质量工具以及Minitable的运用.ppt

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（Quality Tool） 7：测量系统分析（MSA）,第七事业部品质部,3,描述性统计（ Descriptive Statistics）,-单值图（Individual Value Plot) -箱图（Boxplot） -柏拉图（Pareto） -直方图（Histogram） -时间序列图（Time Series Plot） -边际图（Marginal Plot） -3D表面图（3D Surface Plot) -柱状图（Bar Chart） -饼图（Pie Chart）,第七事业部品质部,4,单值图（Individual Plot),Graph Individual Plot,5,箱图（Boxplot）,Q1-1.5*（Q3-Q1）,Q3 + 1.5 (Q3 - Q1),Q3,Q1,median,Graph Histogram,Outlier,第七事业部品质部,6,直方图（Histogram）,Graph Histogram,类似茎叶图（Stem-and-Leaf ),第七事业部品质部,7,柏拉图（Parto chart),STAT Quality Tools Pareto Chart,第七事业部品质部,8,时间序列图（Time Series Plot）,Graph Time Series Plot,第七事业部品质部,9,边际图（Marginal Plot）,为单值图和直方图/点图/箱图的综合,Graph Marginal Plot,第七事业部品质部,10,3D表面图（3D Surface Plot),Graph 3D Surface Plot,第七事业部品质部,11,Display Descriptive Statistics,Stat Basic Statistics Display Descriptive Statistics,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（1 Sample-Z） -单样本T检验（1 Sample-T） -双样本T检验（2 Sample-T） -成对T检验（Paired T） -相关性检验（Correlation） -方差齐性（相等）检验（Equal Variances) -正态测试（Normality Test） -卡方检验（Chi-square test）,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,Stat Basic Stats 1 Sample-Z,单样本Z检验 （1 Sample-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wire bond的金线拉力（wire pull)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wire pull均值为16g？,Test of mu = 16 vs not = 16 The assumed standard deviation = 1.26 N Mean SE Mean 95% CI Z P 170 12.9300 0.0966 (12.7406, 13.1194) -31.77 0.000,置信区间(confidence interval)，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,Stat Basic Stats 1 Sample-T,单样本T检验 （1 Sample-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-Sample T: 得分 Test of mu = 100 vs not = 100 Variable N Mean StDev SE Mean 95% CI T P 得分 27 96.3704 8.7185 1.6779 (92.9215, 99.8193) -2.16 0.040,置信区间(confidence interval),与Z检验的区别？,第七事业部品质部,17,双样本T检验 （2 Sample-T）,Stat Basic Stats 2 Sample-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。,N Mean StDev SE Mean 不施磷肥 10 570.0 16.3 5.2 施磷肥 10 600.0 26.7 8.4 Difference = mu (不施磷肥) - mu (施磷肥) Estimate for difference: -30.0000 95% CI for difference: (-51.2082, -8.7918) T-Test of difference = 0 (vs not =): T-Value = -3.03 P-Value = 0.009 DF = 14,不相关的样本,第七事业部品质部,18,Stat Basic Stats Paired T,成对T检验 （Paired T）,N Mean StDev SE Mean 运动前 17 60.1176 2.3607 0.5725 运动后 17 59.6118 2.3326 0.5657 Difference 17 0.505882 0.343640 0.083345 95% CI for mean difference: (0.329199, 0.682566) T-Test of mean difference = 0 (vs not = 0): T-Value = 6.07 P-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）,Pearson correlation of 得分 and 失分 = 0.279 P-Value = 0.158,Stat Basic Stats Correlation,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（Equal Variances),Stat ANOVA Test for equal variances,F Test。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（Normality Test）,Stat Basic Stats Normality Test,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-square test）,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-Square Test: 满意, 比较满意, 不太满意, 不满意 Chi-Square contributions are printed below expected counts 满意 比较满意 不太满意 不满意 Total 市区 31 5 2 2 40 24.00 8.67 4.33 3.00 2.042 1.551 1.256 0.333 近郊 21 10 4 5 40 24.00 8.67 4.33 3.00 0.375 0.205 0.026 1.333 远郊 20 11 7 2 40 24.00 8.67 4.33 3.00 0.667 0.628 1.641 0.333 Total 72 26 13 9 120 Chi-Sq = 10.391, DF = 6, P-Value = 0.109,Stat Tables Chi-square test (table in worksheet),第七事业部品质部,23,方差分析（ANOVA）,- One Way ANOVA - Two Way ANOVA - Analysis of means - General Linear Model,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、HSUs MCB检验,“多重比较”的几种方法,第七事业部品质部,25,One Way ANOVA,One-way ANOVA: Source DF SS MS F P Factor 3 95.80 31.93 3.69 0.036 Error 15 129.88 8.66 Total 18 225.68,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？