基于Matlab-Simulink的Weibull分布的极大似然估计

29420114HENANSCIENCEVol.29No.4Apr.20112011-01-28305000221963－.1004-3918201104-0466-03Matlab/SimulinkWeibull450002WeibullMLESimulink“”MLEWeibullMLE.WeibullMLE.WeibullMatlabSimulinkTB114.3AWeibullWeibullW．[1]WeibullWeibullWeibullWeibullWeibull.MLEWeibull[2].WeibullMLE.[3-9].Simulink、.Simulink[10].SimulinkWeibullMLESimulink“”WeibullMLE.1WeibullWeibullft=mηt-γηm-1·exp-t-γηmt≥γ1mm＞0ηη＞0γγ≥0γ＝0Weibulltt≥γ.Weibullnt1≤t2≤…≤tn.WeibulllnLtmηγ=nlnm-lnη+m-1ni=1Σlnti-γη-ni=1Σti-γηm2坠lnL坠m坠lnL坠γ坠lnL坠η201141m-ni=1Σti-γmlnti-γni=1Σti-γm+1nni=1Σlnti-γ=0m-1mni=1Σ1ti-γ-nni=1Σti-γm-1ni=1Σti-γm=0ηm=1nni=1Σti-γmΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣΣ.m赞η赞γ赞3～5m赞η赞γ赞、、.2WeibullMLESimulink2．1SimulinkSimulink、.3～5SimulinkSimulink1.ConstantMatlabt＝t1t2…tn34AlgebraicConstraintm赞γ赞SwitchWeibull23WeibullWeibull0Displaym赞η赞γ赞.Simulink.1WeibullMLESimulinkFig.1SimulinkmodelofWeibulldistributionofMLE2．235384043454748505254555760616365345Matlab/SimulinkWeibull467--29467737784104[11].WeibullWeibull.MtalabSimulinkMtalab＞＞t＝3538404345474850525455576061636567737784Simulink“AlgebraicConstraint”130.“Startsimulation”、、m赞=1.857η赞=26.21γ赞=32.38.3MatlabWeibullwblfitMLEWeibull.SimulinkWeibullWeibullWeibullWeibull.WeibullMLEWeibullMLE[12-13].2.Wbllike.1HallinanAJ．AreviewoftheWeibullDistributionJ．JournalofQualityTechnology199325285－93.2．M．1984.3QiaoHZTsokosCP．EstimationofthethreeparameterWeibullprobabilitydistributionJ．MathematicsandComputersinSimulation1995391－2173－185．4GoveJHFairweatherSE．MaximumlikelihoodestimationofWeibullfunctionparametersusingageneralinteractiveoptimizerandgroupeddataJ．ForestEcologyandManagement198928161－69．5．WeibullJ．1987453374－375．6．WeibullJ．200425539-42．7．WeibullJ．200739131－34.8．MATLABJ．20071100－103.9TanZhibin．AnewapproachtoMLEofWeibulldistributionwithintervaldataJ．ReliabilityEngineering＆SystemSafety2009941394－403.10．Matlab7．0/Simulink6．0M．2005.11．J.198622485-87.12LemonGH．MaximumlikelihoodestimationsforthethreeparametersWeibulldistributionbasedoncensoredsamplesJ．Technmetrics1975172247－254．13．J．19962521－8.MaximumLikelihoodEstimationwithWeibullDistributionBasedonMatlab/SimulinkShiJingzhaoShaoRuinaChenXinchangHenanAgriculturalUniversityZhengzhou450002ChinaAbstractInthispaperusingSimulinkgraphicalmodelingmethoddirectlypaintsaWeibulldistributionofMLEmodelandmodifytheparametersofeachmoduletocompletethe3parameterWeibulldistributionofMLE．Theexampleshowsthattheapproachisfeasibleandtheresultisreliable．Modelalsousedas2parametersWeibulldistribution．KeywordsreliabilityWeibulldistributionmaximumlikelihoodestimationMatlabSimulink468--