CHAPTER 1 INTRODUCTION TO RELIABILITY - …

1 ICHAPTER :Inthepresentscenarioofglobalcompetition andliberalization,itisimperativethatIndi anindustriesbecomefullyconsciousofthenee dtoproducereliableproductsmeetinginterna tional standards. Eventhoughthe ReliabilityEngineering hastakenbirthduringWorldWarIIwithasignif icantcontributionbydefensepersonnel, todayithastakenanewshape byblendingitself inall phases of the product life cycle every device, instrument or systemandalso it is true that of complex situation, RELIABILITY of aproduct or service is bestassuredwhenit is designedbythe designengineer andbuilt inbyproductionengineer, ,either by itself or as a part of a larger assembly, the quality ofperformance wouldbe judgedby howlong the product gives usefulservice; thisisindicatedbytheword RELIABILITY . Onecanfindmanydefinitionsforreliabilitye ngineering, , Reliabilityis probability that acomponent, device, equipment or asystemwillperformitsintendedfunctionade quatelyfor aspecificperiodof timeunderagivenset of conditions.

2 Accordingtothedefinition, thebasiciiielementsofreliabilityareproba bility,adequateperformance, above definitioncovers all four aspects of product, unlikequality, , whichisundertheinfluenceof timeandenvironmentunlikequality, whichisadegreeof ,whereasitisnotpossibletomanufacturehigh qualitysystemswithlessqualitycomponents. , of amotor car. If any car fails, evenafterfollowingmanufacturer sinstructionsspecified,thecarwillbeconsi deredas unreliable. If it does not fail before its stated life, it would , Thecardesignerstrytomakethecarinsensitiv etothelikelyvariations. Thefactoryqualityengineertriestoreduceva riationsandeliminatedefects. If boththedesigner andthequalityengineerhadbeencompletelysu ccessful andeverycarhadbeenivusedidentically, thenevery car wouldhave the same RELIABILITY .

3 ,99provetobetroublefree,ifusedandmaintai nedcorrectlyandonefailstoworkasintended, thenitcanbesaidthatthereliabilityofeachc aris99percent,Sincereliabilityisaprobabi lity, it isexpressedindecimalsof t (t)= :Afailureisthepartial ortotal lossorchangeinthepropertiesof adeviceinsuchawaythat quantitativereliabilityof adevice. Ingeneral, somecomponentshavewell definedfailures; othersdonot. Inthebeginning,whenthe itemor component is installed, the itemfails withhighfrequency, Theyareveryhighat number of failuresper unit oftime. Due to wear and tear with the usage, the itemgraduallydeterioratesandfrequencyof failuresagainincreases. (Bathtubcurve) :Reliabilityisnowawell recognizedandrapidlydevelopingbranchof engineering. Manufacturing of a perfect component is almostimpossible because of inherent variations and the cost for partsimprovementisveryhighandtheapproach becomesunwieldywithlargeandcomplexsystem s.

4 Sincereliabilitystudyisconsideredessenti al forproper utilization and maintenance of engineering systems andviequipment, it has gained much importance among the problemswhileplanninganddesigningthesyst emforareasonablelevel of thefollowingtwomethodsnamely Improvingthecomponents ByusingredundancytechniqueAnumber of techniques are available to enhance the of structured redundancy and maintenance it isnot possibletoproducecomponentswithhighrelia bilityduetonumberofconstraints,suchascos t,non-availabilityofproductionfacilities etc., , Elementredundancy :LetC1andC2bethetwoelementswithreliabili tiesR1(t)andR2(t)respectivelyconnectedin parallel Inthisarrangementofelements,thereliabili tyofthesystemwillbemuchbetterduetothepre senceof redundant element andproperoperationof oneelement is sufficient for the successful operation of the :viiiToimprovethereliabilityof thesystem, anothersimilarsystemisconnectedeither inseriesor parallel totheexistingoneiscalledtheconcept of unit redundancy.

5 ConsiderasystemwithtwoelementsC1andC2ass hownbelow. Forimprovingthereliabilityof thesystem, asimilarsysteminparallelisaddedtotheexis tingsystem, Activeredundancy :Redundant systemconsisting of two or more theredundant unitsareoperatedsimultaneouslyinsteadof switchingononlywhenneedarises. :Incaseofstandbyredundancythealternateme ansofperformingthefunctionisnotoperatedu ntil itisneeded. Thealternativemeansisswitchedononlywhent heprimarymeansof performingthefunctionfails. Standbyredundancyismoreappropriatefor mechanical of RELIABILITY canbe achievedunder the inreliabilityperunit of complex. The systemcanbe analyzedby decomposing it intosmallersubsystemsandestimatingreliab ilityof eachsubsystemtoassessthetotal systemreliability. reliabilitiesof thelogical manner the constraints for the successful operationof of thesystembyapplyingtherulesof theprobabilityaccordingtotheconfiguratio nof thecomponentswithinthesystemisalsoknowna ssystemreliability.

