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Lecture7FaultSimulation

第七講：故障模擬2022/12/131VLSITest:Lecture7Lecture7FaultSimulation

Contents

內(nèi)容目錄ProblemandmotivationFaultsimulationalgorithmsRandomFaultSamplingSummary2022/12/132VLSITest:Lecture7Contents

內(nèi)容目錄Problemandmotiv1ProblemandMotivation

問題和驅(qū)動(dòng)FaultsimulationProblem:GivenAcircuitAsequenceoftestvectorsAfaultmodelDetermineFaultcoverage-fraction(orpercentage)ofmodeledfaultsdetectedbytestvectorsSetofundetectedfaultsMotivationDeterminetestqualityandinturnproductqualityFindundetectedfaulttargetstoimprovetests2022/12/133VLSITest:Lecture71ProblemandMotivation

問題和驅(qū)動(dòng)1.1FaultsimulatorinaVLSIDesignProcess

VLSI設(shè)計(jì)過(guò)程中的故障模擬器VerifieddesignnetlistVerificationinputstimuliFaultsimulatorTestvectorsModeledfaultlistTestgeneratorTestcompactorFaultcoverage?RemovetestedfaultsDeletevectorsAddvectorsLowAdequateStop2022/12/134VLSITest:Lecture71.1FaultsimulatorinaVLSI1.2FaultSimulationScenario

故障模擬假定Circuitmodel:mixed-levelMostlylogicwithsomeswitch-levelforhigh-impedance(Z)andbidirectionalsignalsHigh-levelmodels(memory,etc.)withpinfaultsSignalstates:logicTwo(0,1)orthree(0,1,X)statesforpurelyBooleanlogiccircuitsFourstates(0,1,X,Z)forsequentialMOScircuitsTiming:Zero-delayforcombinationalandsynchronouscircuitsMostlyunit-delayforcircuitswithfeedback2022/12/135VLSITest:Lecture71.2FaultSimulationScenario

1.2FaultSimulationScenario(continued)

故障模擬假定（續(xù)）Faults:Mostlysinglestuck-atfaultsSometimesstuck-open,transition,andpath-delayfaults;analogcircuitfaultsimulatorsarenotyetincommonuseEquivalencefaultcollapsingofsinglestuck-atfaultsFault-dropping--afaultoncedetectedisdroppedfromconsiderationasmorevectorsaresimulated;fault-droppingmaybesuppressedfordiagnosisFaultsampling--arandomsampleoffaultsissimulatedwhenthecircuitislarge2022/12/136VLSITest:Lecture71.2FaultSimulationScenario2FaultSimulationAlgorithms

故障模擬算法Serial/串行算法Parallel/并行算法Deductive/演繹算法Concurrent/并發(fā)算法Differential/差分算法2022/12/137VLSITest:Lecture72FaultSimulationAlgorithms

2.1SerialAlgorithm

串行算法Algorithm:Simulatefault-freecircuitandsaveresponses.Repeatfollowingstepsforeachfaultinthefaultlist:ModifynetlistbyinjectingonefaultSimulatemodifiednetlist,vectorbyvector,comparingresponseswithsavedresponsesIfresponsediffers,reportfaultdetectionandsuspendsimulationofremainingvectorsAdvantages:Easytoimplement;needsonlyatrue-valuesimulator,lessmemoryMostfaults,includinganalogfaults,canbesimulated2022/12/138VLSITest:Lecture72.1SerialAlgorithm

串行算法Algor2.1SerialAlgorithm(Cont.)

串行算法（續(xù)）Disadvantage:Muchrepeatedcomputation;CPUtimeprohibitiveforVLSIcircuitsAlternative:SimulatemanyfaultstogetherTestvectors

Fault-freecircuitCircuitwithfaultf1Circuitwithfaultf2CircuitwithfaultfnComparatorf1detected?Comparatorf2detected?Comparatorfndetected?2022/12/139VLSITest:Lecture72.1SerialAlgorithm(Cont.)

