统计与品管质量工具以及Minitable的运用

1,2,1：统计描述2：区间估计与假设检验3：方差分析（ANOVA）4：回归分析（Regression）5：实验设计（DOE）6：质量工具（QualityTool）7：测量系统分析（MSA）,第七事业部品质部,3,描述性统计（DescriptiveStatistics）,-单值图（IndividualValuePlot)-箱图（Boxplot）-柏拉图（Pareto）-直方图（Histogram）-时间序列图（TimeSeriesPlot）-边际图（MarginalPlot）-3D表面图（3DSurfacePlot)-柱状图（BarChart）-饼图（PieChart）,第七事业部品质部,4,单值图（IndividualPlot),GraphIndividualPlot,第七事业部品质部,5,箱图（Boxplot）,Q1-1.5*（Q3-Q1）,Q3+1.5(Q3-Q1),Q3,Q1,median,GraphHistogram,Outlier,第七事业部品质部,6,直方图（Histogram）,GraphHistogram,类似茎叶图（Stem-and-Leaf),第七事业部品质部,7,柏拉图（Partochart),STATQualityToolsParetoChart,第七事业部品质部,8,时间序列图（TimeSeriesPlot）,GraphTimeSeriesPlot,第七事业部品质部,9,边际图（MarginalPlot）,为单值图和直方图/点图/箱图的综合,GraphMarginalPlot,第七事业部品质部,10,3D表面图（3DSurfacePlot),Graph3DSurfacePlot,第七事业部品质部,11,DisplayDescriptiveStatistics,StatBasicStatisticsDisplayDescriptiveStatistics,结果解释对截止12.10日的火箭队主客场得分进行了描述性统计。从结果可以看出：主场得分（mean：平均值99.60）大于客场得分（mean=94.47)。,1：数据量少3：火箭队发挥不稳定（得分）2：对手强弱分明,偏斜度,峰度,第七事业部品质部,12,区间估计与假设检验,-小概率事件-单样本Z检验（1Sample-Z）-单样本T检验（1Sample-T）-双样本T检验（2Sample-T）-成对T检验（PairedT）-相关性检验（Correlation）-方差齐性（相等）检验（EqualVariances)-正态测试（NormalityTest）-卡方检验（Chi-squaretest）,第七事业部品质部,13,总体：整个集合的全体特征,样本：具有总体特征的子集,根据样本确定总体!,为什么需要区间估计与假设检验？,区间估计与假设检验,第七事业部品质部,14,天打雷劈,小概率事件,不要破坏花花草草。打雷了，下雨了，还是收衣服好！,第七事业部品质部,15,StatBasicStats1Sample-Z,单样本Z检验（1Sample-Z）,实际显著性水平，可以把p值理解为假设的支持率或可信程度。,某段时间内，对wirebond的金线拉力（wirepull)进行了170次测量，得到均值为13.93g，方差为1.26g，能否以95%的置信度认为该段时间内wirepull均值为16g？,Testofmu=16vsnot=16Theassumedstandarddeviation=1.26NMeanSEMean95%CIZP17012.93000.0966(12.7406,13.1194)-31.770.000,置信区间(confidenceinterval)，区间估计总是与一定的概率保证相对应的,第七事业部品质部,16,StatBasicStats1Sample-T,单样本T检验（1Sample-T）,设随机变量X服从标准正态分布N(0，1)，随帆变量Y服从自由度为n的x2分布，且X与Y相互独立，则,One-SampleT:得分Testofmu=100vsnot=100VariableNMeanStDevSEMean95%CITP得分2796.37048.71851.6779(92.9215,99.8193)-2.160.040,置信区间(confidenceinterval),与Z检验的区别？,第七事业部品质部,17,双样本T检验（2Sample-T）,StatBasicStats2Sample-T,为了估计磷肥对某种农作物增产的作用，现选20块土壤条件大致相同的土地。其中10块不施磷肥.另外10块施磷肥，得到亩产量进行比较。,NMeanStDevSEMean不施磷肥10570.016.35.2施磷肥10600.026.78.4Difference=mu(不施磷肥)-mu(施磷肥)Estimatefordifference:-30.000095%CIfordifference:(-51.2082,-8.7918)T-Testofdifference=0(vsnot=):T-Value=-3.03P-Value=0.009DF=14,不相关的样本,第七事业部品质部,18,StatBasicStatsPairedT,成对T检验（PairedT）,NMeanStDevSEMean运动前1760.11762.36070.5725运动后1759.61182.33260.5657Difference170.5058820.3436400.08334595%CIformeandifference:(0.329199,0.682566)T-Testofmeandifference=0(vsnot=0):T-Value=6.07P-Value=0.000,为了估计进行运动活动后，人体体重的变化情况，选取17个人，在运动前后分别测量其体重，然后对数据进行分析,相关样本,第七事业部品质部,19,相关性检验（Correlation）,Pearsoncorrelationof得分and失分=0.279P-Value=0.158,StatBasicStatsCorrelation,没有显著的相关性，数据相互独立,第七事业部品质部,20,方差齐性（相等）检验（EqualVariances),StatANOVATestforequalvariances,FTest。