质量工具以及Minitable的运用ppt课件

1、1.21：统计描画2：区间估计与假设检验3：方差分析ANOVA4：回归分析Regression5：实验设计DOE6：质量工具Quality Tool7：丈量系统分析MSA.第七事业部质量部3描画性统计 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-边沿图Marginal Plot-3D外表图3D Surface Plot)-柱状图Bar Chart-饼图Pie Chart.第七事业部质量部4单值图Individual Plot)Gra

2、ph Individual Plot.第七事业部质量部5箱图BoxplotQ1-1.5*Q3-Q1Q3 + 1.5 (Q3 - Q1) Q3 Q1 median Graph HistogramOutlier .第七事业部质量部6 直方图Histogram Graph Histogram类似茎叶图Stem-and-Leaf ).第七事业部质量部7柏拉图Parto chart)STAT Quality Tools Pareto Chart.第七事业部质量部8时间序列图Time Series PlotGraph Time Series Plot.第七事业部质量部9边沿图Marginal Plot为单

3、值图和直方图/点图/箱图的综合Graph Marginal Plot.第七事业部质量部103D外表图3D Surface Plot)Graph 3D Surface Plot.第七事业部质量部11Display Descriptive StatisticsStat 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展了描画性统计。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：火箭队发扬不稳定得分2：对手强弱清楚Variable 场次 N Mean S

4、E Mean StDev Minimum Q1 Median Q3 Maximum Skewness Kurtosis 得分 客场 17 94.47 2.12 8.74 80.00 89.00 94.00 99.00 117.00 0.84 1.70 主场 10 99.60 2.56 8.09 89.00 89.75 104.00 105.50 109.00 -0.45 -1.89 偏斜度峰度.第七事业部质量部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Corre

5、lation-方差齐性相等检验Equal Variances)-正态测试Normality Test-卡方检验Chi-square test.第七事业部质量部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!为什么需求区间估计与假设检验？区间估计与假设检验.第七事业部质量部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！.第七事业部质量部15Stat Basic Stats 1 Sample-Z单样本Z检验 1 Sample-Z实践显著性程度，可以把p 值了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)进展了

6、170次丈量，得到均值为13.93g，方差为1.26g，能否以95%的置信度以为该段时间内wire pull均值为16g？Test of mu = 16 vs not = 16The assumed standard deviation = 1.26 N Mean SE Mean 95% CI Z P170 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.第七事业部质量部16Stat Basic Stats 1 Sample-T单样本T检验 1 Sample-T

7、设随机变量X 服从规范正态分布N(0，1)，随帆变量Y 服从自在度为n 的x2 分布，且X 与Y 相互独立，那么One-Sample T: 得分 Test of mu = 100 vs not = 100Variable 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？.第七事业部质量部17双样本T检验 2 Sample-TStat Basic Stats 2 Sample-T为了估计磷肥对某种农作

8、物增产的作用，现选20 块土壤条件大致一样的土地。其中10 块不施磷肥.另外10 块施磷肥，得到亩产量进展比较。 N Mean StDev SE Mean不施磷肥 10 570.0 16.3 5.2施磷肥 10 600.0 26.7 8.4Difference = mu (不施磷肥) - mu (施磷肥)Estimate for difference: -30.000095% CI for difference: (-51.2082, -8.7918)T-Test of difference = 0 (vs not =): T-Value = -3.03 P-Value = 0.009 DF

9、= 14不相关的样本.第七事业部质量部18Stat 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 0.5657Difference 17 0.505882 0.343640 0.08334595% 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

10、了估计进展运动活动后，人体体重的变化情况，选取17个人，在运动前后分别丈量其体重，然后对数据进展分析相关样本.第七事业部质量部19相关性检验CorrelationPearson correlation of 得分 and 失分 = 0.279P-Value = 0.158Stat Basic Stats Correlation没有显著的相关性，数据相互独立.第七事业部质量部20方差齐性相等检验Equal Variances)Stat ANOVA Test for equal variancesF Test。对两个研讨总体的总体平均数的差别进展显著性检验以外，我们还需求对两个独立样本所属总体的总

11、体方差的差别进展显著性检验，统计学上称为方差齐性相等检验。可以为方差齐性.第七事业部质量部21正态测试Normality TestStat Basic Stats Normality TestP=0.8090.05,可以以为服从正态分布MEAN.第七事业部质量部22卡方 检验Chi-square test满意比较满意不太满意不满意市区31522近郊211045远郊201172电视节目称心度调查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: 称心, 比较称心, 不太称心, 不称心 Chi-Square contributions