,Stat ANOVA One way (stacked)/One way (unstacked),第七事业部品质部,26,Two Way ANOVA,Balanced Data,Two-way ANOVA: peel test versus temperature, pressure Source DF SS MS F P temperature 2 10.7619 5.38095 14.56 0.002 pressure 2 2.1660 1.08301 2.93 0.105 Interaction 4 1.9329 0.48322 1.31 0.338 Error 9 3.3262 0.36958 Total 17 18.1870,Stat ANOVA Two Way ANOVA,第七事业部品质部,27,Analysis of means,Stat ANOVA Analysis of means,第七事业部品质部,28,General Linear Model,Analysis of Variance for peel test, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Temp 2 3.5113 3.5113 1.7557 4.46 0.036 Pressure 2 3.0218 3.0218 1.5109 3.84 0.051 Time 1 1.0571 1.0571 1.0571 2.69 0.127 Error 12 4.7206 4.7206 0.3934 Total 17 12.3108,Stat ANOVA General Linear Model,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（Fitted Line Plot),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。,The regression equation is 需求量Y（吨） = 62651 - 979 X1（元） + 0.286 X2（元） Predictor Coef SE Coef T P VIF Constant 62651 4013 15.61 0.000 价格X1（元） -979.1 319.8 -3.06 0.018 14.6 收入X2（元） 0.28618 0.05838 4.90 0.002 14.6 S = 1738.98 R-Sq = 90.2% R-Sq(adj) = 87.4% Analysis of Variance Source DF SS MS F P Regression 2 195318937 97659469 32.29 0.000 Residual Error 7 21168473 3024068 Total 9 216487410,Std. Error of the Estimate,Stat Regression Regression,outliers,第七事业部品质部,32,逐步回归（Stepwish）,Stat Regression Stepwish,Response is 需求量Y（吨） on 3 predictors, with N = 10 Step 1 2 Constant 52141 62651 和消费者收入X2（元） 0.114 0.286 T-Value 5.19 4.90 P-Value 0.001 0.002 价格X1（元） -979 T-Value -3.06 P-Value 0.018 S 2488 1739 R-Sq 77.13 90.22 R-Sq(adj) 74.27 87.43 Mallows C-p 15.6 5.2 Best alternatives: Variable 价格X1（元） X1+10 T-Value 3.23 -2.46 P-Value 0.012 0.043,第七事业部品质部,33,曲线拟合（Fitted Line Plot),The regression equation is 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）*2 S = 2613.66 R-Sq = 77.9% R-Sq(adj) = 71.6% Analysis of Variance Source DF SS MS F P Regression 2 168668800 84334400 12.35 0.005 Error 7 47818610 6831230 Total 9 216487410 Sequential Analysis of Variance Source DF SS F P Linear 1 166972842 26.98 0.001 Quadratic 1 1695958 0.25 0.634,Stat Regression Fitted Line Plot,Linear Quadratic Cubic,95%Confidence Interval,95%Prediction Interval,第七事业部品质部,34,实验设计（Design of Experiment）,1：实验设计目的 2：析因实验设计（Factorial Design） 3：部分析因实验设计（Fractional Factorial） 4：田口设计（Taguchi Design） 5：表面响应（Response Surface ） 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（on target） 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（Factorial Design）,第七事业部品质部,37,Term Effect Coef SE Coef T P Constant 11.1683 1.125 9.92 0.000 A 5.3608 2.6804 1.125 2.38 0.044 B -0.1672 -0.0836 1.125 -0.07 0.943 C -0.8197 -0.4098 1.125 -0.36 0.725 A*B -1.9625 -0.9812 1.125 -0.87 0.409 A*C -0.6534 -0.3267 1.125 -0.29 0.779 B*C 2.6931 1.3466 1.125 1.20 0.266 A*B*C 3.1799 1.5900 1.125 1.41 0.195 S = 4.50168 R-Sq = 55.76% R-Sq(adj) = 17.05% Analysis of Variance for Y (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 3 117.75 117.75 39.25 1.94 0.202 2-Way Interactions 3 46.12 46.12 15.37 0.76 0.548 3-Way Interactions 1 40.45 40.45 4 0.45 2.00 0.195 Residual Error 8 162.12 162.12 20.27 Pure Error 8 162.12 162.12 20.27 Total 15 366.45,Least Squares