串2.2ParallelFaultSimulation

并行故障模擬Compiled-codemethod;bestwithtwo-states(0,1)Exploitsinherentbit-parallelismoflogicoperationsoncomputerwordsStorage:onewordperlinefortwo-statesimulationMulti-passsimulation:Eachpasssimulatesw-1newfaults,wherewisthemachinewordlengthSpeedupoverserialmethod~w-1Notsuitableforcircuitswithtiming-criticalandnon-Booleanlogic2022/12/1310VLSITest:Lecture72.2ParallelFaultSimulation

2.2.1ParallelFaultSim.Example

并行故障模擬實(shí)例abcdefg111111101101000101s-a-1s-a-0001cs-a-0detectedBit0:fault-freecircuitBit1:circuitwithcs-a-0Bit2:circuitwithfs-a-12022/12/1311VLSITest:Lecture72.2.1ParallelFaultSim.Exam2.3DeductiveFaultSimulation

演繹故障模擬One-passsimulationEachlinekcontainsalistLkoffaultsdetectableonkFollowingtrue-valuesimulationofeachvector,faultlistsofallgateoutputlinesareupdatedusingset-theoreticrules,signalvalues,andgateinputfaultlistsPOfaultlistsprovidedetectiondataLimitations:Set-theoreticrulesdifficulttoderivefornon-BooleangatesGatedelaysaredifficulttouse2022/12/1312VLSITest:Lecture72.3DeductiveFaultSimulation

2.3.1DeductiveFaultSim.Example

演繹故障模擬實(shí)例abcdefg11101{a0}{b0,c0}{b0}{b0,d0}Le=LaULcU{e0}={a0,b0,c0,e0}Lg=(Le

Lf)U{g0}={a0,c0,e0,g0}U{b0,d0,f1}Notation:Lkisfaultlistforlinek

kniss-a-nfaultonlinekFaultsdetectedbytheinputvector2022/12/1313VLSITest:Lecture7

2.3.1DeductiveFaultSim.Ex2.4ConcurrentFaultSimulation

并發(fā)故障模擬Event-drivensimulationoffault-freecircuitandonlythosepartsofthefaultycircuitthatdifferinsignalstatesfromthefault-freecircuit.Alistpergatecontainingcopiesofthegatefromallfaultycircuitsinwhichthisgatediffers.ListelementcontainsfaultID,gateinputandoutputvaluesandinternalstates,ifany.Alleventsoffault-freeandallfaultycircuitsareimplicitlysimulated.Faultscanbesimulatedinanymodelingstyleordetailsupportedintrue-valuesimulation(offersmostflexibility.)Fasterthanothermethods,butusesmostmemory.2022/12/1314VLSITest:Lecture72.4ConcurrentFaultSimulatio2.4.1Conc.FaultSim.Example

并發(fā)故障模擬實(shí)例abcdefg1110111110110010100100110100111111000011000000010111a0b0c0e0a0b0b0c0e0d0d0g0f1f12022/12/1315VLSITest:Lecture72.4.1Conc.FaultSim.Example3FaultSampling

故障采樣Arandomlyselectedsubset(sample)offaultsissimulated.Measuredcoverageinthesampleisusedtoestimatefaultcoverageintheentirecircuit.Advantage:Savingincomputingresources(CPUtimeandmemory.)Disadvantage:Limiteddataonundetectedfaults.2022/12/1316VLSITest:Lecture73FaultSampling

故障采樣Arandoml3.1MotivationforSampling

故障采樣的驅(qū)動(dòng)力Complexityoffaultsimulationdependson:NumberofgatesNumberoffaultsNumberofvectorsComplexityoffaultsimulationwithfaultsamplingdependson:NumberofgatesNumberofvectors2022/12/1317VLSITest:Lecture73.1MotivationforSampling

故障3.2RandomSamplingModel

隨機(jī)采樣模型AllfaultswithafixedbutunknowncoverageDetectedfaultUndetectedfaultRandompickingNp=totalnumberoffaults(populationsize)

C=faultcoverage(unknown)Ns=samplesizeNs<<Npc=samplecoverage(arandomvariable)2022/12/1318VLSITest:Lecture73.2RandomSamplingModel

隨機(jī)采樣3.3ProbabilityDensityofSampleCoverage

采樣故障覆蓋率的概率密度

(x--C)2--------------

1

2s

2p(x)=Prob(x<c<x+dx)=--------------e

s(2p)

1/2p(x)CC+3sC-3s1.0xSamplecoverage

C(1-C)Variance,s2=------------

NsMean=CSamplingerrorssx2022/12/1319VLSITest:Lecture73.3ProbabilityDensityofSam3.4SamplingErrorBounds

采樣錯(cuò)誤限度

C(1-C)|x-C|=3[--------------]

1/2

NsSolvingthequadraticequationforC,wegetthe3-sigma(99.7%confidence)estimate:WhereNsissamplesizeandxisthemeasuredfaultcoverageinthesample.Example:Acircuitwith39,096faultshasanactualfaultcoverageof87.1%.Themeasuredcoverageinarandomsampleof1,000faultsis88.7%.Theaboveformulagivesanestimateof88.7%3%.CPUtimeforsampleimulationwasabout10%ofthatforallfaults.