12、are printed below expected counts 称心 比较称心 不太称心 不称心 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 0.333Total 72 26 13 9 120Chi-Sq = 10.391, DF = 6, P-Value = 0.109Stat

13、Tables Chi-square test (table in worksheet).第七事业部质量部23方差分析ANOVA- One Way ANOVA- Two Way ANOVA- Analysis of means- General Linear Model.第七事业部质量部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.第七事业部质量部25One Way ANOVAOne-way ANOVA: Source DF SS MS F PFactor 3 95.80 31.93 3.69

14、0.036Error 15 129.88 8.66Total 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个月再进展一致检验，这4种复习方法的效果之间有没有显著性差别？Stat ANOVA One way (stacked)/One way (unstacked).第七事业部质量部26Two Way ANOVABalanced Data Tw

15、o-way ANOVA: peel test versus temperature, pressure Source DF SS MS F Ptemperature 2 10.7619 5.38095 14.56 0.002pressure 2 2.1660 1.08301 2.93 0.105Interaction 4 1.9329 0.48322 1.31 0.338Error 9 3.3262 0.36958Total 17 18.1870Stat ANOVA Two Way ANOVA.第七事业部质量部27Analysis of meansStat ANOVA Analysis of

16、means.第七事业部质量部28General Linear ModelAnalysis of Variance for peel test, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PTemp 2 3.5113 3.5113 1.7557 4.46 0.036Pressure 2 3.0218 3.0218 1.5109 3.84 0.051Time 1 1.0571 1.0571 1.0571 2.69 0.127Error 12 4.7206 4.7206 0.3934Total 17 12.3108Stat

17、 ANOVA General Linear Model.第七事业部质量部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).第七事业部质量部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,)=0Cov(Xi,Xj)=0.第七事业部质量部31线性回归Regression某种商品的需求量Y、价钱X1 和消费者收入X2 的统计资料如所示，试估计Y对X1

18、 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 VIFConstant 62651 4013 15.61 0.000价钱X1元 -979.1 319.8 -3.06 0.018 14.6收入X2元 0.28618 0.05838 4.90 0.002 14.6S = 1738.98 R-Sq = 90.2% R-Sq(adj) = 87.4%Analysis of VarianceSource DF SS MS F PRegression 2

19、 195318937 97659469 32.29 0.000Residual Error 7 21168473 3024068Total 9 216487410Std. Error of the EstimateStat Regression Regressionoutliers.第七事业部质量部32逐渐回归StepwishStat Regression StepwishResponse is 需求量Y吨 on 3 predictors, with N = 10Step 1 2Constant 52141 62651和消费者收入X2元 0.114 0.286T-Value 5.19 4.90

20、P-Value 0.001 0.002价钱X1元 -979T-Value -3.06P-Value 0.018S 2488 1739R-Sq 77.13 90.22R-Sq(adj) 74.27 87.43Mallows C-p 15.6 5.2Best alternatives:Variable 价钱X1元 X1+10T-Value 3.23 -2.46P-Value 0.012 0.043.第七事业部质量部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

21、和消费者收入X2元*2S = 2613.66 R-Sq = 77.9% R-Sq(adj) = 71.6%Analysis of VarianceSource DF SS MS F PRegression 2 168668800 84334400 12.35 0.005Error 7 47818610 6831230Total 9 216487410Sequential Analysis of VarianceSource DF SS F PLinear 1 166972842 26.98 0.001Quadratic 1 1695958 0.25 0.634Stat Regression F

22、itted Line PlotLinear Quadratic Cubic95%Confidence Interval95%Prediction Interval.第七事业部质量部34实验设计Design of Experiment1：实验设计目的2：析因实验设计Factorial Design3：部分析因实验设计Fractional Factorial4：田口设计Taguchi Design5：外表呼应Response Surface 6：本卷须知.第七事业部质量部35实验设计目的1：确定那些参数对呼应的影响最大2：确定参数设置在什么程度，以使呼应到达或者尽能够接近目的值on target3

23、：确定参数设置在什么程度，以使呼应的分散度或方差尽能够减小4：确定参数设置在什么程度，以使不可控参数躁声参数对呼应的影响尽能够小.第七事业部质量部36析因设计Factorial DesignStdOrderRunOrderCenterPtBlocksABCY3111-11-112.961211-1-1-18.672103111-1-110.5715411-1118.2521651111115.96461111-111.01871111114.015811-1-117.67369111-1112.931410111-119.55212111111-110.15212111-1-126.61913

