Minitab(4)实验计划法-DOE[1]

實驗計劃法Minitab(4)DOESUBTRON程石良統計檢定#123456789101112131415161718192021222324252627282930y1234323445623445563453354321354y2467565656678567757577465789678y3981099810910789111210991091098109101211121110DataFrequency86421086420MeanStDevN3.6671.241306.2331.22330Variabley1y2Histogramofy1,y2NormalDataFrequency12.010.59.07.56.04.53.01.51614121086420MeanStDevN3.6671.241309.61.24830Variabley1y3Histogramofy1,y3Normaly1與y2在統計量上並無不同y1與y3在統計量上有可能不同?S2aS2bS1222222baSSS下標1代表組間變異下標2代表組內變異(殘差)21SFn1,n2分配xF4,22.52.01.51.00.50.00.60.50.40.30.20.10.0F(4,2)distribution自由度為n1與n2的F統計量:)(//2221222122222121,21forSSSSFnn樣本變異數同一母體變異數Pvalue人員A機台9.5人員A1A29.5613人員A1A2人員平均9.5613B141499.5機台平均613B281210總平均9.5總平均機台平均6139.59.5B機台機台BANOVA人員A1A2B(人員)平均SB2B14149(9-9.5)2×2=0.5B281210(10-9.5)2×2=0.5A(機台)平均6139.5SA2(6-9.5)2×2=24.5(13-9.5)2×2=24.5(4-9.5)2+(8-9.5)2+(14-9.5)2+(12-9.5)2=59機台ANOVA人員A1A2B(人員)平均SB2B14149(9-9.5)2×2=0.5B281210(10-9.5)2×2=0.5A(機台)平均6139.5SA2(6-9.5)2×2=24.5(13-9.5)2×2=24.5(4-9.5)2+(8-9.5)2+(14-9.5)2+(12-9.5)2=59機台Two-wayANOVA:yversusA,BSourceDFSSMSFPA149495.440.258B1110.110.795Error199Total359One-wayANOVA:yversusASourceDFSSMSFPA149499.80.089Error2105Total359One-wayANOVA:yversusBSourceDFSSMSFPB1110.030.870Error25829Total3592樣本ANOVA總變異sT2A因子變異sA2B因子變異sB2C因子變異sC2殘差變異se2…..人員A1A2B(人員)平均SB2B13,513,159(9-9.5)2×4=1B27,911,1310(10-9.5)2×4=1A(機台)平均6139.5SA2(6-9.5)2×4=49(13-9.5)2×4=49機台(3-9.5)2+(5-9.5)2+(13-9.5)2+(15-9.5)2+(7-9.5)2+(9-9.5)2+(11-9.5)2+(13-9.5)2=126ANOVASourceDFSSMSFPA1989849.000.002B1221.000.374Interaction118189.000.040Error482Total7126S=1.414R-Sq=93.65%R-Sq(adj)=88.89%AnalysisofVarianceforRegressionSourceDFSSMSFPRegression210050.09.620.019ResidualError5265.2LackofFit11818.09.00.040PureError482.0Total7126組內變異(隨機誤差)組內變異(隨機誤差)組間變異(A因子)組間變異(B因子)無法解析的變異8=(3-4)2+(5-4)2+(7-8)2+(9-8)2+…(13-12)2SourceSumSquareD.F.MeanSquareF-valuep-value層間A0.170220.085111.80.000012片間B0.5841100.05848.10.000000片內C19.390582.4238336.00.000000殘差e1.99082760.0072St22.1356296事實上都有影響—進行單要因可能會有迷失22因子設計B-1/5-8因子符號12濃度(g/L)A6090觸媒(g/L)B1020AB11282527121819232132363222313029水準產量(g/L)Source:SixSigmaBB訓練教材B-1/5-8ABy11282132121822311125213612192230112721321223222922因子設計22因子設計22因子設計22因子設計22因子設計22因子設計22因子設計22因子設計22因子設計22因子設計22因子設計StdOrderRunOrderCenterPtBlocksAcBcyRESI1111111281.3333322112132-1.3333333111218-244112231155111125-1.66667661121362.6666777111219-1881122300991111270.333331010112132-1.33333111111122331212112229-122因子設計22因子設計RESI1Percent43210-1-2-3-4999590807060504030201051Mean0.2142.664535