質(zhì)量工具以及Minitable的運(yùn)用ppt課件

1、1.21：統(tǒng)計(jì)描畫2：區(qū)間估計(jì)與假設(shè)檢驗(yàn)3：方差分析ANOVA4：回歸分析Regression5：實(shí)驗(yàn)設(shè)計(jì)DOE6：質(zhì)量工具Quality Tool7：丈量系統(tǒng)分析MSA.第七事業(yè)部質(zhì)量部3描畫性統(tǒng)計(jì) Descriptive Statistics-單值圖Individual Value Plot)-箱圖Boxplot-柏拉圖Pareto-直方圖Histogram-時(shí)間序列圖Time Series Plot-邊沿圖Marginal Plot-3D外表圖3D Surface Plot)-柱狀圖Bar Chart-餅圖Pie Chart.第七事業(yè)部質(zhì)量部4單值圖Individual Plot)Gra

2、ph Individual Plot.第七事業(yè)部質(zhì)量部5箱圖BoxplotQ1-1.5*Q3-Q1Q3 + 1.5 (Q3 - Q1) Q3 Q1 median Graph HistogramOutlier .第七事業(yè)部質(zhì)量部6 直方圖Histogram Graph Histogram類似莖葉圖Stem-and-Leaf ).第七事業(yè)部質(zhì)量部7柏拉圖Parto chart)STAT Quality Tools Pareto Chart.第七事業(yè)部質(zhì)量部8時(shí)間序列圖Time Series PlotGraph Time Series Plot.第七事業(yè)部質(zhì)量部9邊沿圖Marginal Plot為單

3、值圖和直方圖/點(diǎn)圖/箱圖的綜合Graph Marginal Plot.第七事業(yè)部質(zhì)量部103D外表圖3D Surface Plot)Graph 3D Surface Plot.第七事業(yè)部質(zhì)量部11Display Descriptive StatisticsStat Basic Statistics Display Descriptive Statistics結(jié)果解釋對(duì)截止12.10日的火箭隊(duì)主客場(chǎng)得分進(jìn)展了描畫性統(tǒng)計(jì)。從結(jié)果可以看出：主場(chǎng)得分mean：平均值99.60大于客場(chǎng)得分mean=94.47)。1：數(shù)據(jù)量少3：火箭隊(duì)發(fā)揚(yáng)不穩(wěn)定得分2：對(duì)手強(qiáng)弱清楚Variable 場(chǎng)次 N Mean S

4、E Mean StDev Minimum Q1 Median Q3 Maximum Skewness Kurtosis 得分 客場(chǎng) 17 94.47 2.12 8.74 80.00 89.00 94.00 99.00 117.00 0.84 1.70 主場(chǎng) 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.第七事業(yè)部質(zhì)量部12區(qū)間估計(jì)與假設(shè)檢驗(yàn)-小概率事件-單樣本Z檢驗(yàn)1 Sample-Z-單樣本T檢驗(yàn)1 Sample-T-雙樣本T檢驗(yàn)2 Sample-T-成對(duì)T檢驗(yàn)Paired T-相關(guān)性檢驗(yàn)Corre

5、lation-方差齊性相等檢驗(yàn)Equal Variances)-正態(tài)測(cè)試Normality Test-卡方檢驗(yàn)Chi-square test.第七事業(yè)部質(zhì)量部13總體：整個(gè)集合的全體特征樣本：具有總體特征的子集根據(jù)樣本確定總體!為什么需求區(qū)間估計(jì)與假設(shè)檢驗(yàn)？區(qū)間估計(jì)與假設(shè)檢驗(yàn).第七事業(yè)部質(zhì)量部14天打雷劈小概率事件不要破壞花花草草。打雷了，下雨了，還是收衣服好！.第七事業(yè)部質(zhì)量部15Stat Basic Stats 1 Sample-Z單樣本Z檢驗(yàn) 1 Sample-Z實(shí)踐顯著性程度，可以把p 值了解為假設(shè)的支持率或可信程度。某段時(shí)間內(nèi)，對(duì)wire bond的金線拉力wire pull)進(jìn)展了

