book-Effects Analysis and Reliability Modeling of Complex Production Systems

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EffectsAnalysisandReliabilityModeling8ofComplexProductionSystemsContents8.8.4SNCRPlant............................2808.8.5SNCRPlant.ReliabilityPrediction8.1IntroductiontoFailureModesAnalysisandEvaluationModel...................281andReliabilityEvaluation.....................2208.8.6QualitativeFTAEvaluation...............2838.8.7NOxEmissions:QuantitativeFTAEvaluation2878.2FailureModesandEffectsAnalysis............2208.8.8CriticalityAnalysis......................2928.2.1ProductAnalysis........................2218.8.9SparePartsAvailability,What-IfAnalysis..2958.2.2FailureMode,Effects,andCausesAnalysis.2228.8.10SystemModificationsforENFReduction8.2.3RiskEvaluation.........................222andEffectsAnalysis.....................3008.2.4CorrectiveActionPlanning...............2258.2.5FMEAConcludingRemarks..............2298.9MarkovAnalysisandTime-DependentComponents/Systems.........................3018.3FailureMode,Effects,andCriticalityAnalysis..2298.9.1RedundantParallelSystems..............3028.3.1QualitativeFMECA.....................2318.9.2ParallelSystemwithRepairableComponents3048.3.2QuantitativeFMECA....................2318.9.3StandbyParallelSystems.................3068.3.3NumericalExamples....................2328.10CommonModeFailuresandCommonCauses...3098.4IntroductiontoFaultTreeAnalysis.............2368.10.1UnavailabilityofaSystemSubjecttoCommonCauses.....................3108.5QualitativeFTA..............................2398.10.2NumericalExample,DependentEvent.....3118.5.1FaultTreeConstructionGuidelines........2398.5.2NumericalExample1.FaultTreeConstruction...........................240Givenacomplexsystemmadeofthousandsofparts8.5.3BooleanAlgebraandApplicationtoFTA...241andcomponents,suchasanAirbusA380,aflexible8.5.4QualitativeFTA:ANumericalExample....242manufacturingsystem,anitemofhealth-careequip-8.6QuantitativeFTA............................244ment(e.g.,aradiationmachine,acardiograph),apar-8.6.1QuantitativeFTA,NumericalExample1....248ticleaccelerator,etc.,thereareseveralmodesinwhich8.6.2QuantitativeFTA,NumericalExample2....2528.6.3NumericalExample.QuantitativeAnalysisthesystemdoesnotfunctionproperly,i.e.,inaccor-inthePresenceofaMixofStatisticaldancewithspecifications.ThefirstproblemistheDistributions...........................254identificationofallthesemodes,eventherarestand8.7Application1–FTA..........................263mosthiddenones,especiallyifthesafetyofpeople8.7.1FaultTreeConstruction..................264andtheenvironmentcouldbecompromised.Thesec-8.7.2QualitativeFTAandStandards-Basedondproblemistheidentificationoftheminimalcondi-ReliabilityPrediction....................266tionswhichcanbringasystemintooneofitspossible8.7.3QuantitativeFTA.......................269statesofnotfunction(i.e.,failures).8.8Application2–FTAinaWastetoEnergySystem277Whataboutthenumberoffailureevents,thedown-8.8.1IntroductiontoWasteTreatment...........277time,theuptime,andtheavailabilityofacomplexsys-8.8.2Casestudy.............................2788.8.3EmissionsandExternalities:temgivenaperiodoftimeT?Howcantheperfor-LiteratureReview.......................279manceofasystembeimproved?Howcantheexter-R.Manzini,A.Regattieri,H.Pham,E.Ferrari,MaintenanceforIndustrialSystems219©Springer2010 2208EffectsAnalysisandReliabilityModelingofComplexProductionSystemsnalitiesgeneratedbyapieceofequipmentbereducedandtoidentifyandcarrythecorrespondentcorrectiveforagivenreliabilitysystemconfiguration?actionsout.ThefinalgoalistoanticipateproblemsAverycriticalproblemdealswiththetreatmentandminimizetheiroccurrenceandimpact.Practically,ofdependencyamongfailureandrepaireventsforthetargetistoprioritizethefailuremodes(productorthebasiccomponentsofthesystemunderinvestiga-process)byanindexusuallycalledriskprioritynum-tion.TheMarkovchaintechniquecaneffectivelysup-ber(RPN)whichisveryusefulindesigningactivitiesportthemodelingactivityofsuchaproductionsys-toreducethecriticalities.FMEAsareoftenreferredtotem.bytype,suchasdesignFMEA(DFMEA)andprocessThemodelsandmethodsproposedandexemplifiedFMEA(PFMEA).inthischapterwillsupporttheintroductionofcost-DFMEAisfocusedontheproduct,thefailurebasedoptimizationmodelsforplanningandexecutingmodesandtheircausesbeingrelatedtoproductfunc-themaintenanceactionsandthesparepartsfulfillmenttionsandcomponents.Theprimaryobjectiveistoun-andmanagement,asproperlydiscussedinthefollow-coverthepotentialfailuresassociatedwiththeproductingchapters.thatcouldcausemalfunctions,safetyhazardsfortheuser,orshortenedproductlife.IdeallytheDFMEAshouldbeconductedthrough-8.1IntroductiontoFailureModesouttheentireproductdesignprocess,fromthepre-liminarydesignuntiltheproductgoesintoproduction,AnalysisandReliabilityEvaluationwithaniterativeprocedure.PFMEAexamineshowfailuresinmanufacturingTheobjectiveofthischapteristheintroductiontoandassemblyprocessescanaffectoperationandqual-modelsandmethodssupportingtheproductionsystemityofaproductorservice.PFMEAindicateswhatcandesignerandthesafetyand/ormaintenancemanagerbedonetopreventpotentialprocessfailurespriortotoidentifyhowsubsystemsandcomponentscouldfailthefirstproductionrun.IdeallythePFMEAshouldandwhatarethecorrespondingeffectsonthewholebeconductedthroughouttheprocessdesignphase.system,andtoquantifythereliabilityparametersforOverall,FMEAisintendedtobeadynamicandit-complexsystems.Asystemiscomplexwhenitiserativeprocesswherepractitionersreviewandupdatemadeofphysicalandlogicalcombinationsofseveraltheanalysisasnewinformationbecomesavailable,primarycomponents,alotofbasicitemswhosefail-correctiveactionsareimplemented,designphasesureandrepairbehaviorsareknownintermsofrelia-progress,etc.bilityperformanceindexes,e.g.,failurerate,expectedFMEArequiresdifferentskills;hence,itisabso-numberoffailures(ENF),andthemeantimetore-lutelynecessarytobuildanFMEAgroupusuallyorga-pair(MTTR).Thischapterisorganizedasfollows:nizedandconductedbyaFMEAprocessowner.Thisfirstlysomemodelsandtoolsi.e.,failuremodesandgroupmayincluderepresentativesfromthefollow-effectsanalysis(FMEA)andfailuremode,effects,andingareas:productdesign,testing,materials,suppli-criticalityanalysis(FMECA)fortheidentificationofers/OEM,manufacturingandassembling,quality,andfailuremodesandcausesareillustratedandexempli-fieldservice.Theprojectleaderplaysafundamentalfied;afterwardsfaulttreeanalysis(FTA)isintroducedroleindefiningtherulesandtheorganizationofwork.andappliedtoseveralsignificantexamples;and,fi-FMEAcanrepresentaverypowerfulapproachbutnally,Markovchainmodelingisillustratedandap-incompliancewithrulesandpersonnelcommitment,plied.otherwiseFMEAisonlyatime-consumingactivity.Thereareseveralguidelinesandstandardsforthere-quirementsofFMEAaswellastherecommendedre-8.2FailureModesandEffectsAnalysisportingformat.Someofthemainpublishedstandardsforthistypeofanalysisinclude:FMEAisasystematicinductivetechniquedesignedtoidentifythepotentialfailuremodesforaproductorMIL-STD-1629A;aprocess,toassesstheriskassociatedwiththosefail-J1739fromtheSocietyofAutomotiveEngineersuremodes,toranktheissuesintermsofimportance,fortheautomotiveindustry; 