工程管理外文文献

StudyonTheoryofReliabilityAnalysisinConstructionRiskManagemenDENGTiejun&QIUYike(CollegeofCivilEngineering,HunanUniversity,Changsha410082,Hunan,China)Abstract:Thestateoftheartofreliabilityanalysisforconstructionsystemsisinvestigated.Itispointedoutthatmostofthecurrentresearchinconstructionreliabilityanalysisarelimitedtoasinglespecificgoalormanagementproblem.Startingfromthetheoryofsystemengineering,theconceptofreliabilityforconstructionsystems,whichisdifferentfromthereliabilityofstructuraldesignbutcloselyrelatedtoitisdefined;andtherelationshipbetween“GoalSubsystem”and“ProcedureSubsystem”ispresentedbytakingintoaccountofthefeaturesofconstructionpractice.Analgorithmofthereliabilityanalysisforthe“GoalSubsystem”and“ProcedureSubsystem”isproposed,andtheapproachesforimprovingthesystemreliabilityareexplored.Theclassificationofreliabilitylevelsanditsrelationshipwithconstructionriskmanagementarealsopresented,andthepossibilitiesoffutureapplicationofthereliabilitytheoryinconstructionriskmanagementdiscussed.Keywords:reliabilityanalysis;constructionriskmanagement;systemsengineering;theclassificationofreliabilitylevelsIntroductionSince1916BarChartwasinventedbyH.L.Ganttandappliedintotheflowproduction,flowproductionmethodswasextensivelyadoptedintheorganizationoftheengineeringconstruction.Till2000GabrielA.Barrazaproposed‘S'and‘SS'curvestomodeltheengineeringconstruction.Thatmodelextendedthedeterministiccost-schedulecontrolmethodintoaprobabilisticmodel.Basedontheprobabilisticanalysisforthereliabilityofcost-schedulecontrolusingprobabilitytheoryandmathematicalstatisticaltechniques,thismethodcangivearationalframeworkforthedecisioninengineeringconstruction}}}.Allthisprovesafactthatconstructionreliabilityhaslongbeenstudiedandappliedintheconstructiontechnologyandmanagement.However,thepreviousresearchesstudiedthecontrolandmanagementonlyofasingleobjectiveamongthewholeobjectivesystemforconstruction.Theydidn'tconsidertheuniquecharacteristicsoftheengineeringconstructionasawholesystem;thereforetheyfailtoinstructthepracticalissuesoccurringintherealconstructionprojectmanagementbasedontheirreliabilityanalysis.Themodernconstructionisanincreasinglycomplicatedprocesssystem.Fromtheviewofsystemengineering,eachprocedureortaskinanengineeringprojectcanonlybeaccomplishedaftermeetingsimultaneouslyseveralobjectivesunderbothexternalandinternalconstraints.Aswaspointedout[2],foranengineeringprojectunderreasonableeconomicconstraint,itsperformancecanbedefinedintermsof(1)degreeofmeetingthequalitystandards,(2)assuranceofmeetingthetimedurationrequirement,(3)credibilityofconstructionsafety,and(4)satisfactionofmeetingthesiteenvironmentrequirement.Hence,thereliabilityofaconstructionprojectreferstothefeasibility,possibilityandsafetyofthewholeproductionactivities.Thatis,inordertoguaranteethereliabilityofaconstructionproject,wehavetoassurethefeasibility,possibility,credibilityandsafetyofaprojectunderspecifiedconditions.Generally,however,allthefactorsaffectingtheaccomplishmentoftheprojectarerandomvariables.DenotedbyPt，thereliabilityofconstructioncanbemathematicallymeasuredbytheprobabilityof‘meetingthedesignrequirement'or‘meetingthepre-specifiedprojectperformanceaccordingtotheprojectplanning'.Associatedwiththereliabilityofconstructionisitsprobabilityoffailure,denotedbyPf.Thetwoeventsareexclusive,i.e.,Pt+Pf=1,orPt=1-Pf,whereOWPtWl,OWPfWl.Obviously,thereliabilityofconstructioncanalsobedescribedbythenrobabilitvoffailureofaconstructionproject,thatis,wecanjudgethereliabilityofaprojectfromitsprobabilityoffailurebeinglessthantheacceptablerisklevel.Asaresult,itisdesirabletoapplytheprincipleofreliabilityanalysisontotheengineeringriskmanagement,aimingtoimprovetheabilityofriskaversionforanengineeringproject.Asectionshouldbeprovidedtobrieflyintroducetherestofthepaper.ReliabilityAnalysisofConstructionObjectiveSystemsTheperformanceofanengineeringconstructionactivitycanbedefinedintermsofQuality(Q),TimeDuration(T),Safety(S),Normal(N)andCosts(C).Accordinglythereliabilityoftheconstructionactivityshouldbeexpressedasahierarchymulti-objectivesystem,withfirstlayerbeingTimeDuration(T),Safety(S),Normal(N),andsecondlayertheCosts(C).Figure1demonstratestherelationshipamongtheobjectives.Fig.lRelationmodelforobjectivesystemofconstructionactivityAsfarasaspecificconstructionprocedureisconcerned,therearesomedifferenttaskstorealizeacertainobjectiveinthefirstobjectivelayer,say,Y}.Therelationshipofthesetaskscanbecategorizedasfollowingcases.(1)Independence.Eachtaskisindependentfromtheothers,andeachcontributessomehowtotherealizationoftheobjective.However,whenthesetasksapplysimultaneously,thefollowingtaskhelpstherealizationofthecontributionfromtheprevioustask.Forexample,inthecastingofmassconcrete,thefollowingseparatetaskscontributeindependentlytothetemperaturecontrol,whichistheobjectiveoftheconstructionprocedure:addingtheconcreteadditivetoreducethehydrateheat,coveringtheplasticinordertokeepwarm,embeddingcoolingpipelines,etc.(2)Logicalcorrelation.Onlyaftertheprevioustaskcanthefollowingtaskbegin.Forexample,therelationbetweenlocalizationofformworksandthemeasure/lininginestablishingtheformworksofreinforcementconcretemembercastinsitu.(3)Thecombinationofthe(1)and(2),i.e.,thetasksarebothindependentandlogicallycorrelated.Hence,forcase(1),讦denoteby©..(OW©..W1)theeffectivenessoftheit"task。。theijiJrealizationofobjectiveYi,thenti_ilWherepti(n)isthereliabilityofobjectivewhenntasksareindependent.Forcase(2)whenmtasksareapplied,pti(m)=min{©ik/k=1,2,3,,m}⑵wherepti(m)isthereliabilityofobjectivewhenmtasksarelogicallycorrelated.Forcase(3),thetargetreliabilitycanbecalculatedfromequation(1)and(2).Supposethecostsoftheithtaskareforcase(1)andCikforcase(2),respectively.Thenforcase(3)whichisthecombinationofcase(1)andcase(2),thetotalcostforrealizingtheobjectiveY}inthefirstlayeris■nreiG二》理+工赊j=1it=i⑶Forcase(1),aftertheprevious(n-1)tasks,theadditiveeffectivenessfromthenthtask,whichcanimprovethereliabilityoftheobjectiverealization,canbederivedfromequation:wherePfi(n-i),Pfi(m)areprobabilitiesoffailureafter(n-1)andntasks,respectively.Therefore,forcase(1),weshouldchoosethemosteffectivetaskamongthealternativesbasedonthereliabilityofobjectwhichhasalreadypossessesaftertheprevioustasks.Insodoing,thefollowingtaskscanbereduced,andthecostsdeductedaccordingly.Forcase(2),however,weshouldguaranteethequalityofeachtask.Itisnotacceptabletoimproveunreasonablytheeffectivenessoftasksbecauseitwillincreasethecosts.ReliabilityAnalysisofProcedureSubsystemReliabilityCalculationofProcedureSubsystemProductasconstructionoutputismanufacturedaftertheconstructionprocedures;thereforetheunitofconstructionsystemisconstructionprocedure.Inthecontextofreliabilityanalysis,theunitconstructionprocedurespartitioningthewholeprojectcanbemodeledasaseries-parallelsystem;thesub-divisionproceduresforaunitconstructionprocedurecanalsobemodeledasseries-parallelreliabilitysystem.Basedonthereliabilityanalysistheory,theprobabilityofreliabilityofaseriesconnectionsystemwheneveryprocedureisindependentistheproductofprobabilityofeachprocedure:n巴=口号⑸wherejisnumberofconstituentconstructionproceduresoftheseriesconnectionsystem,j=l,2,…，n.Becauseeachpartoftheparallelsysteminfluencesthefeasibilityofconstructionschemeandthusthereliabilityofconstructiondirectly,whichisaparallelconnectionnon-redundantsystem,therefore,theprobabilityoffailureofaparallelconnectionconstructionsystemistheminimumoftheprobabilitiesofbranches,i.e.:P尸min{Pk,k=1,2,3,……}⑹tkWherePkistheprobabilityoffailureofkthbranch.comestoaseries-parallelsystem,thereliabilityofthewholesystemiscalculatedaftertheprobabilityofseriesconnectionbranchandparallelconnectionbrancharecalculatedbyequation(5)and(6)separately.ReliabilityImprovementApproachestoProcedureSubsystemsMostoftenmodeledreliabilitysystemsforconstructionproceduresareseries,parallelandseries-parallel.Fortheconstructionprocedurewithseriesbranches,theprobabilityofreliabilityistheproductofthereliabilityofeachconstituentsystemasshowninEq.(5).Herein,toenhancethereliabilityofthesystem,thereliabilityofeachconstructionproceduremustbeenhanced.Inaddition,emphasisshouldbeputonthoseconstructionprocedures,thereliabilityofwhichcanbeguaranteedbysomeeasymeasures.Fortheconstructionprocedurewithparallelconnection,however,itisknownfromEq.(6)thatnotonlyshouldweenhancethereliabilityofthesystemaswedoforseriesconnectionsystem,butalsoweshouldminimizethedifferenceofeachconstructionproceduretooptimizethemeasuresforreliabilityimprovement.Inaddition,numberofconstructionproceduresofproceduresubsysteminfluencesthereliabilityofthesubsystem.Eq.(5)forseriesconnectionshowsevidentlythatsystemreliabilitydependsonthenumber(i.e.,branches)ofconstructionprocedures.However,theproceduresindifferentseriesconnectionsubsystemsdonotnecessarilyhavelogiccorrelationoneachothersometimes.So,combinationoftherelatedproceduresbenefitstotheguarantyofthesystemreliabilitywhentheconstructionprocedurereliabilityisundercontrolled.ClassificationofConstructionSystemReliabilityLevelsThereliabilityrequirementsforconstructionsystemaredifferentfromthoseforthestructuraldesign.Forinstance,inbuildingstructure,weusereliabilityindexBtodescribethereliabilityofthestructure,anditsformulais⑸：where,口s,osarethemeanandstandarddeviationofactioneffectsofthestructuralcomponents;口R,oRarethemeanandstandarddeviationoftheresistanceofstructuralcomponents;thetargetreliabilityindexBisshowninTable1.Tubk1TurIpIkjL-altJmtil#limitInsLiucluralTypesdFDamageFirstSafety'LevelSecondTh:rdDuctileDamige5.73.22.7brittleDamage斗二:U3.2TheBvaluehascorrespondingrelationshipwithPfForBvalueinTable1,thecorrespondingPfisshowninTable2.Table2Cofrsspcjudiiigr«hlioiishipbetween.T^litibiLityindex丹』idprobtibilityoffailureReQciblULyInkk2.73.23.7丄FailurePrnbiibilityPt34XIt)-3fi.8X1()"10X1()41加itMXIO-6FromTable2,wecouldknowthatwhenB=2.7时,Pf=3.4X10-3,pt=l-3.4X10-3=99.66%,butfrom(5)and(6),wecouldfindthatitisextremelydifficulttosatisfythereliabilityrequirementforconstructionsystem.Takeaseriessystemforexample,iftherequiredreliabilityofeachconstructionprocedureis99%,thenumberofconstructionprocesswiththesystemreliabilityequalorhigherthan90%,islog0.91/log0.99=10.5,butthenumberofactualconstructionprocessmaybegreaterthan11.Atthistime,even讦reliabilitylevelintheconstructionprocessis"ExtremelyHigh"(accordingtothestandardsinTable3}6}),itisstillimpossibletoreach"ExtremelyHigh"insystemreliabilitylevel.Therefore,theclassificationofconstructionreliabilitylevelsandthatofstructuraldesigncannotbeidentical,anditalsotellsusthatourconstructionisprecededundercertainrisks.Thus,itisgenerallyconsideredthatwhenthereliabilityofconstructionsystemisnotlessthan0.8,thesystemreliabilityishighenough,ortheriskoftheprojectislowenough,tobeaccepted.InWe5Cfcissifkationofstructionr«Lkibi]ityr«quir#ni«ntReUnbiHtyLevelReliabilityProbibilityRiskLevelExtremelyHighO.9O-D.g9VeryLowry-i£jhO.Xil-J.NL)luowHighU.70