对两个研究总体的总体平均数的差异进行显著性检验以外，我们还需要对两个独立样本所属总体的总体方差的差异进行显著性检验，统计学上称为方差齐性（相等）检验。,可认为方差齐性,第七事业部品质部,21,正态测试（NormalityTest）,StatBasicStatsNormalityTest,P=0.8090.05,可以认为服从正态分布,MEAN,第七事业部品质部,22,卡方检验（Chi-squaretest）,电视节目满意度调查,H0：这三组居民对电视节目的意见是一致的H1：这三组居民对电视节目的意见不一致,Chi-SquareTest:满意,比较满意,不太满意,不满意Chi-Squarecontributionsareprintedbelowexpectedcounts满意比较满意不太满意不满意Total市区315224024.008.674.333.002.0421.5511.2560.333近郊2110454024.008.674.333.000.3750.2050.0261.333远郊2011724024.008.674.333.000.6670.6281.6410.333Total7226139120Chi-Sq=10.391,DF=6,P-Value=0.109,StatTablesChi-squaretest(tableinworksheet),第七事业部品质部,23,方差分析（ANOVA）,-OneWayANOVA-TwoWayANOVA-Analysisofmeans-GeneralLinearModel,第七事业部品质部,24,一、SNKq检验二、DUNCAN检验三、TUKEY检验四、Fisher检验五、Dunnett检验六、HSUsMCB检验,“多重比较”的几种方法,第七事业部品质部,25,OneWayANOVA,One-wayANOVA:SourceDFSSMSFPFactor395.8031.933.690.036Error15129.888.66Total18225.68,从某学校同一年级中随机抽取19名学生，再将他们随机分成4组，在2周内4组学生都用120分钟复习同一组英语单词，第一组每个星期一一次复习60分钟；第二组每个星期一和三两次各复习30分钟；第三组每个星期二、四、六三次复习各20分钟；第四组每天（星期天除外）复习10分钟。2周复习之后，相隔2个月再进行统一测验，这4种复习方法的效果之间有没有显著性差异？,StatANOVAOneway(stacked)/Oneway(unstacked),第七事业部品质部,26,TwoWayANOVA,BalancedData,Two-wayANOVA:peeltestversustemperature,pressureSourceDFSSMSFPtemperature210.76195.3809514.560.002pressure22.16601.083012.930.105Interaction41.93290.483221.310.338Error93.32620.36958Total1718.1870,StatANOVATwoWayANOVA,第七事业部品质部,27,Analysisofmeans,StatANOVAAnalysisofmeans,第七事业部品质部,28,GeneralLinearModel,AnalysisofVarianceforpeeltest,usingAdjustedSSforTestsSourceDFSeqSSAdjSSAdjMSFPTemp23.51133.51131.75574.460.036Pressure23.02183.02181.51093.840.051Time11.05711.05711.05712.690.127Error124.72064.72060.3934Total1712.3108,StatANOVAGeneralLinearModel,第七事业部品质部,29,回归分析（Regression）,-回归模型-线性回归（Regression）-步进回归（Stepwish）-曲线拟合（FittedLinePlot),第七事业部品质部,30,回归模型,多元回归模型,估计多元回归方程式,多元回归方程式,扰动项，N(0,2)且Cov(i,j)=0(ij),拟合程度检验、相关系数检验、参数显著性检验(t检验)和回归方程显著性检验（F检验）,Cov(X,)=0,Cov(Xi,Xj)=0,第七事业部品质部,31,线性回归（Regression）,某种商品的需求量Y、价格X1和消费者收入X2的统计资料如所示，试估计Y对X1和X2的线性回归方程。