6西格玛主要统计分析工具介绍

SixSigmaProcessMappingProcessMappingFishboneDiagramFishboneDiagramParetoParetoMSAMSAMinitabMinitabSixSigmaSixSigmaFMEAFMEAProcessMapping„„„„SixSigmaSixSigmaDMAICDMAIC„„‹‹SupplierSupplier‹‹InputInput‹‹//Process/ActivitiesProcess/Activities‹‹OutputOutput‹‹CustomerCustomer——„„//„„„„//——1„„SixSigmaSixSigma„„‹‹‹‹‹‹„„‹‹——1„„——1„„——1„„3000——1„„‹‹SixSigmaSixSigma‹‹‹‹SixSigmaSixSigmaERPERPBPRBPR““””““””——2„„„„‹‹——2„„y2CIPCIP——2„„‹‹SixSigmaSixSigmayyXXFishboneDiagramFishboneDiagram„„„„19531953„„CTxCTxYYyyXXFishboneDiagram1.1.CTxCTxYY2.2.yyXX3.3.4.4.FMEAFMEAFishboneDiagram——1„„22„„‹‹‹‹FishboneDiagram——1„„y2CIPCIPFishboneDiagram——1„„CIPCO2CO2y2y2FishboneDiagram——2„„SixSigmaSixSigma„„‹‹‹‹FishboneDiagram——2„„FishboneDiagram——2„„PersonnelMachinesMaterialsMethodsMeasurementsEnvironmentPersonnelMachinesMaterialsMethodsMeasurementsEnvironmentParetoDiagramPareto„„„„ParetoPareto““””„„ParetoPareto““80/2080/20””Pareto1.1.2.2.3.3.Pareto——1„„22SixSigmaSixSigma„„‹‹‹‹‹‹Pareto——1„„PersonnelMachinesMaterialsMethodsMeasurementsEnvironmentPersonnelMachinesMaterialsMethodsMeasurementsEnvironmentPareto——1„„Others3816216678170430428630645.625.99.38.43.63.43.745.671.580.989.392.996.3100.0010002000300040005000600070008000020406080100DefectCountPercentCum%PercentCountParetoChartforfactorsOthers3816216678170430428630645.625.99.38.43.63.43.745.671.580.989.392.996.3100.0010002000300040005000600070008000020406080100DefectCountPercentCum%PercentCountParetoChartforfactorsPareto——1„„‹‹SixSigmaSixSigma‹‹Pareto——2„„SixSigmaSixSigma„„‹‹‹‹‹‹Pareto——2„„Others0.170.140.150.200.900.901.154.73.94.25.524.924.931.9100.095.391.487.381.756.831.93210100806040200DefectCountPercentCum%PercentCountParetoChartforC181%Others0.170.140.150.200.900.901.154.73.94.25.524.924.931.9100.095.391.487.381.756.831.93210100806040200DefectCountPercentCum%PercentCountParetoChartforC181%„„„„„„‹‹//NN‹‹„„‹‹nn„„‹‹//„„‹‹„„‹‹„„MeanMean‹‹//„„StandardDeviationStandardDeviation‹‹//ˆ1ˆ///1µµµµxXxnxXnii∑==)(1NxNii∑=−=µσ1)ˆ(ˆ1−−==∑=nxsniiµσ„„‹‹xx21)(222)(σµσπdtexFxxut∫∞−−−=µ„„‹‹‹‹11„„‹‹„„‹‹////USLUSLLSLLSL‹‹//„„‹‹‹‹‹‹‹‹‹‹————„„//‹‹//‹‹‹‹USLUSLLSLLSL‹‹Z„„ZZUSLUSLLSLLSLUSLUSLLSLLSL„„ZZ„„ZZσµσµLSLZUSLZ−=−=SixSigmaZ6σSixSigmaZ6σZBench„„„„PPUSLUSLUSLUSL„„PPLSLLSLLSLLSL„„PPTOTTOTPPTOTTOT=P=PUSLUSL+P+PLSLLSL„„ZZBenchBenchPPTOTTOTZZ„„ZZSTSTZZLTLT1.51.5σσZbench66σ3.4PPMCpkPpk„„CpkCpk33σCpkCpk„„PpkPpkCpkCpkσPpkPpk3/minZZCpk=USLLSLµσUSLLSLσσ1σ2σ3σ34.56Short-TermCapabilityIndicesLong-TermCapabilityIndices+3s-3stermshortpsLSLUSLC−∗−=6termlongps6LSLUSLP−∗−=()()()LSLpkUSLpkpkC,CminC=()()()LSLpkUSLpkpkC,CminC=()()termshortUSLpks3xUSLC−∗−=()()termshortLSLpks3LSLxC−∗−=()()termlongUSLpks3xUSLP−∗−=()()termlongLSLpks3LSLxP−∗−=TLSLUSLMSA„„„„‹‹‹‹‹‹„„==++ƠƠ22ƠƠ22ƠƠ22„„‹‹‹‹„„‹‹//‹‹‹‹„„‹‹‹‹‹‹‹‹‹‹„„‹‹‹‹‹‹„„‹‹‹‹//Accuracy)Accuracy)‹‹11‹‹‹‹‹‹‹‹‹‹————‹‹22‹‹‹‹‹‹33‹‹‹‹‹‹‹‹44‹‹‹‹‹‹‹‹1010//2~32~31010//55GageR%RGageR%R‹‹ANOVAANOVA‹‹66‹‹••ƠƠgagegage••55••••ANOVAANOVA••ƠƠgagegage••••66‹‹ANOVAANOVA%%GR&RGR&R%Tolerance%ToleranceGageR&RGageR&R%%GR&RGR&R2.5752.575==USLUSL----LSLLSL5.155.1599%10015.5&%22==−=+==×=LSLUSLLSLUSLRGRgagegageσσσσ99%66‹‹ANOVAANOVA%%GR&RGR&R%%StudyVariationStudyVariation••15%15%••15%15%30%30%••30%30%%%StudyVariationStudyVariationANOVAANOVAGR%RGR%R100%VariationTotal×=σσgagetionStudyVaria66‹‹ANOVAANOVA••1.41σσgageparttopart×=−−66‹‹ANOVAANOVA„„„„=5„„2~4•••2——GageR&RGageR&R1010220.50.5mmmm——GageR&RGageR&RANOVAANOVAMinitabMinitabStatQualityToolsGageR%R(Crossed)StatQualityToolsGageR%R(Crossed)——GageR&RGageR&R——GageR&RGageR&RStdDevStdDevStudyStudyVarVar%Study%StudyVarVar%Tolerance%ToleranceSource(SD)(5.15*SD)(%SV)(SV/Toler)Source(SD)(5.15*SD)(%SV)(SV/Toler)TotalGageR&R0.0666150.3430632.6668.61TotalGageR&R0.0666150.3430632.6668.61Repeatability0.0359400.1850917.6237.02Repeatability0.0359400.1850917.6237.02Reproducibility0.0560880.2888527.5057.77Reproducibility0.0560880.2888527.5057.77Operator0.0302000.1555314.8131.11Operator0.0302000.1555314.8131.11Operator*Part0.0472630.2434023.1748.68Operator*Part0.0472630.2434023.1748.68PartPart--ToTo--Part0.1927810.9928294.52198.56Part0.1927810.9928294.52198.56TotalVariation0.2039651.05042100.00210.08TotalVariation0.2039651.05042100.00210.08NumberofDistinctCategories=4NumberofDistinctCategories=4——GageR&RGageR&R%%GR&RGR&R%Tolerance%Tolerance68.6168.61%%StudyVariationStudyVariation32.6632.6644——GageR&RGageR&R„„——„„„„„„//10%10%„„GageR&RGageR&R„„GageR&RGageR&R„„————„„——————„„%GageR&R30%%GageR&R30%„„GageR&RGageR&R„„ANOVAANOVAGageR&RGageR&R**„„YYXXGageR&RGageR&R„„55SixSigmaSixSigma„„==--„„‹‹‹‹‹‹SixSigma„„‹‹////P&EP&ESixSigma„„‹‹////==**==‹‹P&EP&E““””SixSigma„„SixSigmaSixSigma‹‹‹‹SixSigma„„SixSixSigmaSigma=-001~7001~7319/0.58/SixSigma67967963463456,90456,90417521752565622176,292176,292345434548888121200308930890099101,601101,6013185318555551111175,772175,7722914291410410433224,689224,689--12,52812,528--43,09643,0962891289127002700309630