Means for Y Mean SE Mean A -1 8.488 1.592 1 13.849 1.592 B -1 11.252 1.592 1 11.085 1.592 C -1 11.578 1.592 1 10.758 1.592 A*B -1 -1 7.590 2.251 1 -1 14.914 2.251 -1 1 9.385 2.251 1 1 12.784 2.251 A*C -1 -1 8.571 2.251 1 -1 14.585 2.251 -1 1 8.405 2.251 1 1 13.112 2.251 B*C -1 -1 13.008 2.251 1 -1 10.148 2.251 -1 1 9.495 2.251 1 1 12.021 2.251 A*B*C -1 -1 -1 7.430 3.183 1 -1 -1 18.587 3.183 -1 1 -1 9.712 3.183 1 1 -1 10.584 3.183 -1 -1 1 7.750 3.183 1 -1 1 11.240 3.183 -1 1 1 9.059 3.183 1 1 1 14.984 3.183,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（Fractional Factorial）,第七事业部品质部,40,Term Effect Coef SE Coef T P Constant 12.372 2.064 5.99 0.004 A 8.831 4.415 2.064 2.14 0.099 B -1.596 -0.798 2.064 -0.39 0.719 C -2.009 -1.004 2.064 -0.49 0.652 S = 5.83855 R-Sq = 55.36% R-Sq(adj) = 21.89% Analysis of Variance for Y (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 3 169.1 169.1 56.38 1.65 0.312 Residual Error 4 136.4 136.4 34.09 Pure Error 4 136.4 136.4 34.09 Total 7 305.5,Least Squares Means for Y Mean SE Mean A -1 7.957 2.919 1 16.788 2.919 B -1 13.170 2.919 1 11.574 2.919 C -1 13.377 2.919 1 11.368 2.919 Alias Structure I + A*B*C A + B*C B + A*C C + 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（Taguchi Design）,Taguchi设计思想 参数分类： （1）控制参数（control factors):可以控制的参数。例如汽缸直径、单向阀等。 （2）噪声参数（noise factors）：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,Taguchi Analysis: Y versus A, B, C, D, E The following terms cannot be estimated, and were removed. A*B A*C A*D A*E B*C C*D C*E D*E Response Table for Signal to Noise Ratios Nominal is best (10*Log(Ybar*2/s*2) Level A B C D E 1 11.130 11.519 9.740 10.269 11.077 2 9.527 9.138 10.917 10.388 9.580 Delta 1.602 2.381 1.177 0.120 1.497 Rank 2 1 4 5 3 Response Table for Means Level A B C D E 1 16.73 17.65 15.87 16.91 15.60 2 15.47 14.56 16.33 15.29 16.60 Delta 1.26 3.09 0.46 1.63 1.00 Rank 3 1 5 2 4,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（Response Surface Methodology),Response (Original),Centre Point (Added),Axis Point (Added),Fitted curve 1,Fitted curve 2,Predicted Point,Original Point (Observed),第七事业部品质部,47,第七事业部品质部,48,解析度（Resolution）： Resolution V： 二因子交互作用以及主因子效应互不影响 Resolution IV：二因子交互作用有混淆，但不与主因子作用混淆 Resolution IIV：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（Quality Tool）,控制图（Control Charts） -Xbar-R -Xbar-S -Z-MR 工序能力（Capability Analysis) -Normality -Between/Within,第七事业部品质部,50,均值极差图(Xbar-R),Stat Control Charts Variables Charts for subgroups Xbar-R,Test Results for Xbar Chart of Xbar-R TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL). Test Failed at points: 5 Test Results for R Chart of Xbar-R TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 7,第七事业部品质部,51,Stat Control Charts Variables Charts for subgroups Xbar-S,均值方差图(Xbar-S),Test Results for Xbar Chart of Xbar-S TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 4 TEST 7. 15 points within 1 standard deviation of center line (above and below CL). Test Failed at points: 19, 20 Test Results for S Chart of Xbar-S TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 4, 7, 16 TEST 2. 