DOEMinitab操作教程

1、Six Sigma-1DOE Minitab操作教程 1、男球鞋案例 2、化学实验设计案例 3、传统的一次一因子实验Six Sigma-21、男球鞋案例1、资料登陆2、选择统计工具2 sample t3、图形4、选择统计工具Paired t5、图形6、为什么会得到不同的结论Six Sigma-31、资料登陆 1、把资料登陆到Minitab软件，输入资料的操作类似Excel软件，如下图：Six Sigma-42、选择统计工具2 sample t 路径：StatBasic Statistics2-Sample t 选择Samples in different columns First选择Mate

2、rial A Second选择Material B然后点击GraphsSix Sigma-5点击每一个方框，使其选中，然后单击OK。Six Sigma-6点击 到Session视窗Results for: BOYS SHOE.MTW Two-Sample T-Test and CI: Material A, Material B Two-sample T for Material A vs Material B N Mean StDev SE MeanMaterial A 10 10.63 2.45 0.78Material B 10 11.04 2.52 0.80Difference = m

3、u (Material A) - mu (Material B)Estimate for difference: -0.41000095% CI for difference: (-2.754808, 1.934808)T-Test of difference = 0 (vs not =): T-Value = -0.37 P-Value = 0.717 DF = 17H0：两种材料寿命没有差异Ha：两种材料寿命有差异P0.05,接收H0。 Six Sigma-73、图形DataMaterial BMaterial A1514131211109876Individual Value Plot

4、of Material A, Material B两种材料没有显著差异，研发处的建议被拒绝。Six Sigma-8DataMaterial BMaterial A1514131211109876Boxplot of Material A, Material B两种材料没有显著差异，研发处的建议被拒绝。Six Sigma-94、选择统计工具Paired t路径：StatBasic StatisticsPaired t选择Samples in columnsFirst sample: 选择Material ASecond sample:选择Material B然后点击GraphsSix Sigma

5、-10点击每一个方框，使其选中，然后单击OK。然后回到然后回到Session窗口：窗口：Paired T-Test and CI: Material A, Material B Paired T for Material A - Material B N Mean StDev SE MeanMaterial A 10 10.6300 2.4513 0.7752Material B 10 11.0400 2.5185 0.7964Difference 10 -0.410000 0.387155 0.12242995% CI for mean difference: (-0.686954, -0.

6、133046)T-Test of mean difference = 0 (vs not = 0): T-Value = -3.35 P-Value = 0.009H0：两种材料寿命没有差异Ha：两种材料寿命有差异PDOEFactorialCreate Factorial DesignType of Design:选择设计种类Number of Factors:选择因子数目Design：选择设计（解析度、中心点、反复数）Factor：输入名称和水准Options：（取消）随机化选项执行实验：收集实验数据Six Sigma-18Minitab：StatDOEFactorialCreate Fac

7、torial Design选择设计种类选择因子数目Six Sigma-19选择设计（解析度、中心点、反复数）DesignSix Sigma-20Factor：输入名称和水准输入名称和水准Six Sigma-21Options：（取消）随机化选项在正式实验时不能取消此项选择！此处仅教学使用正常实验要随机进行！Six Sigma-22实验矩阵因子A 因子B 因子CSix Sigma-23执行实验：收集实验数据打印实验矩阵执行实验，收集实验数据，将数据登陆到Minitab。Six Sigma-242、分析实验过程StatDOEFactorialAnalyze Factorial DesignResp

8、onse:输入回应值Terms:选取分析因子（全因子：变数和交互作用部分因子：仅变数）Graphs：主因图：常态机率和柏拉图， Cube Plot、残差图Six Sigma-25StatDOEFactorialAnalyze Factorial Design:输入回应值Six Sigma-26Terms:选取分析因子全因子选3部分因子选1或2 Six Sigma-27Graphs：选择图表Six Sigma-28效应柏拉图TermEffectBCABCCABBACA25201510508.47FactorNameATemperatureBConcentrationCCatalystPareto