,Theregressionequationis需求量Y（吨）=62651-979X1（元）+0.286X2（元）PredictorCoefSECoefTPVIFConstant62651401315.610.000价格X1（元）-979.1319.8-3.060.01814.6收入X2（元）0.286180.058384.900.00214.6S=1738.98R-Sq=90.2%R-Sq(adj)=87.4%AnalysisofVarianceSourceDFSSMSFPRegression21953189379765946932.290.000ResidualError7211684733024068Total9216487410,Std.ErroroftheEstimate,StatRegressionRegression,outliers,第七事业部品质部,32,逐步回归（Stepwish）,StatRegressionStepwish,Responseis需求量Y（吨）on3predictors,withN=10Step12Constant5214162651和消费者收入X2（元）0.1140.286T-Value5.194.90P-Value0.0010.002价格X1（元）-979T-Value-3.06P-Value0.018S24881739R-Sq77.1390.22R-Sq(adj)74.2787.43MallowsC-p15.65.2Bestalternatives:Variable价格X1（元）X1+10T-Value3.23-2.46P-Value0.0120.043,第七事业部品质部,33,曲线拟合（FittedLinePlot),Theregressionequationis需求量Y（吨）=46411+0.2044和消费者收入X2（元）-0.000000和消费者收入X2（元）*2S=2613.66R-Sq=77.9%R-Sq(adj)=71.6%AnalysisofVarianceSourceDFSSMSFPRegression21686688008433440012.350.005Error7478186106831230Total9216487410SequentialAnalysisofVarianceSourceDFSSFPLinear116697284226.980.001Quadratic116959580.250.634,StatRegressionFittedLinePlot,LinearQuadraticCubic,95%ConfidenceInterval,95%PredictionInterval,第七事业部品质部,34,实验设计（DesignofExperiment）,1：实验设计目的2：析因实验设计（FactorialDesign）3：部分析因实验设计（FractionalFactorial）4：田口设计（TaguchiDesign）5：表面响应（ResponseSurface）6：注意事项,第七事业部品质部,35,实验设计目的,1：确定那些参数对响应的影响最大2：确定参数设置在什么水平，以使响应达到或者尽可能靠近目标值（ontarget）3：确定参数设置在什么水平，以使响应的分散度（或方差）尽可能减小4：确定参数设置在什么水平，以使不可控参数（躁声参数）对响应的影响尽可能小,第七事业部品质部,36,析因设计（FactorialDesign）,第七事业部品质部,37,TermEffectCoefSECoefTPConstant11.16831.1259.920.000A5.36082.68041.1252.380.044B-0.1672-0.08361.125-0.070.943C-0.8197-0.40981.125-0.360.725A*B-1.9625-0.98121.125-0.870.409A*C-0.6534-0.32671.125-0.290.779B*C2.69311.34661.1251.200.266A*B*C3.17991.59001.1251.410.195S=4.50168R-Sq=55.76%R-Sq(adj)=17.05%AnalysisofVarianceforY(codedunits)SourceDFSeqSSAdjSSAdjMSFPMainEffects3117.75117.7539.251.940.2022-WayInteractions346.1246.1215.370.760.5483-WayInteractions140.4540.4540.452.000.195ResidualError8162.12162.1220.27PureError8162.12162.1220.27Total15366.45,LeastSquaresMeansforYMeanSEMeanA-18.4881.592113.8491.592B-111.2521.592111.0851.592C-111.5781.592110.7581.592A*B-1-17.5902.2511-114.9142.251-119.3852.2511112.7842.251A*C-1-18.5712.2511-114.5852.251-118.4052.2511113.1122.251B*C-1-113.0082.2511-110.1482.251-119.4952.2511112.0212.251A*B*C-1-1-17.4303.1831-1-118.5873.183-11-19.7123.18311-110.5843.183-1-117.7503.1831-1111.2403.183-1119.0593.18311114.9843.183,无Block,第七事业部品质部,38,第七事业部品质部,39,部分析因实验设计（FractionalFactorial）,第七事业部品质部,40,TermEffectCoefSECoefTPConstant12.3722.0645.990.004A8.8314.4152.0642.140.099B-1.596-0.7982.064-0.390.719C-2.009-1.0042.064-0.490.652S=5.83855R-Sq=55.36%R-Sq(adj)=21.89%AnalysisofVarianceforY(codedunits)SourceDFSeqSSAdjSSAdjMSFPMainEffects3169.1169.156.381.650.312ResidualError4136.4136.434.09PureError4136.4136.434.09Total7305.5,LeastSquaresMeansforYMeanSEMeanA-17.9572.919116.7882.919B-113.1702.919111.5742.919C-113.3772.919111.3682.919AliasStructureI+A*B*CA+B*CB+A*CC+A*B,无Block,第七事业部品质部,41,第七事业部品质部,42,田口设计（TaguchiDesign）,Taguchi设计思想参数分类：（1）控制参数（controlfactors):可以控制的参数。