6 Several methodsexist toimprovethexisystemreliabilitylikeusing largesafetyfactors,reducingthecomplexity ofthesystem, , :Inseriesconfigurationallcomponentsmustb econnectedinseriesinordertomakethesystem toperformcontinuously. if anyonecomponent connectedseriallyfails, theSystemwill Thecomponentsareinterconnectedinsuchaway that theentireSystemwill worksatisfactorilyif all thecomponentsworkwithoutfail. () eachcomponent hasaconstant failurerateofthenthesystemreliabilityise qualto(1) :Asystemcanhaveseveral componentstoperformthesameoperation and the satisfactory performance of any one of thesecomponents is sufficient to ensure the successful operation of The systemwill functionsatisfactorily evenany one of theparallelunitsoperatessatisfactorily. (2)Iflifetimesofthecomponentsfollowexpon entialdistributionthen(3)Ifallcomponents areidentical(4) :Inmixedconfiguration, theelementsareconnectedinseriesandparall el arrangement toperformarequiredsystemoperation.

7 Inmixedconfiguration, tocomputethesystemreliability, thenetworkisbroken123nOUTIN xivintoseriesorparallel subsystems. Thereliabilityof eachsubsystemisfoundandthenthesystemreli abilitymaybeobtainedonthebasisoftherelat ionship among the sub systems. The schematic :The Systemconsists of different stages connectedinseries asshown in Figure Each stage contains number of redundantelements. For example stage-1 consists of niredundant elementsconnectedinparallel. Thereliabilityof thesystemRsistheproduct (5) SeriesConfiguration:A number of activities such as industrial process, economicsystemsandmechanical devicescanberepresentedasmulti stagesystems. Thesemulti stagesystemsaregenerallycategorizedaccor dingtothecomponent configurationat eachstage.

8 Thesystemconsistsofdifferent stagesconnectedinparallel elementsinseries. Forsuccessful runningofsystem, one pathis sufficient. Redundant components are addedinparallel-seriessystemtoenhancethe reliabilityof thestagesaswell (6) Out Of M Configuration:Ageneralizationof n parallel components occurs whenarequirementexistsforkoutof m k=1thesystemwill becomeparallel configuration. If k=m, out of msystems,generallythebinomial lawcanbeusedwithidentical operationofacomponentthentheprobabilityt hat exactlyk out of mcomponentsaresuccessful isgivenbyP(m,x)=B(m,x).Px.(1 p)m x(7)WhereB(m,x)isbinomialco the minimumnumber of components requiredfor (8)whereisbinomialco a constant failure rate, the RELIABILITY for a k out of mconfigurationisexpressedas(9) ParallelConfiguration:Acomplexsystemonsi mplificationcanproduceanon , :Astructureiscalledacomplexwhenthereliab ilityblockdiagrameither cannot be reduced to a serial or parallel structure withindependent elements.

9 For anycomplexsystem, twostepshavetobefollowedfor obtainingthereliabilityor unreliabilityexpressionsof : , , thecoherent :General networksystemincludesbridgenetworks, nonseries non parallel structures and other complex systems where the structure is not explicit and :Redundancy makes it possible to achieve highreliable ,weight andcomplexity of the systemsubstantially. It is therefore,essential tooptimizereliabilityofthesystembykeepin gconstraintslikecost,weight, , there may be specific constraints oncost, weight andvolumeorevenanoptimal allocationof redundancyitself tomaximizesystemreliability. Inseries typeof systemsconsistingof kstages(orsubsystems) , , weight, volume, etc.,whichcannot beviolatedandaredundancyallocation, whichsatisfiesthese constraints while maximizingreliabilityis desirable.

10 Alternatelyfixedconstraintvaluesmaynotbe availableforcost,weight,andvolumeetc., ratherwhat maybedesiredisafamilyof redundancyallocation,eachmember of the familyhavingreliabilitymust be either costlier, the selectionamong the members of the family ofoptimal redundancy allocations, the decisionmaker is assuredthatwhatever the cost, weight and volume, the maximumreliability isattained. Forclarityandeaseof reference, ,GiventheSetofConstraints:Stage i consists of ni+1 units inparallel, eachof whichhasindependentprobabilityqi(0<qi<1) of failinglinear cost constraintsexistsasni=(n1, )asfollows:j=1, (10)xxiwhereeachCij>0, non negativeintegersnitomaximizesystemReliab ilityRs,whereinthepresentmodelRsisgivenb y(11) , ,NoSpecificSetofConstraints:Whenthere is no specific set of constraints, a family of un-dominatedallocationscanbegenerated.