-U.79OrdiniryLuWm的H妙VicryLow0.25-0.4?Very丨虺hExtremelyLow0.D1-0.24ExtreLiielyHighApplicationofReliabilityTheoryinConstructionRiskManagementConstructionReliability&RiskManagementInriskmanagement,riskindexisintroducedtohelpmakeriskdecisiononprojectplans.Riskindexisdefinedas⑹：R=1-PC⑻ssWherePsistheprobabilityoftheprojectsuccess,with0x1}=1-©(0.183)=1-0.5714=42.86%Fromexperiencetheprobabilityofthatthestrengthoftheconcretemadefromthecementwith58.6-62.4MPareachesthestrengthofconcretereachingC40,is95%whilethatofthecementwith52.6-58.6MPais80%.TheprobabilityofgettingC40concreteis95%X42.86%+80%X57.14%=86.43%Consideringthattheconstructionproceduresofconcretefabrication,includingpreparation,casting,andcuringareaseriessystemandthesuccessprobabilityofthemareP1,P2andP3respectively,theprobabilityforthestrengthofconcretereachingC40isPt=P1XP2XP3=86.42%X90%x90%=70.00%。ThedeterminationofriskindexandprojectplanevaluationsFromthepointofviewofprojectmanagementbalanceandthedevelopmentofthewholeenterprise,theweightforchoosingthelocalfactoryproductis80070andtheweightforeconomicalinterestsis20%.Duringtheperiodofconstruction,thelocalbrandcementwillfirstbeusedinthe#1pierandbeextendedtotherest25piersifthestrengthrequirementcanbesatisfied.Consideringthattheconcretevolumeneededfor#1pieris480m3,thatoftherest25is14400m3andthecostofeach而concretemadefrom#425willbedecreasedby30yuan(RMB),446,400yuan(RMB)totalcostcanbesavediftheconcretestrengthof#1piercansatisfythestrengthrequirement.Iftheconcretestrengthof#1piercannotreachtherequirement,however,itwillcause200,000yuan(RMB)loss.ThusC2s=44.64/(44.64+20.00)=0.69Cs=80%C1s+20%C2s=80%X1.0+20%X0.69=0.938andriskindexR=1-PsCs=1-0.7X0.938=0.3434Therefore,theriskismediumandtheplanisapplicable.Butqualitycontrolandcontingencyplanningshouldbestrengthened.ConclusionTheobjectivesystemofconstructionisalayeredmulti-objectivesystemwithobjectivesdependingoneachother.Therearethreestatusesforrelationsbetweenimplementationmeasuresofobjective{Quantity,Timelimitforaproject,Safety,Normal}onthefirstlayerofthissystem.Therelationsbetweenobjectivereliabilityandmeasureeffectivenessundersuch3statusesweresetupinthispaper.Constructionprocessisaproceduresystem,wherethereliabilityrelationsbetweenconstructionproceduresareseriesconnection,parallelconnectionandseries-parallelconnection.Thesystemreliabilitycanbecalculatedafterdeterminingoftheprocedurereliabilities.Thispaperanalysesthemethodstoenhancesystemreliabilitybasedontheprobabilitycalculationequation.Thispapershowsthattheconstructionsystemreliabilitylevelisdifferentfromthatofstructuraldesign,whichmeansthattheconstructionprocessisundergoingunderacertainriskcondition.Therefore,theriskmanagermconstructionisnecessary.Thereliabilityanalysisandcalculationofconstructionsystemlaidthefoundationofdefinitionoftheconstructionriskmanageandofferedanevaluationcriterionfortheassessmentanddecisionofconstructionscheme.Thispaperillustratestheapplicationofconstructionreliabilityanalysistotheconstructionriskmanagewithpractice.References[1]GabrielABarraza,EdwardBackW,FernandMata.ProbabitisticmonitoringofprojectperformanceusingSS-curves.JConstEngrg,ASCE,2000,March/April:144-148DengTiejun.Theestablishmentandapplicationexplorationoftheconstructionreliabilityprinciples.JournalofHunanUniversity(NaturalScienceEdition),2000,27(4):13-16DengTiejun.Reliabilityanalysismethodsinconstructionplanevaluation.TheJournalofHunanUniversity(NaturalScienceEdition),2001,28(1):88-82ThePeople'sRepublicofChinaStandards.UnifiedStandardDesignofBuildingStructures,GBJ68-84.9LuYoujie,LuJiayi.RiskManagementofProjects.Beijing:TsinghuaUniversityPress,1998.49