8.2FailureModesandEffectsAnalysis221AIAGFMEA-3fromtheAutomotiveIndustryAc-lifeapplicationdealingwithafundamentalpartoftionGroupfortheautomotiveindustry;adrinkvendingmachine:thedistributionvalvesys-ARP5580fromtheSocietyofAutomotiveEngi-tem.Theseautomaticmachinesforthepreparationofneersfornonautomotiveapplications;variousdrinksarenormallyequippedwithamultiwayIEC812fromtheInternationalElectrotechnicalvalveusedforsupplyingwaterorsteamtodifferentCommission;collectingvessels,accordingtothedrinkrequired.TheBS5760fromtheBritishStandardsInstitution.multiwayvalveisexposedtoconsiderablestressesduetotemperaturesandpressures,andusuallyitsbehaviorInaddition,manyindustriesandcompanieshavede-cansignificantlyinfluencethetotalreliabilityofthevelopedtheirownprocedurestomeetthespecificre-machine(Fig.8.1).quirementsoftheirproducts/processes.Thestandardsareslightlydifferent,butthecoreoftheFMEAprocedureisthesame:8.2.1ProductAnalysis1.FMEAgroupformationandrulesharing;2.productorprocessanalysis;3.FMECA;TheFMEAteammustanalyzethemachine(ingen-4.riskevaluation;eral,thesystem)withthegoaltodefinethesys-5.correctiveactionplanning.temstructurehavingitssubsystemsandcomponentsplacedatdifferenthierarchicallevels.Thisstructure,Inthefollowingpages,theDFMEAprocedure(MIL-usuallyinatop-downform,representsaveryusefulSTD-1629Astandard)isdetailedbymeansofareal-permanentreferencewhenthesystemisverycom-DistributionvalvesubsystemSubsystem1SwitchADistributionValveactuatorvalvesubsystemDrinkvendingDischargepipemachineSubsystem3………..Subsystem4………..Fig.8.1Distributionvalvesubsystem,drinkvendingmachine 2228EffectsAnalysisandReliabilityModelingofComplexProductionSystemsplex.Thissubsectionarrangementisusuallygener-Eachfailuremodecanhavedifferentcausesasre-atedaccordingtothedifferentfunctionsperformedbyportedincolumn8oftheFMEAworksheet.Consid-subsystems,suchassupplyelectricalenergy,storageeringoxidationasafailuremodeforswitchA,theenddata,andsoundrecording.Normallyeachsubsystemeffectisadifficultsupplyofbeverageandthecausesofperformsasinglefunction.Inthisphasetheanalysisoxidationcanbealossofwaterandsteamandaprob-canusuallyrequirealotofinformation,suchasde-lemwithgaskets(tearandwear).signdrawings,descriptionandoperationdocumenta-SeveralFMEAstyles(e.g.,MIL-STD-1629A)tion,andsupplierinformation.potentiallyprovideafailuredetectionmethodandIntherealcasediscussed,thesystemhasseveralacompensatingprovisionsaction(FMEAworksheet,subsystems,butthefocusisonthedistributionvalvecolumns10and11).Thissupplementaryinformationsubsystem(itemcode1100).Itscriticalcomponentsisveryusefulwhencorrectiveactionsareinvestigatedareanelectricalswitch(switchA),thevalveactua-andimplemented.tor,andthedischargepipe:itisveryimportantinthisphasetoconcentratetheanalysisonasmallgroupofcomponentshavingastrongimpactonreliability.Machineshavehundredsorthousandsofitems,and8.2.3RiskEvaluationathoroughinvestigationisnotapplicable.ThecoretaskoftheFMEAistheevaluationofrisksassociatedwiththepotentialproblemsidentifiedthroughthefailuremodesidentificationandanalysis.8.2.2FailureMode,Effects,andCausesThepurposeofFMEAistotakeactionsinordertoAnalysiseliminateorreducefailures,startingwiththehighest-priorityones.Itmaybeusedtoevaluateriskmanage-mentprioritiesformitigatingknownthreatvulnerabil-Failuresmaypotentiallyoccurforeachsubsystemorities.FMEAhelpstoselectsomeremedialactionsbyfunction,resultinginseveraleffectssuchaslossofreducingthecumulativeimpactsoflife-cycleconse-production,noentranceofpeople,andabsenceofquencesresultingfromasystemfailure.lighting.Usuallyeachfailure,orfailuremode,canTheriskofeachfailureiscalledriskprioritynum-haveseveralcauses.ber(RPN)anditisexpressedbytheproductofsever-AbasicstepoftheFMEAprocedureisthedefi-ity(S),occurrence(O),anddetection(D).nitionofthesequenceoffailuremodes,effects,andForagenericcauseoffailurei,causes.Typicallydataarearrangedintoastructuredstandardworksheetorahierarchicaldiagram,asre-RPNiDSiOiDi:(8.1)portedinFigs.8.2and8.3,respectively(distributionvalvesubsystemdrinkvendingmachineexample).Severity(Si)istheamountofharmordamagetheSwitchA(item1100.1),whosemainfunctionistofailureeffectmaycausetopeopleorequipment.Thisallowthedistributionvalvetosupplythebeverage,parameterisratedfollowingaqualitativescale.Fromhasthreeprincipalfailuremodes:oxidation,mechan-theMIL-STD-1629Astandardthecorrespondentmag-icalbreak,andpindisconnectionfromtheconnector.nitudesrangefrom1to4asexpressedinTable8.1;Columns1and2intheworksheetshowninFig.8.2thisrateisreportedincolumn7oftheFMEAwork-show,respectively,theitemanditscorrespondentfail-sheetinFig.8.2.uremodes.Occurrence(Oi)istheratestatingthelikelihoodofSpeakingabouteffects,onecandistinguishamongoccurrenceforeachcauseoffailure.Theprobabilitydifferentcategories:alocaleffect(FMEAworksheet,ofoccurrencerangesfromextremelyunlikelytofre-column3),i.e.,strictlyconcerningtheitemana-quent.Alsointhiscasetheevaluationisqualitativelyzed,anext-higher-leveleffect(FMEAworksheet,butitisclearlylinkedtothefailurerate.Thisconceptcolumn4),i.e.,involvingitemssetonthenext-higherwillbestressedlateronwhenwespeakaboutcritical-assemblylevel,andanendeffect(FMEAworksheet,ityanalysis.FromtheMIL-STD-1629Astandardthecolumn5),themostimportantintheFMEA.classificationofoccurrenceisexpressedinTable8.2. 8.2FailureModesandEffectsAnalysis223PNR(13)Di-Det(12)(11)rovisionsompensatingPC)0(1DetectionMethodFailure)Oi-Occ9(delvalveliaaftbysotttnpeccce)losspumppumpsirrerermtpump8(ausesdfocroora(residuals)Conicnicniertwaterfromfromincorrecteskliafromincorrecttearwearuroylylicstressorlawbmbmfrincorrectramsseeeocclusioneroerssssupsteamgasketsgasketswvibrationsvibrationsassemblynpaaspipethermalvibrationsassemblysupply)Si-Sev7(eeggararevegevearebebf)ffectsfoveo6(EylbylpbeveragebeveragefpndEpofofoylpusupstlpltulosslossuciusciffffisupplysupplyoidnonondwaterwater)igher(5HevelLextN)ffects4(EocalL)3(Mission/OperationalModehasePnconnectorwochassisriskprioritynumber,distributionvalvesubsystem)r2(ModesclfromafrombreaknrretacutRPNFailurenietnoifsttoearkdiasxeaomechanicaldisconnectionwgdisconnectionsuperficialpipesystemlyAp)actuatorp1(/FunctionussupplyFMEAworksheet.sswitch-valve-egdischarge-Itempermissiona.1.2re.3cleanve1100supply1100b1100keepFig.8.2 