24、11-1-1-16.18871411-1119.866111511-11-16.46131611-1-117.828.第七事业部质量部37Term Effect Coef SE Coef T PConstant 11.1683 1.125 9.92 0.000A 5.3608 2.6804 1.125 2.38 0.044B -0.1672 -0.0836 1.125 -0.07 0.943C -0.8197 -0.4098 1.125 -0.36 0.725A*B -1.9625 -0.9812 1.125 -0.87 0.409A*C -0.6534 -0.3267 1.125 -0.29

25、 0.779B*C 2.6931 1.3466 1.125 1.20 0.266A*B*C 3.1799 1.5900 1.125 1.41 0.195S = 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 PMain Effects 3 117.75 117.75 39.25 1.94 0.2022-Way Interactions 3 46.12 46.12 15.37 0.76 0.5483-Way Intera

26、ctions 1 40.45 40.45 4 0.45 2.00 0.195Residual Error 8 162.12 162.12 20.27 Pure Error 8 162.12 162.12 20.27Total 15 366.45Least Squares Means for Y Mean SE MeanA -1 8.488 1.592 1 13.849 1.592B -1 11.252 1.592 1 11.085 1.592C -1 11.578 1.592 1 10.758 1.592A*B -1 -1 7.590 2.251 1 -1 14.914 2.251 -1 1

27、9.385 2.251 1 1 12.784 2.251A*C -1 -1 8.571 2.251 1 -1 14.585 2.251 -1 1 8.405 2.251 1 1 13.112 2.251B*C -1 -1 13.008 2.251 1 -1 10.148 2.251 -1 1 9.495 2.251 1 1 12.021 2.251A*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 3.1

28、83 -1 1 1 9.059 3.183 1 1 1 14.984 3.183无Block.第七事业部质量部38.第七事业部质量部39部分析因实验设计Fractional FactorialStdOrderRunOrderCenterPtBlocksABCY811111115.9622111-1-110.5763111-1-126.61441111114.013511-11-19.8667611-11-16.461711-1-117.6735811-1-117.828.第七事业部质量部40Term Effect Coef SE Coef T PConstant 12.372 2.064 5.

29、99 0.004A 8.831 4.415 2.064 2.14 0.099B -1.596 -0.798 2.064 -0.39 0.719C -2.009 -1.004 2.064 -0.49 0.652S = 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 PMain Effects 3 169.1 169.1 56.38 1.65 0.312Residual Error 4 .4 .4 34.09 Pure E

30、rror 4 .4 .4 34.09Total 7 305.5Least Squares Means for Y Mean SE MeanA -1 7.957 2.919 1 16.788 2.919B -1 13.170 2.919 1 11.574 2.919C -1 13.377 2.919 1 11.368 2.919Alias StructureI + A*B*CA + B*CB + A*CC + A*B无Block.第七事业部质量部41.第七事业部质量部42田口设计Taguchi DesignTaguchi设计思想参数分类：1控制参数control factors):可以控制的参数

31、。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、本钱很高，不宜控制，所以归入噪声参数指点思想： 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能够一致的产品TargetTargetTargetTarget.第七事业部质量部43ABCDEY1111123.391112213.81122118.661222210.582121220.932122116.042211223.192212115.731111118.241112211.1312211

32、16.851222214.242121227.52122115.89221129.964221216.3221111119.031112220.561221114.951222220.352121214.64212219.0942211210.042212116.841111114.351112223.871221120.921222216.82121216.412122117.462211211.582212115.89.第七事业部质量部44Taguchi Analysis: Y versus A, B, C, D, E The following terms cannot be estim

33、ated, and were removed.A*BA*CA*DA*EB*CC*DC*ED*EResponse Table for Signal to Noise RatiosNominal is best (10*Log(Ybar*2/s*2)Level A B C D E1 11.130 11.519 9.740 10.269 11.0772 9.527 9. 10.917 10.388 9.580Delta 1.602 2.381 1.177 0.120 1.497Rank 2 1 4 5 3Response Table for MeansLevel A B C D E1 16.73 1