6、170次丈量，得到均值為13.93g，方差為1.26g，能否以95%的置信度以為該段時(shí)間內(nèi)wire pull均值為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置信區(qū)間(confidence interval)，區(qū)間估計(jì)總是與一定的概率保證相對(duì)應(yīng)的.第七事業(yè)部質(zhì)量部16Stat Basic Stats 1 Sample-T單樣本T檢驗(yàn) 1 Sample-T

7、設(shè)隨機(jī)變量X 服從規(guī)范正態(tài)分布N(0，1)，隨帆變量Y 服從自在度為n 的x2 分布，且X 與Y 相互獨(dú)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置信區(qū)間(confidence interval)與Z檢驗(yàn)的區(qū)別？.第七事業(yè)部質(zhì)量部17雙樣本T檢驗(yàn) 2 Sample-TStat Basic Stats 2 Sample-T為了估計(jì)磷肥對(duì)某種農(nóng)作

8、物增產(chǎn)的作用，現(xiàn)選20 塊土壤條件大致一樣的土地。其中10 塊不施磷肥.另外10 塊施磷肥，得到畝產(chǎn)量進(jìn)展比較。 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不相關(guān)的樣本.第七事業(yè)部質(zhì)量部18Stat Basic Stats Paired T成對(duì)T檢驗(yàn) Paired T N Mean StDev SE Mean運(yùn)動(dòng)前 17 60.1176 2.3607 0.5725運(yùn)動(dòng)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為

10、了估計(jì)進(jìn)展運(yùn)動(dòng)活動(dòng)后，人體體重的變化情況，選取17個(gè)人，在運(yùn)動(dòng)前后分別丈量其體重，然后對(duì)數(shù)據(jù)進(jìn)展分析相關(guān)樣本.第七事業(yè)部質(zhì)量部19相關(guān)性檢驗(yàn)CorrelationPearson correlation of 得分 and 失分 = 0.279P-Value = 0.158Stat Basic Stats Correlation沒有顯著的相關(guān)性，數(shù)據(jù)相互獨(dú)立.第七事業(yè)部質(zhì)量部20方差齊性相等檢驗(yàn)Equal Variances)Stat ANOVA Test for equal variancesF Test。對(duì)兩個(gè)研討總體的總體平均數(shù)的差別進(jìn)展顯著性檢驗(yàn)以外，我們還需求對(duì)兩個(gè)獨(dú)立樣本所屬總體的總

11、體方差的差別進(jìn)展顯著性檢驗(yàn)，統(tǒng)計(jì)學(xué)上稱為方差齊性相等檢驗(yàn)?？梢詾榉讲铨R性.第七事業(yè)部質(zhì)量部21正態(tài)測(cè)試Normality TestStat Basic Stats Normality TestP=0.8090.05,可以以為服從正態(tài)分布MEAN.第七事業(yè)部質(zhì)量部22卡方 檢驗(yàn)Chi-square test滿意比較滿意不太滿意不滿意市區(qū)31522近郊211045遠(yuǎn)郊201172電視節(jié)目稱心度調(diào)查H0：這三組居民對(duì)電視節(jié)目的 意見是一致的H1：這三組居民對(duì)電視節(jié)目的意見不一致Chi-Square Test: 稱心, 比較稱心, 不太稱心, 不稱心 Chi-Square contributions

12、are printed below expected counts 稱心 比較稱心 不太稱心 不稱心 Total市區(qū) 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遠(yuǎn)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).第七事業(yè)部質(zhì)量部23方差分析ANOVA- One Way ANOVA- Two Way ANOVA- Analysis of means- General Linear Model.第七事業(yè)部質(zhì)量部24一、SNKq檢驗(yàn)二、DUNCAN檢驗(yàn)三、TUKEY檢驗(yàn)四、Fisher檢驗(yàn)五、Dunnett檢驗(yàn)六、HSUs MCB檢驗(yàn) “多重比較的幾種方法.第七事業(yè)部質(zhì)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從某學(xué)校同一年級(jí)中隨機(jī)抽取19名學(xué)生，再將他們隨機(jī)分成4組，在2周內(nèi)4組學(xué)生都用120分鐘復(fù)習(xí)同一組英語(yǔ)單詞，第一組每個(gè)星期一一次復(fù)習(xí)60分鐘；第二組每個(gè)星期一和三兩次各復(fù)習(xí)30分鐘；第三組每個(gè)星期二、四、六三次復(fù)習(xí)各20分鐘；第四組每天星期天除外復(fù)習(xí)10分鐘。2周復(fù)習(xí)之后，相隔2個(gè)月再進(jìn)展一致檢驗(yàn)，這4種復(fù)習(xí)方法的效果之間有沒有顯著性差別？Stat ANOVA One way (stacked)/One way (unstacked).第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)量部27Analysis of meansStat ANOVA Analysis of