E-15StDev1.688N12AD0.460P-ValueProbabilityPlotofRESI1NormalP-value=0.2140.05符合常態性假設22因子設計FactorialFit:yversusAc,BcEstimatedEffectsandCoefficientsfory(codedunits)TermEffectCoefSECoefTPConstant27.5000.571348.140.000Ac8.3334.1670.57137.290.000Bc-5.000-2.5000.5713-4.380.002Ac*Bc1.6670.8330.57131.460.183S=1.97906R-Sq=90.30%R-Sq(adj)=86.66%AnalysisofVariancefory(codedunits)SourceDFSeqSSAdjSSAdjMSFPMainEffects2283.333283.333141.66736.170.0002-WayInteractions18.3338.3338.3332.130.183ResidualError831.33331.3333.917PureError831.33331.3333.917Total11323.000EstimatedCoefficientsforyusingdatainuncodedunitsTermCoefConstant30.0000Ac3.33333Bc-10.0000Ac*Bc3.3333322因子設計TermStandardizedEffectABBA8765432102.306FactorNameAABBParetoChartoftheStandardizedEffects(responseisy,Alpha=.05)StandardizedEffectPercent7.55.02.50.0-2.5-5.0999590807060504030201051FactorNameAABBEffectTypeNotSignificantSignificantBANormalProbabilityPlotoftheStandardizedEffects(responseisy,Alpha=.05)22因子設計ResidualPercent5.02.50.0-2.5-5.0999050101FittedValueResidual3530252020-2ResidualFrequency3210-1-243210ObservationOrderResidual12111098765432120-2NormalProbabilityPlotoftheResidualsResidualsVersustheFittedValuesHistogramoftheResidualsResidualsVersustheOrderoftheDataResidualPlotsfory22因子設計LeastSquaresMeansforyMeanSEMeanAc123.330.8079231.670.8079Bc130.000.8079225.000.8079Ac*Bc1126.671.14262133.331.14261220.001.14262230.001.142622因子設計22因子設計22因子設計Meanofy213231302928272625242321AcBcMainEffectsPlot(datameans)foryBcMean213432302826242220Ac12InteractionPlot(datameans)fory22因子設計22因子設計22因子設計AcBc3230282624221.00.50.0-0.5-1.01.00.50.0-0.5-1.0ContourPlotofyvsBc,Ac120y02530Bc35-10-11AcSurfacePlotofyvsBc,Ac22因子設計(練習)B-1/5-50因子符號12鑽徑(um)A150300轉速(krpm)B1020AB1118.218.912.914.41215.914.515.114.22127.22422.422.5224143.936.339.9水準孔徑誤差(um)ABy1118.21118.91112.91114.41215.91214.51215.11214.22127.221242122.42122.522412243.92236.32239.9Source:SixSigmaBB訓練教材B-1/5-5022因子設計(練習)EstimatedEffectsandCoefficientsfory(codedunits)TermEffectCoefSECoefTPConstant23.8310.611238.990.000A16.6388.3190.611213.610.000B7.5373.7690.61126.170.000A*B8.7134.3560.61127.130.000S=2.44476R-Sq=95.81%R-Sq(adj)=94.76%AnalysisofVariancefory(codedunits)SourceDFSeqSSAdjSSAdjMSFPMainEffects21334.481334.48667.241111.640.0002-WayInteractions1303.63303.63303.63150.800.000ResidualError1271.7271.725.977PureError1271.7271.725.977Total151709.8323因子設計(練習)B-1/5-35因子符號12碳酸濃度(g/L)A26噴壓(kg/cm2)B1.52.5線速(m/min)C23水準乾膜顯開寬度(與設計值相減)ABCy111-3111-1112-11120121-1121012211221211021112122212122