34、7.65 15.87 16.91 15.602 15.47 14.56 16.33 15.29 16.60Delta 1.26 3.09 0.46 1.63 1.00Rank 3 1 5 2 4类别S/N比品质特性控制因子1有有B A2有无E3无有D4无无C.第七事业部质量部45因子交互作用以及规划.第七事业部质量部46RSMResponse Surface Methodology)Response (Original)Centre Point (Added)Axis Point (Added)Fitted curve 1Fitted curve 2Predicted PointOrigina

35、l Point (Observed).第七事业部质量部47.第七事业部质量部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)-抑制环境噪声的影响DOE一些本卷须知做好前期的实验方案的设计.第七事业部质量部49质量工具Quality Tool控制图Control Charts-Xbar-R-Xbar-S-Z-MR工序才干Capability Ana

36、lysis)-Normality-Between/Within.第七事业部质量部50均值极差图(Xbar-R)Stat Control Charts Variables Charts for subgroups Xbar-RTest 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 Xba

37、r-R TEST 1. One point more than 3.00 standard deviations from center line.Test Failed at points: 7.第七事业部质量部51Stat 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 a

38、t points: 4TEST 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, 16TEST 2. 9 points in a row on same side of

39、 center line.Test Failed at points: 13, 14, 15, 16, 17, 18, 19, 20.第七事业部质量部52Stat Control Charts Variables Charts for Individuals I-MZ单值挪动I-MZTest 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.第七事业部质量部53才干分析(Normal)Stat Qu

40、ality Tools Capability Analysis Normal.第七事业部质量部54才干分析(Between/Within)Stat Quality Tools Capability Analysis Between/Within.第七事业部质量部55才干分析( Sixpack )Stat Quality Tools Capability Analysis Between/Within.第七事业部质量部56Gage Run Chart Gage Linearity and Bias StudyGage StabilityGage R&R Study (Crossed) - ANO

41、VA Method Gage R&R Study (Crossed) - X and R methodGage R&R Study (Nested) Attribute Gage Study (Analytic Method)丈量系统分析MSA.第七事业部质量部57A 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

42、. 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 ChartGage Run Chart.第七事业部质量部58Gage linearity tells you how accurate your measurements are through the expected

43、 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 StudyGage Linearity and Bias Study.第七事业部质量部59GR&R StudyOverall VariationPart-to-Part VariationMeasurement Syst

44、em VariationVariation due to gageVariation due to partReproducibilityOperatorPartRepeatabilityGage repeatability and reproducibility studies determine how much of your observed process variation is due to measurement system variation. XBar-RANOVA.第七事业部质量部60Two-Way ANOVA Table With Interaction Source

45、 DF SS MS F PPart 9 88.5334 9.83705 506.092 0.000Appraiser 2 3.1297 1.56485 80.508 0.000Part * Appraiser 18 0.3499 0.01944 0.423 0.977Repeatability 60 2.7603 0.04600Total 89 94.7733 Two-Way ANOVA Table Without Interaction Source DF SS MS F PPart 9 88.5334 9.83705 246.706 0.000Appraiser 2 3.1297 1.56

46、485 39.245 0.000Repeatability 78 3.1101 0.03987Total 89 94.7733Gage R&R Study (Crossed).第七事业部质量部61Gage R&R Study (Crossed)Gage R&R %ContributionSource 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 9

47、2.31Total Variation 1.17928 100.00 Study Var %Study VarSource 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 20.76Part-To-Part 1.04335 6.26009 96.08Total Variation 1.08595 6.51568 100.

48、00Number of Distinct Categories = 4.第七事业部质量部62Look 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

49、&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. .第七事业部质量部63Minitab allows us toUse Gage R&R Study(Nested) when each part is

50、 measured by only one operator, such as in destructive testing.Gage R&R Study (Nested)Source DF SS MS F POperator 2 0.00444 0.002222 0.0039 0.996Part (Operator) 6 3.44000 0.573333 27.8919 0.000Repeatability 9 0.18500 0.020556Total 17 3.62944 %ContributionSource VarComp (of VarComp)Total Gage R&R 0.0

51、20556 6.92 Repeatability 0.020556 6.92 Reproducibility 0.000000 0.00Part-To-Part 0.276389 93.08Total Variation 0.296944 100.00.第七事业部质量部64 Study Var %Study VarSource 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 0.00Part-To-Part 0.525727 3.15436 96.48Total Variation 0.544926 3.26956 100.00Number of Distinct Categories = 4.第七事业部质量部65.第七事业部质量部66 Look at the %Study columns for Total Gage R&R and Part-to-Part. The perce