2248EffectsAnalysisandReliabilityModelingofComplexProductionSystems1.1.1.1-steamorwaterlossbyvalve(jointloosening)1.1-oxidation1.1.1-nosupplyof1.1.1.2-gasketstearbeverage1.1.1.3-gasketswear1.2.1.1-wear1100.1-switchA1.2-mechanicalbreak1.2.1-nosupplyofbeverage1.2.1.2-vibrationsfrompump1.3.1.1-vibrationsfrompump1.3-disconnectionfrom1.3.1-nosupplyofconnectorbeverage1.3.1.2-assemblyincorrect1.1.1.1-normaluseofdisposal1.1.1.2-presswork1.1-wearofinternal1.1.1-nosupplyof1100-distributionvalveincorrectcrownbeverage1.1.1.3-assemblyincorrect1100.2-valveactuator1.2.1.1-assemblyincorrect1.2-gasketstear1.2.1-nosupplyofbeverage1.2.1.2-superficialtreatmentfailed1.1.1.1-pipeocclusion(residuals)1.1-disconnectionfrom1.1.1-waterloss1100.3-dischargepipe1.1.1.2-thermalstresschassis1.1.1.3-vibrationsfrompumpFig.8.3FMEAdiagram,distributionvalvesubsystemIntheFMEAworksheet(Fig.8.2)thisrateispostedinmanualsaddressingFMEA,orthestandardsadoptedcolumn9.bymajorindustriesprovideseveralratingscales,withDetection(Di/isthelikelihoodthatthefailurethepossibilityfortheteamtocreate/modifytheminwillbedetected.Thisparameterintroducesanimpor-ordertofitthespecificanalysis.tantpointofview,oftennotconsideredintheclassicThebasicconceptremainstoratethefailureriskbymagnitude-effectanalysis.Thedifficultyoffailurede-RPN.HighvaluesofRPNrevealcriticalcausesoffail-tectioncanrepresentasignificantproblemincreasingure.ThesumoftheRPNiforalowerlevel(i.e.,sub-thetotalcriticalityofacauseofafailurecharacterizedsystem,subassembly,components)istheoverallRPNbyaverageseverityandoccurrence.Table8.3showsfortheupperlevel,uptotheentireproduct.thecriteriaadoptedfordetectionevaluationandtheConsideringtothedistributionvalveexample,andcorrespondentqualitativenumericalranking.ColumninparticulartoswitchAanditsfirstfailuremode(i.e.,12oftheFMEAworksheetcollectsthisratio.oxidation),thecorrespondentseveritylevelisneartheThescalesadoptedbyMIL-STD-1629Aandpre-maximum(rate3critical)becauseinthisconditionsentedhereareonlyamodel:varioustextbooksandthecustomerhassignificantdifficultiestoobtainthe 8.2FailureModesandEffectsAnalysis225Table8.1Severityratingscale(MIL-STD-1629A)RateDescriptionCriteria1CategoryIVminorAfailurenotseriousenoughtocauseinjury,propertydamage,orsystemdamage,butwhichwillresultinunscheduledmaintenanceorrepair2CategoryIIImarginalAfailurewhichmaycauseminorinjury,minorpropertydamage,orminorsystemdamagewhichwillresultindelayorlossofavailabilityormissiondegradation3CategoryIIcriticalAfailurewhichmaycausesevereinjury,majorpropertydamage,ormajorsystemdamagewhichwillresultinmissionloss4CategoryIcatastrophicAfailurewhichmaycausedeathorweaponsystemloss(i.e.,aircraft,tank,missile,ship,etc.)Table8.2Occurrenceratingscale(MIL-STD-1629A)RateDescriptionCriteria1LevelEextremelyunlikelyProbabilityofoccurrenceisessentiallyzeroduringtheitemoperatingtimeinterval.Asinglefailuremodeprobabilityofoccurrenceislessthan0.001oftheoverallprobabilityoffailureduringtheitemoperatingtime2LevelDremoteAnunlikelyprobabilityofoccurrenceduringtheitemoperatingtimeinterval.Asinglefailuremodeprobabilityofoccurrenceismorethan0.001butlessthan0.01oftheoverallprobabilityoffailureduringtheitemoperatingtime3LevelCoccasionalAnoccasionalprobabilityofoccurrenceduringtheitemoperatingtimeinterval.Asinglefailuremodeprobabilityofoccurrenceismorethan0.01butlessthan0.10oftheoverallprobabilityoffailureduringtheitemoperatingtime4LevelBreasonablyprobableAmoderateprobabilityofoccurrenceduringtheitemoperatingtimeinterval.Asinglefailuremodeprobabilityofoccurrenceismorethan0.10butlessthan0.20oftheoverallprobabilityoffailureduringtheitemoperatingtime5LevelAfrequentAhighprobabilityofoccurrenceduringtheitemoperatingtimeinterval.Asinglefailuremodeprobabilitygreaterthan0.20oftheoverallprobabilityoffailureduringtheitemoperatingtimeintervalTable8.3Detectionratingscale(MIL-STD-1629A)RateDescriptionCriteria1AlmostcertainCurrentcontrolsalmostalwayswilldetectthefailure.Reliabledetectioncontrolsareknownandusedinsimilarprocesses2VeryhighVeryhighlikelihoodcurrentcontrolswilldetectthefailure3HighGoodlikelihoodcurrentcontrolswilldetectthefailure4ModeratelyhighModeratelyhighlikelihoodcurrentcontrolswilldetectthefailure5MediumMediumlikelihoodcurrentcontrolswilldetectthefailure6LowLowlikelihoodcurrentcontrolswilldetectthefailure7SlightSlightlikelihoodcurrentcontrolswilldetectthefailure8VeryslightVeryslightlikelihoodcurrentcontrolswilldetectthefailure9RemoteRemotelikelihoodcurrentcontrolswilldetectthefailure10AlmostimpossibleNoknowncontrolsavailabletodetectthefailuredrink.Thethreecausesoffailuredetectedhaveanav-8.2.4CorrectiveActionPlanningeragevalueofprobabilityofoccurrence,butthehigherlevelofprobabilityisassignedtothewearofgasketsTheriskevaluationisthestartingpointforthedesign(ranked4intheoccurrencescale),acauselinkedtoandtheexecutionofcorrectiveactions.Thegoalofthenaturaluseofthemachine.FMEAistoanticipatepotentialproblemsandtoper-Alltheabove-mentionedcausesarerelativelyeasyformactivitiesinordertoreduceand/orremoverisks.todetect;thewearofgasketsisthehigherlevelofcrit-RPNpermitstheinterventionstobeprioritized.icality(ranked5medium)inthiscasetoo.ItisworthrememberingthatRPNratingsarere-Theresultoftheiterationofthisapproachtolatedtoaspecificanalysis.AcrossovercomparisonofothercomponentsistheriskevaluationsummarizedsomeRPNvaluesamongdifferentapplications(prod-inFig.8.4.uctorprocess)isinfactmeaningless. 2268EffectsAnalysisandReliabilityModelingofComplexProductionSystems)PNR83860446884681(62656685)2Di-Det10440101528979655()11(rovisionsompensatingPC)01(DetectionMethodFailure)Oi-Occ9(33212103valve4322232failed4by2422143431)18(loss4pumppumpdisposal14(residuals)2pump34auses3Cfromfromincorrectofincorrectincorrectincorrecttreatmentfromincorrectwatertearwearusestressincorrectorrocclusionaesteamgasketsgasketswvibrationsvibrationsassemblynormalpressworkassemblyassemblysuperficialpipethermalvibrationsassemblysupply)Si-Sev7(33egar444evebfbeverage)6(ffectsoofEylbeveragebeveragebeveragendppof22Euofofssupplytllosslossuciffsupplysupplysupplyidnononodifficultwaterwater)igher5(HevelLextN)ffects4(EocalL)3(Mission/OperationalModehasePconnectorchassis)2(ModescrownfromfrombreakcutFailureninternalteariotofadioxmechanicaldisconnectionweargasketsdisconnectionsuperficialpipesystemA)actuator1(supplyRiskevaluationfordistributionvalvesystem(MIL-STD-1629Astandard)/Functionsupplyswitch-valve-discharge-Itempermission.1.2.3clean1100supply1100beverages1100keepFig.8.4 8.2FailureModesandEffectsAnalysis227TheRPNanalysisrecommendscorrectiveactionsdefinitionofhighandlowlevels.Thematrixgivesfocusedonreducingasinglefactorormorethanoneapromptideaaboutthecriticalityofthecausesoffail-factor.UsuallytheFMEAteamprovidesanewlevelofure.RPN,theso-calledrevisedRPN,tobecomparedwithTheanalysiscanbecompletedbyotherstudiestheinitialRPN.suchasthecausesbyoccurrence(Fig.8.7)andtheTheFMEAteammustspendtimeanalyzingeffectsclassification(Fig.8.8).theRPNiconfiguration.TypicalinstrumentsareInconclusion,theanalysisofRPNiallowsonetotheParetochartofRPNi,theoccurrence–severityprioritizesomecorrectiveactionsusuallylinkedtothematrix,thecausesbyoccurrenceanalysis,andtheproductdesign.effectsanalysis.Applicationofthesetoolswithref-Forthedistributionvalvecase,theFMEAteamde-erencetothedistributionvalveexampleisshownincidedtoimprovethefirstfourcriticalitiessortedbytheFigs.8.58.8.ParetoanalysisofRPN.ThemostcriticalcauseoffailurehasRPNiD108,Asmentioned,themorecriticalproblemsdealwithwhichcorrespondstoSiD4,OiD3,andDiD9thevibrationsinducedbythepumpandtheresistanceduetovibrationsfromthepumpasaresultofthedis-andtheretainingofvalvegaskets.Inparticular,severalconnectionofswitchAfromtheconnector.correctiveactionsaredefined:OtherscriticalissuesengageswitchAandpumpvibrations:inparticular,amechanicalbreakispossibleArubberbumperinsertioninthefixingsystembe-(RPNiD64,SiD4,OiD2,andDiD8).tweenthepumpandthechassistoreducethevi-SwitchAhasaveryhighoccurrenceamongthebrationsinducedonothercomponents(i.e.,switchgreatestRPNvalues.ItsproblemsarefundamentallyAanddischargepipe).Theresponsibilityissharedduetopumpvibrationsandgaskets.bythemechanicaldesigndivisionandthepro-Theoccurrenceseveritymatrixisanotherinterest-curementdivision.Theactivitystartson1Novem-ingtoolfortheriskassessment.Theusercansetthreeber2008andtheduedateisfixedat1June2009.differentregionsonthetwo-dimensionalspacesever-Anewswitchdesignwithmechanicalredundancyity(onx-axes)andoccurrence(ony-axes)bythetoincreasetheavailabilityofdisposal.Therespon-sibilityissharedbythemechanicaldesigndivisionandtheprocurementdivision.TheactivitystartsCausesRankedbyInitialRPNon1November2008andtheduedateisfixedat1201June2009.108Anewconnectionsystemtoavoiddisconnectionofelectricalpins.Thequalityassurancedivisionmust100guaranteethestudyandtheprocurementdivisionmustsearchforaneweffectivesupplier.Thestart-80ingdateis1November2008andthenewsystemmustworkbefore1April2009.64Anewmaterialornewtreatmentforgaskets.Atthe60606056sametimeanewprofileisneededforthegasket54CauseRPN4848toavoidtearing.Themechanicaldesigndivision40mustdevelopthenewprofile,andthequalityassur-403632ancedivisionexecutestheexperimentstovalidatenewmaterialsandanewprofile.Theprocurement24201818divisionmustsearchfornewsuppliers.Theactiv-161610itystartson1November2008andtheduedateis1April2009.01234567891011121314151617CauseThecorrectiveactionsprovidedhaveasignificantpo-Fig.8.5ParetoanalysisofinitialRPN,distributionvalvesub-tentialeffectonthecriticalityofthedistributionvalve,systemasconfirmedbythe50%decreaseofthecriticality 2288EffectsAnalysisandReliabilityModelingofComplexProductionSystemsOccurrence/SeverityMatrix(InitialRatings)5LowPriorityLineHighPriorityLine4x2x23x2x2SeveritylimitHIGH:7LOW:3OccurrencelimitOccurrenceHIGH:6LOW:42x2x31001234SeverityHigh-prioritycauses:Normaluseofdisposal(Item:1100.2-valveactuator)Sev=4,Occ=4Assemblyincorrect(Item:1100.2-valveactuator)Sev=4,Occ=4Gasketswear(Item:1100.1-switchA)Sev=3,Occ=4Wear(Item:1100.1-switchA)Sev=4,Occ=3Vibrationsfrompump(Item:1100.1-switchA)Sev=4,Occ=3Medium-prioritycauses:Assemblyincorrect(Item:1100.3-dischargepipe)Sev=2,Occ=4Steamorwaterlossbyvalve(Item:1100.1-switchA)Sev=3,Occ=3Gasketstear(Item:1100.1-switchA)Sev=3,Occ=3Pressworkincorrect(Item:1100.2-valveactuator)Sev=4,Occ=2Vibrationsfrompump(Item:1100.1-switchA)Sev=4,Occ=2Assemblyincorrect(Item:1100.1-switchA)Sev=4,Occ=2Assemblyincorrect(Item:1100.2-valveactuator)Sev=3,Occ=2Superficialtreatmentfailed(Item:1100.2-valveactuator)Sev=3,Occ=2Pipeocclusion(residuals)(Item:1100.3-dischargepipe)Sev=2,Occ=3Thermicstress(Item:1100.3-dischargepipe)Sev=2,Occ=2Vibrationsfrompump(Item:1100.3-dischargepipe)Sev=2,Occ=4Low-prioritycauses:Supplyincorrect(Item:1100.3-dischargepipe)Sev=2,Occ=1Fig.8.6Occurrenceseveritymatrix,distributionvalvesubsystemoftheoriginalcausesatleast.TheFMEAproce-Clearly,boththeinitialRPNandtherevisedRPNduresuggestsacalculusofthenewlevelsofsever-arebasedonanestimationoftheirfactors,nomathe-ity,occurrence,anddetectionparameters(so-calledre-maticalmodels,orsomethingsimilarsupportingthesevised)andinconclusionanewrevisedRPNisavail-evaluations.Figure8.9showstheactionplanandtheable.comparisonbetweenRPNvalues. 8.3FailureMode,Effects,andCriticalityAnalysis229Fig.8.7Causesbyoccur-rence(distributionvalvesys-tem)Fig.8.8Effectsclassification(distributionvalvesystem)8.2.5FMEAConcludingRemarkstimesoverlookedbecauseofthelimitedpossibilityofexamination.Finally,itisimportanttorememberthatFMEAisawell-knownqualitativereliabilitymethod.FMEAisonlyaqualitativeprocedurebasedondif-Itisdevotedbothtotheproductandtotheprocessferentscalesofattributessuchasseverity,occurrence,analysis.anddetectionoffailures,whoseevaluationsaredepen-Itprovidesasystematicapproachrequiringalldentontheteaminvolved.Justtoovercomethislastknownorsuspectedpotentialfailurestobeconsid-criticism,FMECAwasdevelopedasanextensionofered.UsuallytheanalysisdirectlyresultsinactionstoFMEA.reducefailuresandanyhowincludesafollow-upsys-ThefundamentalfeatureofFMECAistheintro-temandreevaluationofpotentialcausesofreliabilityductionofthecriticalityfactor,whichisanefforttoproblems.Bypayingattentiontothecustomerpointevaluatethecriticalityofthecomponentsonaquanti-ofview,itpermitsatangibleimprovementofproducttativebasisinsteadofthequalitativeapproachadoptedandprocessreliability.byFMEA.SinceFMEArepresentsavalidsupporttothede-signreviewprovidedbyENISO9001andgivesimmediacytotheproblemsrevisionprocedures,it8.3FailureMode,Effects,andCriticalityshouldbeapproachedtogetherwiththedesignphaseAnalysisasawhole.Somedifficultiesareofcourserelatedtoitsapplica-FMECAdiffersfromFMEAininvestigatingthecrit-tion.Inparticular,FMEAisatime-consumingprocessicalityoffailureindetail.Thisprocesssystematicallywithverycomplextaskstakinghoursordaystocom-determinesfunctions,functionalfailures,andfailurepletetheprocess;itaccountsforeverycauseofprob-modesoftheproductionsystem,i.e.,theequipment,lemsasasingleevent,andthecombinationsofeventswithparticularattentiontotherelatedeffects,severity,arecapturedasasingleinitiatingevent.Moreover,theandfrequencyoffailureeffects.processreliesonrecruitingtherightparticipantsandAfundamentalreferencefortheFMECAisrepre-thepersonnelinvolvedmustbetruthfulaboutthere-sentedbytheMIL-STD-1629Astandard.spectiveactivities.Nevertheless,itisworthmention-Itprovidestwolevelsofcriticalityanalysis:theingsomecomplicationsduetohumanerror,some-qualitativeandthequantitativeFMECA. 2308EffectsAnalysisandReliabilityModelingofComplexProductionSystemsPNrR8632324rD898revisedOrrStion01-3230114101-4101-3101-23424et026-0040204aD9-9-9-9-9-Compleet01-20001-20001-20001-20001-200da1011111011t8-8-8-8-8-Plannedarts200200200200200yt////ilib////assurancedesigndesignassuranceassurancedesignassurancedesign....esponsaRqualitymechprocurementmechprocurementqualityprocurementqualitymechprocurementqualitymechprocurementiontnewtearwithnewtear--underunderundernewnewdescripswitchnewreveal--revealionttototestingtreatmentinsertioninsertiontestingtreatmentinsertionaciveandnewsystemredundancysystemsystemandnewsystemtgasketgasketororforbumperfixingbumperfixingforbumperfixingCorrecdevelopingmaterialprofilerubberpumpmechanicalpumpconnectiondevelopingmaterialprofilepumpPNiR86048rubber6880468rubber10644010ialtiD5686995655675iniOi321343443222324230213241441by2212434231losspumppumppumpdisposalfromfromincorrectofincorrectincorrectincorrecttreatmentfromincorrectCauseswatertearwearstressoruseincorrectocclusionsteamvalvegasketsgasketswearvibrationsvibrationsassemblynormalpressworkassemblyassemblysuperficialfailedpipe(residuals)thermalvibrationsassemblysupplyiS3444322tsofofofsupplysupplyEffeclosslossbeveragesupplysupplysupplybeverageofnobeveragenobeveragenobeverageofwaterwatercutModesEndinternalteardifficultconnectorofchassisoxidationdifficultmechanicalbreakdisconnectionfromwearcrowngasketsdisconnectionfromsuperficialiontFailurecleansupplysupplysupplysystempermissionbeverageskeepPlannedcorrectiveactionsandrevisedRPN,distributionvalvesubsystem.1A.2.3emFuncitvalvepipe1100switch1100actuator1100dischargeFig.8.9 8.3FailureMode,Effects,andCriticalityAnalysis2318.3.1QualitativeFMECAOnonehand,thesimplicityoftheapproachmakesitsuitableasapreliminaryactivityinordertodrivethequalitativeFMECA;however,ontheotherhand,ThequalitativeFMECAapproachisadirectfollow-itissometimesveryhardtoestimatethequalitativeupoftheFMEAresult.Thetargetistoassignapri-evaluationsoffactorsinasignificantway.oritytothefailuremodesandtogroupthemindiffer-entclassesofcriticalities,usuallythree,accordingtoaqualitativecriticalitymatrixincludingtheparam-etersseverityandoccurrence.Thefirstfactorcanbe8.3.2QuantitativeFMECAevaluatedbyfourdifferentlevels,fromminortocatas-trophic,asusedforFMEA(Table8.1).Inthesameway,theoccurrenceofthesecondfactorisevaluatedThisapproachisbasedonaquantitativeprocedureaccordingtoaqualitativescalerangingfromextremelyrepresentingthemostrigorousmethodcurrentlyavail-unlikelytofrequent,asinFMEA(Table8.2).able.Thefundamentalgoalisthedevelopmentofanu-Eachfailuremodeisclassifiedintothematrixde-mericalexpressionoftheitemcriticality.pendingonitsownevaluations,usuallyindicatedasConsideringanitemhavingcsignificantcompo-SiandOiforseverityandoccurrence,respectively.nents,thecorrespondentitemcriticalityisThemostcriticalfailuremodesarerevealedimmedi-cXately,sincethreeareasofcriticalities,low,medium,ICDCCi;(8.2)andstrongasinFig.8.10,areprovidedasastandard.iD1TherelativepositionofeachfailuremodewithrespectwhereCCiisthecriticalityofcomponentidefinedastothepositionofthebestandworstcategoriesgivesaqualitativeideaofitscorrespondingcriticalityXmlevel.CCiDFMCij;(8.3)ThequalitativeFMECAappliedtotheexampleofjD1thedistributionvalvesystemissummarizedbythewheremisthenumberoffailuremodesforcompo-criticalitymatrixinFig.8.11.ComparingsomefailurenentiandFMCijisthefailuremodecriticalityoffail-modes,theoxidationofswitchAcontacts,thewearuremodejforcomponenti.oftheinternalcrownofthevalveactuator,andtheme-Eachfailuremodeischaracterizedbyacriticalitychanicalbreakoftheswitchareverycritical,whilethevaluederivedfromdisconnectionofthedischargepipefromchassisfail-FMCDCU.t/RUPL;(8.4)uremodehasamediumlevelofcriticality.ijiijijLevelA-frequentLevelB-reasonablystrongprobableLevelC-mediumoccasionalOccurrenceLevelD-lowremoteLevelE-extremelyunlikelyIV-minorIII-marginalII-cricalI-catastrophicFig.8.10CriticalitymatrixandcriticalityregionsSeverity 2328EffectsAnalysisandReliabilityModelingofComplexProductionSystems(HIGH))>LevelA-frequent----------LevelB-LEVEL-disconnectionreasonably-oxidation-wearoffromchassisprobableinternalcrownLevelC--gasketstear-mechanicalPROBABILITYoccasionalbreakOCCURRENCEOFOFLevelD--disconnectionremotefromconnectorLEVELLevelE-extremely-superficialcutPROBABILITYunlikelyINCREASING(CategoryIVCategoryIIICategoryIICategoryI(LOW)-minor-marginal-critical-catastrophicSEVERITYCLASSIFICATION(INCREASINGLEVELOFSEVERITY------>)Fig.8.11Criticalitymatrix,distributionvalvesystemwheretistheoperatingtime,CU.t/istheunre-TheprobabilityoflossPListheprobabilityoftheiijliabilityofcomponentiatoperatingtimet,RUislossoffunctionattheoccurrenceoftheconsideredijtheratioofunreliabilityoffailuremodejforcompo-failuremodej.Thisvalueisoftenequalto1,becausenenti,andPLijistheprobabilityoflossoffunction,thefailuregivesrisetoacompletelossoffunctionalityduetothefailuremodejforcomponenti.ofthecomponent.AsshowninEq.8.4,foreachfailuremodethecrit-Inconclusion,thequantitativeFMECArequiresicalityistheproductofthreenumericalfactors.Theaprocedurebasedonseveralsteps:firstone,CU.t/,iscommonforallthefailuremodesidefinitionofthereliabilitystatisticaldistributionofthesamecomponent,andrepresentstheunreliabil-fordifferentcomponentsofeachitem;ityofthecomponentattheoperatingtimet,thusdefinitionofananalysisoperatingtime;disclosingabridgebetweenthequantitativeFMECAidentificationofthepartofunreliabilityassignedtoandthetheoryofreliability.Thedefinitionofthecom-eachpotentialfailuremode;ponentunreliabilityrequirestheoperatingtimeset-ratingoftheprobabilityoflossoffunctionresultingtingandtheevaluationofthetime-dependentfailurefromeachfailuremodethatmayoccur;distributionsthroughwell-knownmathematicalap-calculationofthecriticalityforeachcomponent;proaches,e.g.,Weibullandexponential,asdiscussedcalculationoftotalitemcriticalitybythesumofinChaps.5and6.previouscalculatedcriticalities.TheratioofunreliabilityRUijofthefailuremodejistheprobabilitythatthecomponentfailurewillbeThefinalresultsarenumericalevaluationsofitemcrit-duetotheconsideredfailuremodej;itisthepercent-icalitieswhichrepresentthestartingpointsforacriti-ageoffailures,amongallthefailuresallowedforthecalanalysisandforthecorrectiveactionplan.component,thatwillbecausedbythegivenmode.Itisimportanttonotethatthetotalpercentageassignedtoallmodesmustbeobviouslyequalto100%:8.3.3NumericalExamplesXmWenowpresenttwonumericalexamples.RUijD1(8.5)ConsideranitemX,composedoftwocompo-jD1nentsAandB.Theexperimentalevidencepermits 8.3FailureMode,Effects,andCriticalityAnalysis233Table8.4StatisticaldistributionofreliabilityofcomponentsATable8.5StatisticaldistributionofreliabilityofcomponentsandBofthedistributionvalvesystemf.t/Parametersf.t/ParametersComponentAExponential.t/D0:000207h1SwitchANormalD752hComponentBNormalD6:578hD321hD1:211hValveactuatorExponential.t/D0:001h1DischargepipeWeibullˇD2:766D2;463hanevaluationoftheirreliabilityperformance,summa-NowconsidertheapplicationofthedistributionrizedinTable8.4.valvesystem,thesignificantcomponentsareswitchASettingtheoperatingtimetD6;000h,thecorre-(ID1100.1),thevalveactuator(ID1100.2),andthespondentunreliabilitiesofthetwocomponentsaredischargepipe(ID1100.3).ForeachofthemthefailurestatisticaldistributionsCUADFA.6000/D0:712;aredefinedinTable8.5.CUBDFB.6000/D0:316;Theoperatingtimeissetto1;000h;foradrinkConsidercomponentAresponsibleforagenericvendingmachine,havinganaverageoperatingoffunction,namedfunctionA,andtwofailureabout4hoursperday,thistimerepresentsmoreormodes,namedfailuremodeA.1andfailureless1yearofwork,thatisthetimebetweentwomodeA.2,generating,respectively,twocausesconsequentoverhaulinterventions.Figure8.13showsnamedcauseA.1.1andcauseA.1.2andasinglethefinalresultofthequantitativeFMECAapproach.causeA.2.1.FailuremodeA.1isresponsiblefor60%TheresultsofthequantitativeFMECAhavediffer-ofthefailuresofcomponentA,thentheremainingentlevelsofdetail:thecriticalityindexcanbedefined40%isduetofailuremodeA.2.forasinglefailuremode,orforasinglecomponent,FailuremodeA.1givesrisetoacompletelossofi.e.,groupsoffailuremodes,orfinallyforasinglefunctionA,whiletheprobabilityoflossoffunctionitem,i.e.,groupsofcomponents.forfailuremodeA.2isabout90%.Thisfeatureallowsacompletetop-downanalysisFocusingonfailuremodes,fortheresearchofthemostcriticalitemsofaproduct,itsmostcriticalcomponents,andtheirrelatedfailureFMCA;1DCUARUA;1PLA;1modes.Inspiteofthis,averyeffectivecorrectiveac-D0:7120:61D0:427;tionplancanbedeveloped.Thedistributionvalvesystemhasacriticalityin-FMCA;2DCUARUA;2PLA;2dexof1.289fundamentallyduetothecriticalityofD0:7120:40:9D0:256:switchA(0.689)andofthevalveactuator(0.533).TheThenthecriticalityofcomponentAisdischargepipehasasecondaryeffectonthecriticalityoftheentireitem(Table8.6).CCADFMCA;1CFMCA;2Analyzingthecriticalityoffailuremodes,theoxi-D0:427C0:256D0:683:dationofcontacts,themechanicalbreakforswitchA,andthewearoftheinternalcrownforthevalveac-SimilarlyforcomponentBthecriticalityisCCBD0:269.Inconclusion,itemXhasacriticalitydefinedbyTable8.6Distributionvalvecriticalityandcomponentcritical-thesumofthecriticalitiesofitscomponents:itiesCriticalityICXDCCACCCBD0:683C0:269D0:952:1100distributionvalve1.289Figure8.12presentsatypicalworksheetusedforthe1100.1switchA0.689quantitativeFMECApopulatedwiththedataofthe1100.2valveactuator0.5331100.3dischargepipe0.077previousexamplereferredtoitemX. 