例如汽缸直径、单向阀等。（2）噪声参数（noisefactors）：不可控制的参数。比如，大气压力、发动机转速等。有些参数不一定完全不可控制，只是由于控制起来比较困难、成本很高，不宜控制，所以归入噪声参数指导思想：寻求使产品性能对于噪声不敏感的设计，即所谓稳健（Robust）设计，这样有利于获得性能尽可能一致的产品,Target,Target,Target,Target,第七事业部品质部,43,第七事业部品质部,44,TaguchiAnalysis:YversusA,B,C,D,EThefollowingtermscannotbeestimated,andwereremoved.A*BA*CA*DA*EB*CC*DC*ED*EResponseTableforSignaltoNoiseRatiosNominalisbest(10*Log(Ybar*2/s*2)LevelABCDE111.13011.5199.74010.26911.07729.5279.13810.91710.3889.580Delta1.6022.3811.1770.1201.497Rank21453ResponseTableforMeansLevelABCDE116.7317.6515.8716.9115.60215.4714.5616.3315.2916.60Delta1.263.090.461.631.00Rank31524,第七事业部品质部,45,因子交互作用以及布局,第七事业部品质部,46,RSM（ResponseSurfaceMethodology),Response(Original),CentrePoint(Added),AxisPoint(Added),Fittedcurve1,Fittedcurve2,PredictedPoint,OriginalPoint(Observed),第七事业部品质部,47,第七事业部品质部,48,解析度（Resolution）：ResolutionV：二因子交互作用以及主因子效应互不影响ResolutionIV：二因子交互作用有混淆，但不与主因子作用混淆ResolutionIIV：二因子交互作用与主因子作用有混淆,实验分组(Blocking)实验次序的随机化（randomization)-克服环境噪声的影响,DOE一些注意事项,做好前期的实验方案的设计,第七事业部品质部,49,质量工具（QualityTool）,控制图（ControlCharts）-Xbar-R-Xbar-S-Z-MR工序能力（CapabilityAnalysis)-Normality-Between/Within,第七事业部品质部,50,均值极差图(Xbar-R),StatControlChartsVariablesChartsforsubgroupsXbar-R,TestResultsforXbarChartofXbar-RTEST6.4outof5pointsmorethan1standarddeviationfromcenterline(ononesideofCL).TestFailedatpoints:5TestResultsforRChartofXbar-RTEST1.Onepointmorethan3.00standarddeviationsfromcenterline.TestFailedatpoints:7,第七事业部品质部,51,StatControlChartsVariablesChartsforsubgroupsXbar-S,均值方差图(Xbar-S),TestResultsforXbarChartofXbar-STEST1.Onepointmorethan3.00standarddeviationsfromcenterline.TestFailedatpoints:4TEST7.15pointswithin1standarddeviationofcenterline(aboveandbelowCL).TestFailedatpoints:19,20TestResultsforSChartofXbar-STEST1.Onepointmorethan3.00standarddeviationsfromcenterline.TestFailedatpoints:4,7,16TEST2.9pointsinarowonsamesideofcenterline.TestFailedatpoints:13,14,15,16,17,18,19,20,第七事业部品质部,52,StatControlChartsVariablesChartsforIndividualsI-MZ,单值移动I-MZ,TestResultsforIChartofI-MZTEST1.Onepointmorethan3.00standarddeviationsfromcenterline.TestFailedatpoints:10,第七事业部品质部,53,能力分析(Normal),StatQualityToolsCapabilityAnalysisNormal,第七事业部品质部,54,能力分析(Between/Within),StatQualityToolsCapabilityAnalysisBetween/Within,第七事业部品质部,55,能力分析(Sixpack),StatQualityToolsCapabilityAnalysisBetween/Within,第七事业部品质部,56,GageRunChartGageLinearityandBiasStudyGageStabilityGageRanoperatororparteffectwouldgiveyousomekindofpatternintheplot.,StatQualityToolsGageStudyGageRunChart,GageRunChart,第七事业部品质部,58,Gagelinearitytellsyouhowaccurateyourmeasurementsarethroughtheexpectedrangeofthemeasurements.Gagebiasexaminesthedifferencebetweentheobservedaveragemeasurementandareferenceormastervalue.,StatQualityToolsGageStudyGageLinearityandBiasStudy,GageLinearityandBiasStudy,第七事业部品质部,59,GR&RStudy,Gagerepeatabilityandreproducibilitystudiesdeterminehowmuchofyourobservedprocessvariationisduetomeasurementsystemvariation.,XBar-R,ANOVA,第七事业部品质部,60,Two-WayANOVATableWithInteractionSourceDFSSMSFPPart988.53349.83705506.0920.000Appraiser23.12971.5648580.5080.000Part*Appraiser180.34990.019440.4230.977Repeatability602.76030.04600Total8994.7733Two-WayANOVATableWithoutInteractionSourceDFSSMSFPPart988.53349.83705246.7060.000Appraiser23.12971.5648539.2450.000Repeatability783.11010.03987Total8994.7733,GageR&RStudy(Crossed),第七事业部品质部,61,GageR&RStudy(Crossed),GageR&R%ContributionSourceVarComp(ofVarComp)TotalGageR&R0.090717.69Repeatability0.039873.38Reproducibility0.050834.31Appraiser0.050834.31Part-To-Part1.0885892.31TotalVariation1.17928100.00StudyVar%StudyVarSourceStdDev(SD)(6*SD)(%SV)TotalGageR&R0.301171.8070527.73Repeatability0.199681.1981018.39Reproducibility0.225461.3527720.76Appraiser0.225461.3527720.76Part-To-Part1.043356.2600996.08TotalVariation1.085956.51568100.00NumberofDistinctCategories=4,第七事业部品质部,62,Lookatthe%ContributioncolumnintheGageR&RTable.ThepercentcontributionfromPart-To-Part(92.31)islargerthanthatofTotalGageR&R(7.69).Thistellsyouthatmuchofthevariationisduetodifferencesbetweenparts.WhiletheTotalGageR&R%Contributionisacceptable,thereisroomforimprovement.Forthisdata,thenumberofdistinctcategoriesisfour.AccordingtotheAIAG,youneedatleastfivedistinctcategoriestohaveanadequatemeasuringsystem.,第七事业部品质部,63,MinitaballowsustoUseGageR&RStudy(Nested)wheneachpartismeasuredbyonlyoneoperator,suchasindestructivetesting.,GageR&RStudy(Nested),SourceDFSSMSFPOperator20.004440.0022220.00390.996Part(Operator)63.440000.57333327.89190.000Repeatability90.185000.020556Total173.62944%ContributionSourceVarComp(ofVarComp)TotalGageR&R0.0205566.92Repeatability0.0205566.92Reproducibility0.0000000.00Part-To-Part0.27638993.08TotalVariation0.296944100.00,第七事业部品质部,64,StudyVar%StudyVarSourceStdDev(SD)(6*SD)(%SV)TotalGageR&R0.1433720.8602326.31Repeatability0.1433720.8602326.31Reproducibility0.0000000.000000.00Part-