4.5C

3s=x-------[1+0.44Ns

x(1-x)]1/2

Ns

2022/12/1320VLSITest:Lecture73.4SamplingErrorBounds

采樣錯(cuò)誤4Summary

總結(jié)Faultsimulatorisanessentialtoolfortestdevelopment.Concurrentfaultsimulationalgorithmoffersthebestchoice.Forrestrictedclassofcircuits(combinationalandsynchronoussequentialwithonlyBooleanprimitives),differentialalgorithmcanprovidebetterspeedandmemoryefficiency(Section5.5.6.)Forlargecircuits,theaccuracyofrandomfaultsamplingonlydependsonthesamplesize(1,000to2,000faults)andnotonthecircuitsize.ThemethodhassignificantadvantagesinreducingCPUtimeandmemoryneedsofthesimulator.2022/12/1321VLSITest:Lecture74Summary

總結(jié)FaultsimulatorisLecture7FaultSimulation

第七講：故障模擬2022/12/1322VLSITest:Lecture7Lecture7FaultSimulation

Contents

內(nèi)容目錄ProblemandmotivationFaultsimulationalgorithmsRandomFaultSamplingSummary2022/12/1323VLSITest:Lecture7Contents

內(nèi)容目錄Problemandmotiv1ProblemandMotivation

問題和驅(qū)動(dòng)FaultsimulationProblem:GivenAcircuitAsequenceoftestvectorsAfaultmodelDetermineFaultcoverage-fraction(orpercentage)ofmodeledfaultsdetectedbytestvectorsSetofundetectedfaultsMotivationDeterminetestqualityandinturnproductqualityFindundetectedfaulttargetstoimprovetests2022/12/1324VLSITest:Lecture71ProblemandMotivation

問題和驅(qū)動(dòng)1.1FaultsimulatorinaVLSIDesignProcess

VLSI設(shè)計(jì)過(guò)程中的故障模擬器VerifieddesignnetlistVerificationinputstimuliFaultsimulatorTestvectorsModeledfaultlistTestgeneratorTestcompactorFaultcoverage?RemovetestedfaultsDeletevectorsAddvectorsLowAdequateStop2022/12/1325VLSITest:Lecture71.1FaultsimulatorinaVLSI1.2FaultSimulationScenario

故障模擬假定Circuitmodel:mixed-levelMostlylogicwithsomeswitch-levelforhigh-impedance(Z)andbidirectionalsignalsHigh-levelmodels(memory,etc.)withpinfaultsSignalstates:logicTwo(0,1)orthree(0,1,X)statesforpurelyBooleanlogiccircuitsFourstates(0,1,X,Z)forsequentialMOScircuitsTiming:Zero-delayforcombinationalandsynchronouscircuitsMostlyunit-delayforcircuitswithfeedback2022/12/1326VLSITest:Lecture71.2FaultSimulationScenario

1.2FaultSimulationScenario(continued)

故障模擬假定（續(xù)）Faults:Mostlysinglestuck-atfaultsSometimesstuck-open,transition,andpath-delayfaults;analogcircuitfaultsimulatorsarenotyetincommonuseEquivalencefaultcollapsingofsinglestuck-atfaultsFault-dropping--afaultoncedetectedisdroppedfromconsiderationasmorevectorsaresimulated;fault-droppingmaybesuppressedfordiagnosisFaultsampling--arandomsampleoffaultsissimulatedwhenthecircuitislarge2022/12/1327VLSITest:Lecture71.2FaultSimulationScenario2FaultSimulationAlgorithms

故障模擬算法Serial/串行算法Parallel/并行算法Deductive/演繹算法Concurrent/并發(fā)算法Differential/差分算法2022/12/1328VLSITest:Lecture72FaultSimulationAlgorithms

2.1SerialAlgorithm

串行算法Algorithm:Simulatefault-freecircuitandsaveresponses.Repeatfollowingstepsforeachfaultinthefaultlist:ModifynetlistbyinjectingonefaultSimulatemodifiednetlist,vectorbyvector,comparingresponseswithsavedresponsesIfresponsediffers,reportfaultdetectionandsuspendsimulationofremainingvectorsAdvantages:Easytoimplement;needsonlyatrue-valuesimulator,lessmemoryMostfaults,includinganalogfaults,canbesimulated2022/12/1329VLSITest:Lecture72.1SerialAlgorithm

串行算法Algor2.1SerialAlgorithm(Cont.)

串行算法（續(xù)）Disadvantage:Muchrepeatedcomputation;CPUtimeprohibitiveforVLSIcircuitsAlternative:SimulatemanyfaultstogetherTestvectors

Fault-freecircuitCircuitwithfaultf1Circuitwithfaultf2CircuitwithfaultfnComparatorf1detected?Comparatorf2detected?Comparatorfndetected?2022/12/1330VLSITest:Lecture72.1SerialAlgorithm(Cont.)

串2.2ParallelFaultSimulation

并行故障模擬Compiled-codemethod;bestwithtwo-states(0,1)Exploitsinherentbit-parallelismoflogicoperationsoncomputerwordsStorage:onewordperlinefortwo-statesimulationMulti-passsimulation:Eachpasssimulatesw-1newfaults,wherewisthemachinewordlengthSpeedupoverserialmethod~w-1Notsuitableforcircuitswithtiming-criticalandnon-Booleanlogic2022/12/1331VLSITest:Lecture72.2ParallelFaultSimulation

2.2.1ParallelFaultSim.Example

并行故障模擬實(shí)例abcdefg111111101101000101s-a-1s-a-0001cs-a-0detectedBit0:fault-freecircuitBit1:circuitwithcs-a-0Bit2:circuitwithfs-a-12022/12/1332VLSITest:Lecture72.2.1ParallelFaultSim.Exam2.3DeductiveFaultSimulation

演繹故障模擬One-passsimulationEachlinekcontainsalistLkoffaultsdetectableonkFollowingtrue-valuesimulationofeachvector,faultlistsofallgateoutputlinesareupdatedusingset-theoreticrules,signalvalues,andgateinputfaultlistsPOfaultlistsprovidedetectiondataLimitations:Set-theoreticrulesdifficulttoderivefornon-BooleangatesGatedelaysaredifficulttouse2022/12/1333VLSITest:Lecture72.3DeductiveFaultSimulation

2.3.1DeductiveFaultSim.Example

演繹故障模擬實(shí)例abcdefg11101{a0}{b0,c0}{b0}{b0,d0}Le=LaULcU{e0}={a0,b0,c0,e0}Lg=(Le

Lf)U{g0}={a0,c0,e0,g0}U{b0,d0,f1}Notation:Lkisfaultlistforlinek

kniss-a-nfaultonlinekFaultsdetectedbytheinputvector2022/12/1334VLSITest:Lecture7

2.3.1DeductiveFaultSim.Ex2.4ConcurrentFaultSimulation

并發(fā)故障模擬Event-drivensimulationoffault-freecircuitandonlythosepartsofthefaultycircuitthatdifferinsignalstatesfromthefault-freecircuit.Alistpergatecontainingcopiesofthegatefromallfaultycircuitsinwhichthisgatediffers.ListelementcontainsfaultID,gateinputandoutputvaluesandinternalstates,ifany.Alleventsoffault-freeandallfaultycircuitsareimplicitlysimulated.Faultscanbesimulatedinanymodelingstyleordetailsupportedintrue-valuesimulation(offersmostflexibility.)Fasterthanothermethods,butusesmostmemory.2022/12/1335VLSITest:Lecture72.4ConcurrentFaultSimulatio2.4.1Conc.FaultSim.Example

并發(fā)故障模擬實(shí)例abcdefg1110111110110010100100110100111111000011000000010111a0b0c0e0a0b0b0c0e0d0d0g0f1f12022/12/1336VLSITest:Lecture72.4.1Conc.FaultSim.Example3FaultSampling

故障采樣Arandomlyselectedsubset(sample)offaultsissimulated.Measuredcoverageinthesampleisusedtoestimatefaultcoverageintheentirecircuit.Advantage:Savingincomputingresources(CPUtimeandmemory.)Disadvantage:Limiteddataonundetectedfaults.2022/12/1337VLSITest:Lecture73FaultSampling

故障采樣Arandoml3.1MotivationforSampling

故障采樣的驅(qū)動(dòng)力Complexityoffaultsimulationdependson:NumberofgatesNumberoffaultsNumberofvectorsComplexityoffaultsimulationwithfaultsamplingdependson:NumberofgatesNumberofvectors2022/12/1338VLSITest:Lecture73.1MotivationforSampling

故障3.2RandomSamplingModel

隨機(jī)采樣模型AllfaultswithafixedbutunknowncoverageDetectedfaultUndetectedfaultRandompickingNp=totalnumberoffaults(populationsize)

C=faultcoverage(unknown)Ns=samplesizeNs<<Npc=samplecoverage(arandomvariable)2022/12/1339VLSITest:Lecture73.2RandomSamplingModel

隨機(jī)采樣3.3ProbabilityDensityofSampleCoverage

采樣故障覆蓋率的概率密度

(x--C)2--------------

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