19
2.1 StandardInspectionPolicy ................................. 20
2.1.1 AsymptoticInspectionTimes ....................... 23
2.2 InspectionforFiniteInterval ............................... 26
2.2.1 AsymptoticInspectionTimes ....................... 29
2.3 InspectionforRandomInterval ............................. 31
2.4 ModifiedInspectionModels ............................... 34
2.4.1 ImperfectInspection .............................. 34
2.4.2 IntermittentFault ................................. 35
2.4.3 InspectionforScale ............................... 39
2.5 Problems ................................................ 42
References .................................................... 42
3 RandomInspectionModels .................................... 45
3.1 PeriodicandRandomInspections ........................... 46
3.1.1 SequentialInspection .............................. 50
3.1.2 ComparisonofPeriodicandRandomInspections ...... 52
3.2 RandomInspection ....................................... 55
vii
viii Contents
3.3 InspectionFirstandLast .................................. 58
3.3.1 InspectionFirst ................................... 58
3.3.2 InspectionLast ................................... 61
3.3.3 ComparisonofInspectionFirstandLast ............. 63
3.4 InspectionOvertime ...................................... 65
3.4.1 ComparisonsofPeriodicInspectionandInspection
Overtime ........................................ 66
3.4.2 ComparisonsofInspectionOvertimewithFirst
andLast ......................................... 67
3.5 Problems ................................................ 69
References .................................................... 69
4 GeneralInspectionModels ..................................... 71
4.1 InspectionFirstandLast .................................. 71
4.1.1 InspectionFirst ................................... 72
4.1.2 InspectionLast ................................... 73
4.2 GeneralInspectionModels ................................ 75
4.2.1 InspectionFirst ................................... 75
4.2.2 InspectionLast ................................... 76
4.3 InspectionModelswithThreeVariables ..................... 79
4.3.1 InspectionFirst,LastandMiddle ................... 79
4.3.2 ComparisonsofInspectionFirst,LastandMiddle ..... 82
4.4 ModifiedInspectionModels ............................... 84
4.4.1 ModifiedInspectionFirst .......................... 84
4.4.2 ModifiedInspectionLast ........................... 86
4.4.3 ComparisonsofModifiedInspectionFirstandLast .... 88
4.5 Problems ................................................ 89
References .................................................... 89
5 InspectionModelswithMinimalRepair ......................... 91
5.1 InspectionwithTwoFailures ............................... 92
5.1.1 PeriodicInspection ................................ 93
5.1.2 SequentialInspection .............................. 94
5.2 ModifiedInspectionModel ................................ 95
5.2.1 PeriodicInspection ................................ 96
5.2.2 SequentialInspection .............................. 98
5.3 InspectionforaFiniteInterval ............................. 100
5.3.1 StandardInspection ............................... 100
5.3.2 ModifiedInspectionModel ......................... 102
5.4 Problems ................................................ 105
References .................................................... 105
Contents ix
6 HierarchicalStructureReliability ............................... 107
6.1 BasicSystem ............................................ 109
6.1.1 n-UnitParallelSystem ............................ 109
6.1.2 n-UnitSeriesSystem .............................. 110
6.1.3 k-Out-of-nSystem ................................ 112
6.2 Random K-Out-of-nSystem ............................... 114
6.2.1 Series-ParallelSystem ............................. 115
6.2.2 Parallel-SeriesSystem ............................. 117
6.2.3 Consecutive K-Out-of-5:F System .................. 119
6.3 ComparisonofSeries-ParallelandParallel-SeriesSystems ..... 122
6.3.1 ReliabilityProperties .............................. 122
6.3.2 ReplacementTime ................................ 123
6.3.3 InspectionTime .................................. 125
6.4 Problems ................................................ 127
References .................................................... 128
7 ApplicationExamplesofStorageSystem ........................ 129
7.1 BasicInspectionModel ................................... 130
7.2 ModifiedInspectionModel ................................ 134
7.3 FiniteNumberofInspections .............................. 141
7.4 DegradationatInspection ................................. 145
7.5 Problems ................................................ 153
References .................................................... 153
8 ApplicationExamplesofPhasedArrayRadar ................... 155
8.1 CostModel .............................................. 156
8.1.1 CyclicMaintenance ............................... 157
8.1.2 DelayedMaintenance ............................. 160
8.2 AvailabilityModel ....................................... 162
8.2.1 CyclicMaintenance ............................... 162
8.2.2 DelayedMaintenance ............................. 165
8.2.3 CombinedCyclicandDelayedMaintenances ......... 167
8.3 Problems ................................................ 172
References .................................................... 173
9 ApplicationExamplesofPowerGenerator ....................... 175
9.1 Self-DiagnosisPolicyforGasTurbineFADEC ............... 176
9.1.1 StandardFADECSystem .......................... 176
9.2 MaintenanceofPowerGenerator ........................... 179
9.2.1 ShockModelwithDamageLevel ................... 180
9.2.2 TwoModifiedSchockModels ...................... 185
9.2.3 ShockModelwithMulti-echelonRisks .............. 188
9.3 Problems ................................................ 194
References .................................................... 194