用于監(jiān)測相關(guān)數(shù)據(jù)的AEWMA控制圖.pdf

1、摘要在對(duì)相關(guān)數(shù)據(jù)進(jìn)行監(jiān)測時(shí)，通常是對(duì)相關(guān)數(shù)據(jù)建立模型，根據(jù)模型的預(yù)報(bào)得到殘差控制圖.然而，在數(shù)據(jù)均值發(fā)生漂移后，殘差的動(dòng)態(tài)響應(yīng)使我們難于選擇一種合適的控制圖.這篇論文中，我們提出使用AEWMA控制圖作為一種新的基于預(yù)報(bào)的監(jiān)測方案，并用隨機(jī)模擬的方法對(duì)不同的ARMA(11)AR(1)MA(1)序列比較該新控制圖與以往控制圖，發(fā)現(xiàn)在大多數(shù)情形下AEWMA控制圖有更好的監(jiān)測結(jié)果.關(guān)鍵詞:相關(guān)數(shù)據(jù)基于預(yù)報(bào)的監(jiān)測平均運(yùn)行長度累積分布函數(shù)預(yù)報(bào)恢復(fù)自

2、適應(yīng)的指數(shù)加權(quán)移動(dòng)平均1IntroductionConsidertheproblemofmonitoringaprocessforwhichobservationaldataaresignificantlyautocorrelated.Oneapproachtomonitoringsuchaprocessistousecontrolchartsbasedonresiduals.Aforecastbasedmonitoringscheme

3、involvesidentifyingthepropertimeseriesmodelwhichcharacterizesaprocessobtainingtheappropriateBoxJenkinsonestepahead(OSA)forecastofprocessobservationsandthenapplyingcontrolchartsforiiddatatoforecasterrors(AlwanandRoberts(1

4、988)WardellMoskowitzandPlante(1994)LinandAdams(1996)LuandReynolds(1999a1999b2001)DyerAdamsandConerly(2003)).Iftheassumedtimeseriesmodeliscorrecttheforecasterrorsareiidnormalrandomvariables.Henceincontrolperformanceofthes

5、econtrolchartingtechniquesispredictable.Howeverwhentheprocessstartstobeoutofcontrolourforecastsquicklyadapttochangeintheprocess.Thetendencyoftheforecaststorecoverfromprocessshiftiscalledforecastrecovery.Ryan(1991)Harrisa

6、ndRoss(1991)AdamsWoodallandSuperville(1994)SupervilleandAdams(1994)VanderWiel(1996)TsengandAdams(1996)andHuandRoan(1996)discusstheimpactofrecoveryratesontheARLsofcontrolchartsappliedtoforecasterrorsSupervilleandAdams(199

7、4)recommendtheuseofthecumulativedistributionfunction(CDF)oftherunlengthasameaningfulcriterionforcomparingtheperformanceofmonitoringschemes.AsweknowagoodcontrolchartshouldhavelowARLsandhighCDFvalues.InDyerAdamsandConerly(

8、2003)thecombinedEWMAShewhart(CES)chartisrecommendedforuseinprocesseswhichproduceforecasterrorsexperiencingrelativelyextremelevelsofsustainedforecastrecoverywhilethereversemovingaveragecontrolchartisrecommendedforuseinpro

9、cesseswhichproduceforecasterrorsexperiencinglowlevelsofsustainedforecastrecovery.Thispaperfocusesontheusageofanadaptiveexponentiallyweightedmovingaverage(AEWMA)controlchartasanewschemetoinvestigateforecastrecovery.Perfor

10、mancecriteriaareevaluatedbasedonARLCDFaswellasMRLabettermeasureofcentraltendencyforskeweddistributionssuchastherunlengthdistribution.Section2containsadescriptionoftheprocessmodels.Section3brieflyintroducesthetraditionalc

11、ontrolchartsbasedonresiduals.Insection4theAEWMAcontrolchartappliedtoforecasterrorisprovided.Insection5wemakesimulationsandbasedoncomparisongiverecommendationsforchoosingappropriatechartsaccordingtorecoveryrateandsustaine