统计课程小结

LETDATATELLYOUStatistics,Dataanalysis,AnddecisionG5groupForQTMPresentationG5

Industry

Co.,

Ltd.HEREISACOMPANYIt’sbusinessscopeisAllkindsofmetalstampings22.1%53.6%11.4%12.2%ThemainproductsNotebookCarcomponents

SmartphoneSeverTHEREISACONTRACTNOW:BUT,ITREQUIRETHEPRICETOREDUCEFOR15%.DOYOUSIGNTHECONTRACT?THEN,YOUNEEDTHEDATATOCOMPILESTATISTICSTOANALYSETOMAKETHEDECISIONPartI:TOCOMPILESTATISTICSWecollecttheforty-twodays’datafromthefactoryInthissituation,itseemsthattheprojectwillbelossifyouacceptthecontract.SummarymeasuresforselectedvariablesDPPM:Thenumberofdefectsinmillionofproducts.Amount_DefectsDPPMCost_per_unitGrossprofitCount42.00042.00042.00042.00042.000Mean152423.0715177.35734902.448103.620-0.770Median146488.5005314.00036283.407103.765-0.915Standarddeviation32504.848683.0645786.5950.6210.621Minimum101125.0003734.00024627.068102.525-1.935Maximum213720.0006356.00045661.392104.7850.325Fromthedata,wecangetthefollowinginformation

So,weshouldusetheseinformationtofurtheranalyzetheissue.PartII:DATAANALYSISAccordingtothedata,thediagramcanbedraw

Fromthediagramwecanfindthegrossprofitratioisinverserelativewiththedefectsratio.Then,WewillthroughtheregressionanalysistofindthelinearequationFromtheF-testandT-test,wegetthep-value<SignificantLevel0.05andtheR-square=0.9435,alltheseindicatetheDPPMandtheprofitissignificantcorrelation.FromtheScatterdiagramwecanfindtheDPPMandtheprofitislinearcorrelation.Now,wecangetthelinearequation.Profit=1.9951-0.0001*DPPMSo,DPPMshoulddownto19951andbelow.

TheDPPMisnormaldistribution.Thebiggestvalueoffrequencyappearnearthemean.NOW,WEWILLANALYSETHEDATAOFDPPM

HypothesisTestingTheDPPMdataasindependentsampleswereanalyzedbyTtest.Assumption:H0<=19951Ha>19951For19951isthebreak-evenpointP<SignificantLevel5%WerejectH0andacceptHa,soforthepopulationDMMPwillmorethan19951.Ifacceptthecontractwemustimprovetheproject.SOLUTION1SOLUTION3SOLUTION2IMPROVEMENTTherearethreesolutionstobechoosefortheimprovementSOLUTION1SOLUTION3SOLUTION2Wetestthreesolutionsrespectively,andobtaintherelevantdataThroughANOVA,wegetthep-value<Significantlevel0.05,sotheH0willberejected,thenthreesolutionissignificantdifference.AndtheDMMPsamplemeansofeverysolutionareallunderthebreak-evenpoint19951.Allsolutionisfeasible.Howtochoosethesolution,weneeddecisionsPartIII:MAKETHEDECISIONItisestimatedbyexpert,Wegottheexpectedreturnsofeachsolution

SucceedFailureSolution181Solution2143Solution3102TheexpectedreturnsofeachsolutionWEMAKETHEDECISIONTREETHEoptimaldecisionisSignthecontractandchoosethesolution2tomakeimprovement.Afterimprovement,wecollectedaboutthirtydays’datatocheck.Usethethirtydays’data,wedrawtheP-controlchartFromtheP-chartweknowtheproductiveprocessisinthecontrol.Resultsforone-sampleanalysisforDPPMSummarymeasuresSamplesize30Samplemean3773.462Samplestandarddeviation1051.409ConfidenceintervalformeanConfidencelevel95.0%Samplemean3773.462Stderrorofmean191.960Degreesoffreedom29Lowerlimit3380.860Upperlimit4166.065Usethedataafterimprovement,wecanestimatetheDPPMinnewsituation.Accordingthesampledata,wegetthelowerandupperlimitin95%confidencelevel.Thenusethereturnfun