2348EffectsAnalysisandReliabilityModelingofComplexProductionSystemsFig.8.12Quantitativefailuremode,effects,andcriticalityanalysis(FMECA)worksheet(itemXexample)Table8.7Failuremodecriticalitiesforthedistributionvalveofcriticalitiesamongdifferentitemsofaproduct,andsystemmoreovergivesprioritytothecorrectiveactionstoFailuremodesandcausesModecriticalitybetaken,rankingthefailuremodesandtherelatedWearofinternalcrown0.491causes.NormaluseofdisposalItisimportanttonotethatthisrobustnessispaidPressworkincorrectfor,ontheotherhand,intermsofthetimespentcol-AssemblyincorrectlectingdataanddevelopingthecalculusofcriticalityMechanicalbreak0.351Wearfactors.VibrationsfrompumpMoreover,thequantitativeFMECAalsorequiresOxidation0.281somesubjectiveassumptions;inparticular,theunre-SteamorwaterlossbyvalveliabilityratiooffailuremodejforcomponentiRUijGasketstearGasketswearandtheprobabilityoflossoffailuremodejforcom-Disconnectionfromchassis0.071ponentiPLijdependonpersonalevaluationsbythePipeocclusion(residuals)engineers,thetechnicians,andthepractitionerswhoThermalstresswilldeveloptheanalysis.VibrationsfrompumpDisconnectionfromconnector0.047Forthisreason,someauthorsconsiderFMEAandVibrationsfrompumpinparticularFMECAveryeffectiveinstrumentsintheAssemblyincorrectproduct/processdesignphase,butsuggesttheiruseex-Gasketstear0.042clusivelyforacomparisonamongthedifferentfail-AssemblyincorrectSuperficialtreatmentfaileduremodesor/andthecomponentsofasingleproductSuperficialcut0.006orprocess.Inthecaseofacross-checkoftheresultsAssemblyincorrectamongdifferentproductsorprocesses,thesemethodsSupplyincorrectreachtheirlimits.Anothertypicalresultofthequantitativeapproachtuatorareclearlyverycriticalmodes.Theremainingisthequantitativecriticalitymatrix.Itrepresentsahy-modeshavemarginalcriticalities.bridmatrixmixingtheseverityevaluationandthecrit-Inconclusion,theproductdesignersmustfocusicalityvalueofeachfailuremode.Aswellasthetheirattentiononthecausesofthesecriticalmodes,FMEAcriticalitymatrix,itusuallyindividuatesthreelistedinTable8.7.zonescharacterizedbydifferentlevelsofcriticality.Thecharacteristicnumericalapproachofthequan-Figure8.14showsthequantitativecriticalitymatrixtitativeFMECAallowsarobustcomparisonintermsforthedistributionvalvesystem. 8.3FailureMode,Effects,andCriticalityAnalysis235QuantitativeFMECAworksheetforthedistributionvalvesystemFig.8.13 2368EffectsAnalysisandReliabilityModelingofComplexProductionSystems(HIGH)0.491-wearofinternalcrown)>0.351-mechanicalbreakY------)Cr0.281-oxidation(RITICALITMBERUC0.071-disconnectionfromchassisNYOFELV0.047-disconnectionfromconnectorLEITICALITRING0.042-gasketstearCSEAR0.006-superficialcutINC(CategoryIVCategoryIIICategoryIICategoryI-minor-marginal-critical-catastrophic(LOW)SEVERITYCLASSIFICATION(INCREASINGLEVELOFSEVERITY------>)Fig.8.14QuantitativeFMECAmatrixforthedistributionvalvesystem8.4IntroductiontoFaultTreeAnalysiseventsatalowerlevel,alsocalledsonsofthefather,aretheinput.Figure8.15reportsalistofmaintypolo-FTAisasystematictechniquewhichisusedtoac-giesofevents,gates,andtransfers.quireinformationonasystem,inthecaseofnormalFigure8.16showsalistofgatesavailableinthebehaviorbut,inparticular,inthepresenceofafailure,commercialRelex®Reliabilitysoftware.inordertosupporttheverycomplexdecision-makingFigure8.17illustratesaFTAappliedtoaneleva-processduringthedesignstageaswellasitsmanag-tor,herereferredtoasaparticularproductionsystem.ingandcontrollingactivities.ThisprocessgenerallyThetopeventpassengerinjurywhichoccursinanel-involvespeopledealingwiththesystem,fromsuppli-evatorisanalyzedbyRelex®Reliabilitysoftware.Inerstocustomerspassingthroughmanagersandem-general,thetopeventistheresultofdifferentcombi-ployeesworkingdailywithinthesystem.Thisanaly-nationsofbasiceventsidentifiedforthecomponentssiscanalsosupportthedecision-makingprocessde-ofthesystem.Thebehaviorofeveryelementinthevelopedbysafetyandmaintenanceengineerswhosystemisknownintermsoffailuresandrepairs,andplanandorganizepreventiveand/orbreakdownmain-itcanbemodeledbytheusualparameterscomingtenanceandmonitoringactivitiesontheproductionfromthereliabilityevaluatingactivities.Withrefer-systems.encetothefailurerate,twokindsofcomponentscanThefaulttreeisadeductivesystemanalysisbybemainlydistinguished:passiveandactivecompo-whichtheanalystpostulatesthatthesystemcouldfailnents.Apassive,orquasi-static,componenttransmitsinacertainwayandattemptstofindouthowthesys-asignal,e.g.,acurrentoraforce:thefailureratesaretemoritscomponentscouldcontributetothisfailure.below104perdemand,i.e.,about3107h1.AnBornasaqualitativemodel,itturnedintoaquanti-activecomponentcausesormodifiesasignalabovetativetool:forthisreasoninthischapterqualitativethisvalue.andquantitativeanalysesaredistinguishedandappliedUsuallythereare3ordersofmagnitudebetweentotrivialacademicexamplesandsomeindustrialcasetheseratevalues.Inthecaseoffailureofanactivestudies.component,e.g.,aswitchinanelectricalcircuit,ahy-Afaulttreeisawholesetofentitiescalledgatesdraulicpump,oravalveregulatingthefluidflowinaddressingthebottom-uptransmissionoffaultlogic.apipingsystem,theoutputsignalcouldbeincorrectThesegatesrepresenttherelationshipsofeventsfororabsent,whilethefailureofapassivecomponent,theoccurrenceofahigherevent,calledfatherevent.e.g.,anelectricwireinacircuitorapipeinapipingThehighereventistheoutputofthegate,whilethesystem,canresultinano-signaltransmission. 8.4IntroductiontoFaultTreeAnalysis237SymbolNameDescriptionBasiceventAfaulteventwhichdoesnotrequirefurtherdevelopmentTopeventThiseventisrelatedtoafailuremodeoftheproductionsystem.TheaimofaFTAisthecharacterizationofthiseventConditioningeventItspecifiestheconditionand/ortherestrictionsappliedtoalogicgate(e.g.,aP-ANDgate)IntermediateeventItoccursbecauseofoneormoreformercausesactingthroughlogicgatesANDgateOutputfaultoccursifallinputfaultsoccurORgateOutputfaultoccursifatleastoneoftheinputfaultsoccursXORgateOutputfaultoccursifsolelyoneoftheinputfaultsoccurs(exclusiveORgate)P-ANDgateItisaspecialcaseofanANDgate.Outputfaultoccursif(priorityANDgate)alloftheinputfailsinaspecificsequence,statedbyaconditioningeventINHIBITgateTheoutputiscausedbyasingleinputifonlyitisconditional,i.e.,undertheconditionspecifiedbytheconditioningeventTransferINItpointsoutthatthetreeisdevelopedfurtheratthetransferOUTTransferOUTItshowstheportionofthetreethathastobeattachedtotherelatedtransferINFig.8.15Maingates,eventsandtransfersinafaulttreeanalysis(FTA) 2388EffectsAnalysisandReliabilityModelingofComplexProductionSystemsInordertointroducethereadertothemeaninganduseofafaulttree,Fig.8.18illustratesatwo-inputORgate,whereAandBaretheinputeventsandCistheoutput.ByEq.5.9theprobabilityofeventCcanbeexpressedasfollows:P.C/DP.A/CP.B/P.AB/DP.A/CP.B/P.A/P.BnA/:(8.6)Equation8.6canbeproperlymodifiedinaccor-dancewiththefollowinghypotheses:1.AandBaremutuallyexclusiveevents:(P.AB/D0;P.C/DP.A/CP.B/:Fig.8.16GatelistinRelex®ReliabilitysoftwareFig.8.17FTA,passengerinjuryinanelevator(Relex®Reliabilitysoftware) 8.5QualitativeFTA2398.5.1FaultTreeConstructionGuidelinesBeforetheintroductionofthemainnotationandprop-ertiesofBooleanalgebra,afewguidelinesforthecon-structionofafaultanditsapplicationtoaproductionsystem,withapreviouslyidentifiedtopevent,couldbeuseful.Itisatop-downprocessofanalysisstartingfromthetopeventdefinedforthesystem,oragenericpart(subsystem)ofthesystem:1.Identificationofamoredetailedevent.ThegenericFig.8.18ORgateeventorinputissubstitutedbyanewandmoredetailedoutputevent,asinFig.8.19.2.AandBareindependentevents:2.Classification.Thegenericinputeventisanalyzedindepthbytheidentificationoftwo,ormore,basic(P.B=A/DP.B/;andalternativesconfigurations,e.g.,cases1and2P.C/DP.A/CP.B/P.A/P.B/:inFig.8.20.Thisidentificationisbasedonapro-cessofclassificationappliedtotheinputeventand3.EventBiscompletelydependentoneventA:theintroductionofanORgatewhichclassifiesthe(availableconfiguration(and/orfailure)modesofP.B=A/D1;thestartingevent,asillustratedinFig.8.20.P.C/DP.A/CP.B/P.A/DP.B/:Figure8.17reportsthevalueofunavailability,orfail-ureprobability,foreverybasiceventorcombination;Abstracte.g.,thefailureprobabilityforthebasicEvent11con-eventtrollerfailureisQD0:00741239,whileforGate5doorclosefailureQD0:00989076.Thedetermina-tionofthesemeasuresofunavailability,accomplishedbyENFvalues,MTTRvalues,etc.,istheresultoftheMoredetailedso-calledquantitativeFTA,properlyillustratedandex-eventemplifiedinSect.8.6.ThenextsectionpresentsthequalitativeFTA,whoseaimistheidentificationofFig.8.19Amoredetailedeventtheso-calledcutsets,whicharetheminimalcombi-nationsofprimaryfailurecomponents/eventscausingthetopeventoftheproductionsystem.Event8.5QualitativeFTATheobjectiveofthissectionistoidentifytheminimal+cutsets(MCS)ofafaulttreedefinedforaspecifictopeventinaproductionsystem.AMCSisanintersec-tionofprimary,orbasic,eventsessentialforthetopevent:ifasinglefailureinthecutsetdoesnotoc-cur,thereisnotopeventfailure.TheidentificationofCaseACaseBcutsetscanbeeffectivelysupportedbytheapplica-tionoftheBooleanalgebra,whosebasicnotationandpropertiesareintroducedbelow.Fig.8.20Classificationoffailuremodes 2408EffectsAnalysisandReliabilityModelingofComplexProductionSystems3.Identificationofdistinctcauses.SomedifferentEventcausesforthegenericfailureeventareidentified,andanORgateisintroduced,asinFig.8.21.Thegenericcauseiscapableofgeneratingthefailureevent.4.Failureeventandabsenceofprotection.Ageneric+failureeventiscoupledwiththeabsenceofprotec-tionoraprotectiveaction(seeFig.8.22).AnANDgateisintroduced.5.Concurrentcauses.Thegenericfailureeventoc-cursonlyinthecaseofconcurrentcauses,asex-emplifiedinFig.8.23.CauseACauseBFig.8.21Identificationofdistinctcauses8.5.2NumericalExample1.FaultTreeConstructionFigure8.24presentsapumpingsystemsupplyingEventcoolingwaterfortemperaturecontrolofareactorandtherelatedtankpressure.Inparticular,giventhecatas-trophictopeventreactorexplosionandknowingthereliabilityperformanceindexesforasetofbasiccom-ponents,Fig.8.25showsafaultconstructedaccordingxtothepreviouslyillustratedguidelines.ThebreakageofvalvesV1andV2,ofpumpsP1andP2,ofproces-sorPR,andtheabsenceofelectricpowerPWarethefailurebasiceventsdefinedforthesystem.Onlysup-plyline2,exactlylikeline1,isconsideredinthefaultAbsenceofHazard/failureprotection/tree.eventprotectiveTheproposedfaulttreecorrespondstothehypoth-actionesisofredundantpumpinglinesinparallel,i.e.,theFig.8.22Absenceofprotection/protectiveactioncoolingserviceisensuredbyasinglelineatleast.Ifthetwocircuitsarebothrequiredsimultaneouslytosupplythereactorsdemand,anORgatereplacestheANDgate,andthefaulttreechangesasillustratedinEventFig.8.26.xCause1Cause2Fig.8.23ConcurrentcausesFig.8.24Pressurecontrolinachemicalreactor 8.5QualitativeFTA241NocoldwaterReactorfromline2explosionPressuretankrupture+InternaloverpressionV2doesnotopenP2doesnotworkTemperatureoutofcontrolColdwater++supplierfailsXV2PRbrokenbrokenNoelectricNopowerP2electricbrokenNocoldwaterfromNocoldwaterpowerline1fromline2Fig.8.25Faulttreeconstruc-tion.ANDgate,configura-tionA8.5.3BooleanAlgebraandApplicationBooleanalgebraisthealgebraoftwovaluesintro-toFTAducebyGeorgeBoole,aBritishmathematicianandphilosopherofthenineteenthcentury.Thesevaluesareusuallytakentobe0and1,correspondingtofalseandTheBooleanalgebra,oralgebraofevents,ispartic-true.Inparticular,givenagenericeventA,aBooleanularlyusefulforconductingaFTAfrombothaqualita-variableXAcanbedefinedasfollows:tiveandaquantitativepointofview.Inparticular,this(algebrasupportsthedesignerandmanagerofapro-0ifeventAdoesnotoccurXAD(8.7)ductionsysteminansweringtothiscriticalquestion:1ifeventAoccurs.Whatarethebasic/primaryeventscausingthedefinedtopeventfortheproductionsystem?Tables8.8and8.9refertothemainpropertiesandGivenaproductionsystemandatopeventrelatedrulesoftheBooleanalgebra,usefulforconductingtothesystemfunction,itispossibletoconstructafaultaFTAandinparticularforobtainingtheEFT.Thetree.TheBooleanalgebramateriallysupportstheap-significanceandvalidityoftheBooleanrulescanbeplicationofreducingandsimplifyingpropertiestoob-checkedbytheapplicationofVenndiagrams.tainanequivalentfaulttree(EFT),asaresultofdiffer-AnEFTisatreemadeoftwolevels:level0iden-entMCS.tifiesthetopeventandlevel1thesetofMCS,asil- 2428EffectsAnalysisandReliabilityModelingofComplexProductionSystemsNocoldwaterReactorfromline2explosionPressuretankrupture+InternaloverpressionV2doesnotopenP2doesnotworkTemperatureoutofcontrolColdwater++supplierfails+V2PRbrokenbrokenNoelectricNopowerP2electricbrokenpowerNocoldwaterfromNocoldwaterline1fromline2Fig.8.26Faulttreeconstruc-tion.ORgate,configurationBlustratedinFig.8.27.AMCSdefinesafailuremodeItispossibletoranktheMCSaccordingtotheirofthetopevent,becauseitisasmallercombinationofsize,thusweightingtherelevanceofafailure;more-componentfailurescapableofcausingthetopevent,over,itcouldbeusefultoconductaquantitativeeval-ifallcomponentfailuresoccur.AgenericMCScanbeuationofafaulttreeinordertoproperlyidentifytherepresentedbythefaulttreeinFig.8.28.systemscriticalities,asillustratedbelow.TheapplicationoftheBooleanpropertiesprevi-ouslyillustratedallowsonetoexpresstheMCSforthetopeventinanEFTasfollows:8.5.4QualitativeFTA:XnXnYmiANumericalExampleTOPDMCSiDCij;(8.8)iD1iD1jD1Thisnumericalexamplereferstothesystemrepre-whereMCSiistheMCSiforthetopevent,nisthesentedinFig.8.24,whichisusefulforidentifyingnumberofMCS,miisthenumberofprimaryeventstheMCS,giventhetopeventreactorexplosion.inMCSi,andCijisprimaryeventjforMCSi.InSect.8.5.2twodifferentreliabilityconfigurations,EveryalgebraicoperationinEq.8.8isexecutedinAandB,wereconsidered,butinthiscasetheFTAaccordancewithBooleandefinitionsandproperties,asappliestoconfigurationAmadeupoftworedundantillustratedbelow.linesforcoolingwaterinparallel.Figure8.30presents 