Robustness of the EWMA Control Chart to Non-normality for Autocorrelated Processes

摘要

Mostcommonlyusedcontrolchartsformonitoringqualitycharacteristicsoftheprocessesweredevelopedundertheassumptionthattheobservationsarerandomlysampledfromanormalpopulation.Itiswellknownthatthesecontrolchartshavemorefalsealarmsthanusualwhenprocessesarepositivelyautocorrelated.Oneremedyistoadjustthecontrollimitssuchthatthemodifiedcontrolchartscanachieveanaboutrightfalse-alarmrate.Inthispaper,weinvestigatetherobustnessofsuchmodifiedindividualsShewhartcontrolchartandmodifiedexponentiallyweightedmovingaverage(EWMA)controlcharttotheusualnormalityassumptionofthewhitenoiseterminanAR(1)processwithpositiveautocorrelation.Theperformancesofthecontrolchartsunderstudyareevaluatedonthebasisoftheaveragerunlength(ARL)curves.ItisfoundthatthemodifiedEWMAcontrolchartismorerobusttothenormalityassumptionthanthemodifiedindividualsShewhartcontrolchartintermsofthein-controlARLforsomeheavy-tailedsymmetricdistributionsandsomeskeweddistributions.ResultsalsoshowthatthechoiceoftheEWMAsmoothingparameterAisverycrucialtotheARLperformance.However,choosinganappropriatevalueforλisnoteasyandmanypractitionersmaysimplychooseavalueof0.1or0.2,whicharevaluescommonlysuggestedforthestandardEWMAchartsdesignedforindependentnormaldata.Unfortunately,themodifiedEWMAcontrolchartwiththesepopularvaluesofλdoesnotperformwellenoughforsomeofthepositivelyautocorrelatednon-normaldatainourstudy.Inapreliminarystudyforimprovingtherobustness,weconsidertwocontrolchartswithdataaveragingschemescalledthemoving-averageEWMAchartandsubgroup-averageEWMAchart,respectively.Asmallsimulationstudyshowsthatthesubgroup-averageEWMAcontrolchartwiththesamena?vechoiceofλ=0.1or0.2indeedoutperformsthemodifiedEWMAcontrolchartwithatradeoffofslightinefficiencyonthedetectingpowerforthecaseunderstudy.