9、 Chart of the Effects(response is Yield, Alpha = .05)Lenths PSE = 2.25超过红线代表效应显著Six Sigma-29常态机率图EffectPercent2520151050-5999590807060504030201051FactorNameATemperatureBConcentrationCCatalystEffect TypeNot SignificantSignificantACANormal Probability Plot of the Effects(response is Yield, Alpha = .05

10、)Lenths PSE = 2.25跳到线外的红点表示因子显著。Six Sigma-30StatDOEFactorialFactorial Plots分别选择SetupSix Sigma-31选择Responses及因子Six Sigma-32Inter action PlotTemperature4020BA756555Concentration756555CatalystTemperature160180Concentration2040Interaction Plot (data means) for YieldSix Sigma-33Main Effects Plot Mean of

11、Yield18016075706560554020BA7570656055TemperatureConcentrationCatalystMain Effects Plot (data means) for YieldSix Sigma-34Cube PlotBA4020180160CatalystConcentrationTemperature8083524568726054Cube Plot (data means) for YieldSix Sigma-353、解读实验结果解读Minitab 输出检验ANOVA表格（缩减模式，最佳模式）检验图表（交互作用、主效应、立体、残差、及等方差图）

12、考虑实际上为显著的效应（计算效应在模式中的百分比）数学模式残差分析Six Sigma-36ANOVA表格Estimated Effects and Coefficients for Yield (coded units)Term Effect CoefConstant 64.250 Temperature 23.000 11.500Concentration -5.000 -2.500 Catalyst 1.500 0.750Temperature*Concentration 1.500 0.750Temperature*Catalyst 10.000 5.000Concentration*C

13、atalyst -0.000 -0.000Temperature*Concentration*Catalyst 0.500 0.250Analysis of Variance for Yield (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 3 1112.50 1112.50 370.833 * *2-Way Interactions 3 204.50 204.50 68.167 * *3-Way Interactions 1 0.50 0.50 0.500 * *Residual Error 0 * * *Total

14、7 1317.50我们之前计算的效应我们之前计算的系数误差项目自由度为零Six Sigma-37Estimated Coefficients for Yield using data in uncoded units Term CoefConstant -85.5000Temperature 0.925000Concentration -1.52500Catalyst -71.5000Temperature*Concentration 0.00750000Temperature*Catalyst 0.425000Concentration*Catalyst -0.425000Temperatu

15、re*Concentration*Catalyst 0.00250000Alias StructureTemperatureConcentrationCatalystTemperature*ConcentrationTemperature*CatalystConcentration*CatalystTemperature*Concentration*CatalystSix Sigma-38缩减模式改变选取的项目移除最小的效应检视 机率图 柏拉图 ANOVA 表格重复移除下一个最小的效应一直持续到模式为”最佳模式”最佳模式”的提示 不需要移除太多的项目 保留一些不显著的项目已确认 没有错误的移除

16、显著的项目Six Sigma-39因子AB是否真的显著？TermStandardized EffectCABBACA7060504030201002.92FactorNameAtempBconcCcataPareto Chart of the Standardized Effects(response is yield, Alpha = .10)Six Sigma-40将Alpha设为0.01Six Sigma-41因子AB并不显著.TermStandardized EffectCABBACA7060504030201009.92FactorNameAtempBconcCcataPareto

17、Chart of the Standardized Effects(response is yield, Alpha = .01)Six Sigma-42最佳模式TermStandardized EffectCBACA25201510503.18FactorNameATemperatureBConcentrationCCatalystPareto Chart of the Standardized Effects(response is Yield, Alpha = .05)两个变数和一个交互作用统计上是显著的！Six Sigma-43最佳模式的ANOVA表格 Term Effect Coef

18、 SE Coef T PConstant 64.250 0.4564 140.76 0.000Temperature 23.000 11.500 0.4564 25.20 0.000Concentration -5.000 -2.500 0.4564 -5.48 0.012Catalyst 1.500 0.750 0.4564 1.64 0.199Temperature*Catalyst 10.000 5.000 0.4564 10.95 0.002S = 1.29099 R-Sq = 99.62% R-Sq(adj) = 99.11%Analysis of Variance for Yiel