8.5QualitativeFTA243Table8.8BooleanalgebraandVenndiagramsEventVenndiagramsBooleanalgebraUBooleanvariableAAXAUComplementornegationANAXANDXNAD1XADisjunction˚UaA[BorACBXA[BDXA˚XBDXiABiDA;BD1.1XA/.1XB/Conjunction˝UABorABXABDXA˝XBABYDXiDXAXBiDA;B˚Booleansum,˝BooleanproductTable8.9RulesofBooleanalgebraEventsdomainBooleanalgebraOperationwithA[;DAXAC;DXAC0DXAevents;andUA;D;XA;DXAC0D;D0U[ADUXUCXADXUD1UADAXUXADXAComplementationANAD;XANXAD0CommutativelawA[BDB[AXACXBDXBCXAABDBAXAXBDXBXAAssociativelawA[.B[C/D.A[B/[CXAC.XBCXC/D.XACXB/CXCA.BC/D.AB/CXA.XBXC/D.XAXB/XCDistributivelawA.B[C/D.AB/[.AC/XA.XBCXC/D.XAXB/C.XAXC/A[.BC/D.A[B/.A[C/XAC.XBXC/D.XACXB/.XACXC/LawofabsorptionA[.AB/DAXAC.XAXB/DXAA.AB/DABXA.XAXB/DXAXBIdempotentLawA[ADAXACXADXAAADAXAXADXA 2448EffectsAnalysisandReliabilityModelingofComplexProductionSystemsTopeventLevel0ORLevel1Cutset1CutsetnCutset2Fig.8.27EquivalentfaultCutsetitree(EFT)theEFTresultingfromtheapplicationofthequalita-OnawholetherearefiveMCS,twoonfiveofcar-tiveevaluationofthefaulttreeinFig.8.29,inaccor-dinality1,i.e.,includingonlyonebasicevent(PRdancewiththefollowingexpression:andPW)andtheremainingthreeofcardinality2AND(V1V2;V1P2;P1V2;P1P2).gateTOPDŒ.V1CPR/C.P1CPW/Figures8.29and8.30arebothbasedontheintro-Œ.V2CPR/C.P2CPW/ductionofafewmirroredblocks.AmirroredblockDV1V2CV1PRCV1P2isaneventrepeatedmorethanonceinthesystem:e.g.,thebasiceventnoelectricpowerisrepeatedfourCV1PWCPRV2CPRCPRP2timesanditcertainlyrepresentsaverycriticalcompo-CPRPWCP1V2CP1PRnentforthesystem,especiallyinthecaseofagreatCP1P2CP1PWCPWV2valueoffailurerate.t/.CPWPRCPWP2CPWFigure8.31reportstheequivalentreliabilityblockDV1V2CV1P2CP1V2diagramgeneratedbythefaulttreeinFig.8.29andlawofabsorptionmadeupoftwoparallelandidenticalsubsystemscor-CP1P2CPRCPWrespondingtotheinputsoftheANDgateinFig.8.25.X5Similarly,Fig.8.32presentstheequivalentreliabilityDMCSi:blockdiagramgeneratedbytheEFTinFig.8.30.iD1Figure8.33presentsthefaulttreegeneratedforthenotredundantconfigurationB,wherethetwolinesarebothnecessarytoproperlycontrolthereactortemper-CSi-CutsetiLevel1aturelevel.Inthisspecialconfigurationtherearesixcutsetsofcardinality1,becauseeverybasiceventiscritical.Figure8.34liststhecutsetsobtainedbythequalitativeANDanalysisappliedtothesysteminconfigurationB.Cimi8.6QuantitativeFTACi1Level2TheaimofquantitativeFTAisthedeterminationofCCi2ijsomereliabilityandprobabilisticparameters,mainlyreferredtothetopeventdeclaredfortheproductionFig.8.28EFTandgenericcutsetsysteminvestigated.Thisanalysiscanbeperformed 8.6QuantitativeFTA245TopANDORORORORORORV1NoPRP1NoV2NoPRP2NobrokenelectricbrokenbrokenelectricbrokenelectricbrokenbrokenelectricpowerpowerpowerpowerFig.8.29FTA,reactorexplosion.ConfigurationAredundancy.ReliaSoft®softwareTopORANDANDANDANDANDANDV1V2P1P2P1V2P2V1PRPWbrokenbrokenbrokenbrokenbrokenbrokenbrokenbrokenbrokenbrokenFig.8.30Qualitativefaulttreeevaluation.EFT.ConfigurationAredundancy.ReliaSoft®softwareV2NoPRP2NobrokenelectricbrokenbrokenelectricpowerpowerExtraExtraStartingEndingBlockBlockV1NoPRP1NobrokenelectricbrokenbrokenelectricpowerpowerFig.8.31Equivalentreliabilityblockdiagram,reactorexplosion.ConfigurationAredundancy.ReliaSoft®software 2468EffectsAnalysisandReliabilityModelingofComplexProductionSystemsV2P2V2V1brokenbrokenbrokenbrokenExtraExtraExtraExtraPRPWStartingNode3Node4Node5brokenbrokenBlockV1P1P1P2brokenbrokenbrokenbrokenFig.8.32EquivalentreliabilityblockdiagrambytheEFT.ConfigurationAredundancy.ReliaSoft®softwareTopORORORORORORORV1NoPRP1NoV2NoPRP2NobrokenelectricbrokenbrokenelectricbrokenelectricbrokenbrokenelectricpowerpowerpowerpowerFig.8.33FTA,reactorexplosion.ConfigurationBnoredundancy.ReliaSoft®softwareonceMCShavebeenidentified.Itisasequentialeval-uationwhichfirstlydeterminesthefailureprobabil-Topityforthecomponents,thentheMCS,andfinallytheprobabilitiesforthesystem,giventhetopevent.Themainequationsforthedeterminationoftheseproba-bilitiesaregiveasfollows:ORComponentfailureprobability.Generally,foranycomponent,orbasicprimaryevent,aconstantfailurerateperhourisassumed,andanytime-dependenteffectisignored.IfagenericcomponentV1V2P1P2PRPWisconsidered,itcouldbenecessarytodistinguishbrokenbrokenbrokenbrokenbrokenbrokenastandbyfailureratefromanoperatingfailureFig.8.34Qualitativefaulttreeevaluation.EFT.Configura-rate:asaconsequence,theproperfailureratehastionBnoredundancy.ReliaSoft®softwaretobecoupledtothepropertimeperiod,standby 8.6QuantitativeFTA247timetoroperatingtimet,respectively.Thecom-Componentfailureoccurrencerate.Thisrateisde-ponentfailureprobability,whichmainlyreferstofinedforbothrepairableandnonrepairablecompo-thenonrepairableitems,isnentsorsystems.Fornonrepairableitemsitisde-finedasFj.t/DFj;s.ts/CŒ1Fj;s.ts/Fj;o.to/;(8.9)tw.t/Df.t/De;(8.15)wheresisthestandbyphase,tsistheready(i.e.,standby)timeperiod,oistheoperatingphase,andwheref.t/istheprobabilitydensityfunctionofthetoistheoperatingtimeperiod.ttf.Assuminganexponentialdistributionfortheran-Forbothunrepairableandrepairablefailures.t/domvariablet,onecanapproximatethecumulatedisareasonableapproximationofthisrate.valueF.t/byitsfirst-orderterm,whent<0:1,FailureoccurrencerateofacutsetgivenaTOPasfollows:event.AMCSfailureoccursattimettotC tifallcomponentsexceptonearedownattimet,F.t/Št;(8.10)andtheothercomponentfailsattimettotC t.whereistheconditionalandconstantratedefinedConsequently,forthevariablet.XYInparticular,iftisthetimetofailure(ttf),thenwCSi.t/Dwj.t/qk.t/;(8.16)F.t/isthefailureprobabilityfunction(unreliabil-j2CSik¤jk;j2CSiity)andistheconstantfailurerate.Forrepairablefailurestheconstantasymptoticun-wherewj.t/isthefailurerateofcomponentjinavailabilityofacomponentisquantifiedbyMCSi.MTTRENFforacutset.TheENFforacutsetCSionqjDDŠ;atimeperiodTisDconstantCDconstant(8.11)ENFCSi.T/DWCSi.0;T/DWCSi.T/whereistherepairrate.ZTDwCSi.t/dtFailureprobabilityandunavailabilityofacutsetgivenatopevent.Thegeneralmodelfortheevalu-0ationofcutsetunavailability,equivalenttofailureZTXYprobability,isDwj.t/qk.t/dt;Y0j2CSik¤jqCSi.t/Dqj.t/;(8.12)k;j2CSij2CSi(8.17)whereCSiiscutsetiandqj.t/istheunavailabilitywhereTisthetimeperiod.ofcomponentjwhichbelongstoCSi.ENFofasystemonatimeperiodT,givenatopUnavailabilityofthesystemgivenatopevent.event.aYQS.t/DqCSi.t/D1Œ1qCSi.t/:ENF.T/DWS.T/Xnoii(8.13)DWCSi.T/PrE.CSi/iiXAsimplifiedequationquantifyingtheunavailabilityWCS.T/;(8.18)iofthesystemisiXQS.t/ŠqCSi.t/:(8.14)wherePrf:::gisthefailureprobabilityandE.CSi/iisthefailureeventdefinedforcutseti. 2488EffectsAnalysisandReliabilityModelingofComplexProductionSystemsForthesystemtheENFisgenerallyquantifiedbyTOPthefollowingexpression:XENF.T/ŠWCSi:(8.19)iVirtualMTTRofasystemgivenatopevent.ThefollowingequationsquantifytheMTTRforthepro-ductionsystem,givenatopevent:8G1G2ˆˆQS.T/