Chapter19-Decision-MakingUnderRisk

SlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-1DevelopedBy:Dr.DonSmith,P.E.DepartmentofIndustrialEngineeringTexasA&MUniversityCollegeStation,TexasExecutiveSummaryVersionChapter19MoreonVariationandDecisionMakingUnderRiskSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-2LEARNINGOBJECTIVES1.Certaintyandrisk2.Variablesanddistributions3.Randomsamples4.Averageanddispersion5.MonteCarlosimulationSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-3Sct19.1InterpretationofCertainty,Risk,andUncertaintyCertainty–Everythingknowforsure;notpresentintherealworldofestimation,butcanbe‘assumed’Risk–adecisionmakingsituationwherealloftheoutcomesareknowandtheassociatedprobabilitiesaredefinedUncertainty–OnehastwoormoreobservablevaluesbuttheprobabilitiesassociatedwiththevaluesareunknownObservablevalues–statesofnatureSeeExample19.1–aboutriskSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-4TypesofDecisionMakingDecisionMakingunderCertaintyProcessofmakingadecisionwherealloftheinputparametersareknownorassumedtobeknownOutcomes–knownTermedadeterministicanalysisParametersareestimatedwithcertaintyDecisionMakingunderRiskInputsareviewedasuncertain,andelementofchanceisconsideredVariationispresentandmustbeaccountedforProbabilitiesareassignedorestimatedInvolvesthenotionofrandomvariablesSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-5TwoWaystoConsiderRiskinDecisionMakingExpectedValue(EV)analysisAppliesthenotionofexpectedvalue(Chapter18)CalculationofEVofagivenoutcomeSelectionoftheoutcomewiththemostadvantageousoutcomeSimulationAnalysisFormofgeneratingartificialdatafromassumedprobabilitydistributionsReliesontheuseofrandomvariablesandthelawsassociatedwiththealgebraofrandomvariablesSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-6Sct19.2ElementsImportanttoDecisionMakingUnderRiskTheconceptofarandomvariableAdecisionrulethatassignsanoutcometoasamplespaceDiscretevariableorContinuousvariableDiscretevariable–finitenumberofoutcomespossibleContinuousvariable–infinitenumberofoutcomesProbabilityNumberbetween0and1Expressesthe“chance”indecimalformthatarandomvariablewilltakeonanyspecificvalueSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-7TypesofRandomVariablesContinuousDiscreteSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-8Distributions-ContinuousVariablesProbabilityDistribution(pdf)AfunctionthatdescribeshowprobabilityisdistributedoverthedifferentvaluesofavariableP(Xi)=probabilitythatX=XiCumulativeDistribution(cdf)AccumulationofprobabilityoverallvaluesofavariableuptoandincludingaspecifiedvalueF(Xi)=sumofallprobabilitiesthroughthevalueXi=P(XXi)SlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-9ThreeCommonRandomVariablesUniform–equallylikelyoutcomesTriangularNormalStudyExample19.3SlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-10DiscreteDensityandCumulativeExamplepdfcdfSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-11Sct19.3RandomSamplesRandomSampleArandomsampleofsizenistheselectioninarandomfashionwithanassumedorknownprobabilitydistributionsuchthatthevaluesofthevariablehavethesamechanceofoccurringinthesampleastheyappearinthepopulationBasisforMonteCarloSimulationCansamplefrom:Discretedistributions…orContinuousdistributionsSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-12SamplingfromaContinuousDistributionFormthecumulativedistributioninclosedformfromthepdfGenerateauniformrandomnumberontheinterval{0–1},calledU(0,1)LocateU(0,1)pointony-axisMapacrosstointersectthecdffunctionMapdowntoreadtheoutcome(variablevalue)onx-axisSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-13Sct19.4ExpectedValueandStandardDeviationTwoimportantparametersofagivenrandomvariable:Mean-MeasureofcentraltendencyStandardDeviation-MeasureofvariabilityorspreadTwoConceptstoworkwithinPopulationSamplefromapopulationSlideSetstoaccompanyBlank&Tarquin,EngineeringEconomy,6thEdition,2005©2005byMcGraw-Hill,NewYork,N.YAllRightsReserved19-14SamplePopulationvsSamplePopulation-populationmean2-populationvariance-populationstandarddeviationOftensamplefromapopulationinordertomakeestimatesX2ssSamplemeanSamplevarianceSamplestandarddeviationThesevalues,properl