9 points in a row on same side of center line. Test Failed at points: 13, 14, 15, 16, 17, 18, 19, 20,第七事业部品质部,52,Stat Control Charts Variables Charts for Individuals I-MZ,单值移动I-MZ,Test Results for I Chart of I-MZ TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 10,第七事业部品质部,53,能力分析(Normal),Stat Quality Tools Capability Analysis Normal,第七事业部品质部,54,能力分析(Between/Within),Stat Quality Tools Capability Analysis Between/Within,第七事业部品质部,55,能力分析( Sixpack ),Stat Quality Tools Capability Analysis Between/Within,第七事业部品质部,56,Gage Run Chart Gage Linearity and Bias Study Gage Stability Gage R&R Study (Crossed) - ANOVA Method Gage R&R Study (Crossed) - X and R method Gage R&R Study (Nested) Attribute Gage Study (Analytic Method),测量系统分析（MSA）,第七事业部品质部,57,A gage run chart is a plot of all of your observations by operator and part number. to quickly assess differences in measurements between different operators and parts. A stable process would give you a random horizontal scattering of points; an operator or part effect would give you some kind of pattern in the plot.,Stat Quality Tools Gage Study Gage Run Chart,Gage Run Chart,第七事业部品质部,58,Gage linearity tells you how accurate your measurements are through the expected range of the measurements. Gage bias examines the difference between the observed average measurement and a reference or master value.,Stat Quality Tools Gage Study Gage Linearity and Bias Study,Gage Linearity and Bias Study,第七事业部品质部,59,GR&R Study,Gage repeatability and reproducibility studies determine how much of your observed process variation is due to measurement system variation.,XBar-R,ANOVA,第七事业部品质部,60,Two-Way ANOVA Table With Interaction Source DF SS MS F P Part 9 88.5334 9.83705 506.092 0.000 Appraiser 2 3.1297 1.56485 80.508 0.000 Part * Appraiser 18 0.3499 0.01944 0.423 0.977 Repeatability 60 2.7603 0.04600 Total 89 94.7733 Two-Way ANOVA Table Without Interaction Source DF SS MS F P Part 9 88.5334 9.83705 246.706 0.000 Appraiser 2 3.1297 1.56485 39.245 0.000 Repeatability 78 3.1101 0.03987 Total 89 94.7733,Gage R&R Study (Crossed),第七事业部品质部,61,Gage R&R Study (Crossed),Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R 0.09071 7.69 Repeatability 0.03987 3.38 Reproducibility 0.05083 4.31 Appraiser 0.05083 4.31 Part-To-Part 1.08858 92.31 Total Variation 1.17928 100.00 Study Var %Study Var Source StdDev (SD) (6 * SD) (%SV) Total Gage R&R 0.30117 1.80705 27.73 Repeatability 0.19968 1.19810 18.39 Reproducibility 0.22546 1.35277 20.76 Appraiser 0.22546 1.35277 20.76 Part-To-Part 1.04335 6.26009 96.08 Total Variation 1.08595 6.51568 100.00 Number of Distinct Categories = 4,第七事业部品质部,62, Look at the %Contribution column in the Gage R&R Table. The percent contribution from Part-To-Part (92.31) is larger than that of Total Gage R&R (7.69). This tells you that much of the variation is due to differences between parts. While the Total Gage R&R %Contribution is acceptable, there is room for improvement. For this data, the number of distinct categories is four. According to the AIAG, you need at least five distinct categories to have an adequate measuring system.,第七事业部品质部,63,Minitab allows us to Use Gage R&R Study(Nested) when each part is measured by only one operator, such as in destructive testing.,Gage R&R Study (Nested),Source DF SS MS F P Operator 2 0.00444 0.002222 0.0039 0.996 Part (Operator) 6 3.44000 0.573333 27.8919 0.000 Repeatability 9 0.18500 0.020556 Total 17 3.62944 %Contribution Source VarComp (of VarComp) Total Gage R&R 0.020556 6.92 Repeatability 0.020556 6.92 Reproducibility 0.000000 0.00 Part-To-Part 0.276389 93.08 Total Variation 0.296944 100.00,第七事业部品质部,64,Study Var %Study Var Source StdDev (SD) (6 * SD) (%SV) Total Gage R&R 0.143372 0.86023 26.31 Repeatability 0.143372 0.86023 26.31 Reproducibility 0.000000 0.00000 0.00 Part-To-Pa