19、d (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 3 1112.50 1112.50 370.833 222.50 0.0012-Way Interactions 1 200.00 200.00 200.000 120.00 0.002Residual Error 3 5.00 5.00 1.667Total 7 1317.50Six Sigma-44GLM分析路径：StatANOVAGeneral linear model填入要分析的变数Six Sigma-45General Linear ModelSource DF

20、 Seq SS Adj SS Adj MS F PTemperature 1 1058.00 1058.00 1058.00 634.80 0.000Concentration 1 50.00 50.00 50.00 30.00 0.012Catalyst 1 4.50 4.50 4.50 2.70 0.199Temperature*Catalyst 1 200.00 200.00 200.00 120.00 0.002Error 3 5.00 5.00 1.67Total 7 1317.50Six Sigma-46计算 ES1、在资料表中设四个栏位Source、DF 、 SS 、ES 2、自

21、session视窗复制并贴上Source、DF 、 SS 、ES 3、使用Minitab计算功能，将每一值除以Total SS值并存储结果于ESSix Sigma-47复制并贴上Source、DF 、 SS 、ES Six Sigma-48计算 ESSix Sigma-49ES代表每个变数和交互作用在总SS中所占百分比SOURCE DFSS ESTemperature 1 1058.0 0.80304Concentration 1 50.0 0.03795Catalyst 1 4.5 0.00342Temperature*Catalyst 1 200.0 0.15180Error 3 5.0

22、0.00380Total 7 1317.5 1.00000因子Temperature占百分比为80%Six Sigma-50数学模式Variable CoefConstant 64.250Temperature 11.500 Concentration -2.500Catalyst 0.750Temperature*Catalyst 5.000Yield(Y)=64.25+11.5*Temperature -2.5*Concentration+0.75*Catalyst+5* Temperature*CatalystSymbol012312有了数学模式就可以根据客户需要调整我们的Y.Six S

23、igma-51残差分析路径：StatDOEFactorialAnalyze Factorial DesignSix Sigma-52残差分析Six Sigma-53残差图ResidualPercent210-1-2999050101Fitted ValueResidual807060501.00.50.0-0.5-1.0ResidualFrequency1.00.50.0-0.5-1.02.01.51.00.50.0Observation OrderResidual876543211.00.50.0-0.5-1.0Normal Probability Plot of the Residuals

24、Residuals Versus the Fitted ValuesHistogram of the ResidualsResiduals Versus the Order of the DataResidual Plots for YieldSix Sigma-54传统的一次一因子实验思考：我们用传统的一次一因子实验来做刚才的化学实验，会得到相同的结果吗？ 下面让我们用将二个因子固定住不变，并且一次只改变一个因子的方式来做试验。 Six Sigma-55输入试验矩阵到MinitabSix Sigma-562、自定义实验设计StatDOEFactorialDefine Custom Facto

25、rial Design定义因子定义水准Six Sigma-57解读因子标准顺序实验顺序集区中心点Six Sigma-58 ParetoTermEffectBCA160140120100806040200152.5FactorNameATEMPBCONCCCATAPareto Chart of the Effects(response is Yield, Alpha = .05)Lenths PSE = 12没有考虑交互作用,没有任何因子显著Six Sigma-59常态机率图EffectPercent3020100-10-20-30999590807060504030201051FactorNa

26、meATEMPBCONCCCATAEffect TypeNot SignificantSignificantNormal Probability Plot of the Effects(response is Yield, Alpha = .05)Lenths PSE = 12没有考虑交互作用,没有任何因子显著Six Sigma-60Session输出Estimated Effects and Coefficients for Yield (coded units)Term Effect CoefConstant 59.000TEMP 12.000 6.000CONC -6.000 -3.00

27、0CATA -8.000 -4.000Analysis of Variance for Yield (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 3 243.0 243.0 81.00 * *Residual Error 0 * * *Total 3 243.0Six Sigma-61缩减模式后TermStandardized EffectCATATEMP1412108642012.71Pareto Chart of the Standardized Effects(response is Yield, Alpha = .05)Six Sigma-62缩减模式后常态机率图Standardized EffectPercent3210-1-2-3999590807060504030201051Effect TypeNot Si