16、means.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)量部29回歸分析Regression-回歸模型-線性回歸Regression-步進(jìn)回歸Stepwish-曲線擬合Fitted Line Plot).第七事業(yè)部質(zhì)量部30回歸模型多元回歸模型估計(jì)多元回歸方程式多元回歸方程式擾動(dòng)項(xiàng)， N(0, 2 ) 且Cov(i,j)=0(ij)擬合程度檢驗(yàn)、相關(guān)系數(shù)檢驗(yàn)、參數(shù)顯著性檢驗(yàn)(t 檢驗(yàn))和回歸方程顯著性檢驗(yàn)F 檢驗(yàn)Cov(X,)=0Cov(Xi,Xj)=0.第七事業(yè)部質(zhì)量部31線性回歸Regression某種商品的需求量Y、價(jià)錢X1 和消費(fèi)者收入X2 的統(tǒng)計(jì)資料如所示，試估計(jì)Y對(duì)X1

18、 和X2 的線性回歸方程。The regression equation is需求量Y噸 = 62651 - 979 X1元 + 0.286 X2元Predictor Coef SE Coef T P VIFConstant 62651 4013 15.61 0.000價(jià)錢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.第七事業(yè)部質(zhì)量部32逐漸回歸StepwishStat Regression StepwishResponse is 需求量Y噸 on 3 predictors, with N = 10Step 1 2Constant 52141 62651和消費(fèi)者收入X2元 0.114 0.286T-Value 5.19 4.90

20、P-Value 0.001 0.002價(jià)錢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 價(jià)錢X1元 X1+10T-Value 3.23 -2.46P-Value 0.012 0.043.第七事業(yè)部質(zhì)量部33曲線擬合Fitted Line Plot)The regression equation is需求量Y噸 = 46411 + 0.2044 和消費(fèi)者收入X2元 - 0.000000

21、和消費(fèi)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.第七事業(yè)部質(zhì)量部34實(shí)驗(yàn)設(shè)計(jì)Design of Experiment1：實(shí)驗(yàn)設(shè)計(jì)目的2：析因?qū)嶒?yàn)設(shè)計(jì)Factorial Design3：部分析因?qū)嶒?yàn)設(shè)計(jì)Fractional Factorial4：田口設(shè)計(jì)Taguchi Design5：外表呼應(yīng)Response Surface 6：本卷須知.第七事業(yè)部質(zhì)量部35實(shí)驗(yàn)設(shè)計(jì)目的1：確定那些參數(shù)對(duì)呼應(yīng)的影響最大2：確定參數(shù)設(shè)置在什么程度，以使呼應(yīng)到達(dá)或者盡能夠接近目的值on target3

23、：確定參數(shù)設(shè)置在什么程度，以使呼應(yīng)的分散度或方差盡能夠減小4：確定參數(shù)設(shè)置在什么程度，以使不可控參數(shù)躁聲參數(shù)對(duì)呼應(yīng)的影響盡能夠小.第七事業(yè)部質(zhì)量部36析因設(shè)計(jì)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.第七事業(yè)部質(zhì)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無(wú)Block.第七事業(yè)部質(zhì)量部38.第七事業(yè)部質(zhì)量部39部分析因?qū)嶒?yàn)設(shè)計(jì)Fractional FactorialStdOrderRunOrderCenterPtBlocksABCY811111115.9622111-1-110.5763111-1-126.61441111114.013511-11-19.8667611-11-16.461711-1-117.6735811-1-117.828.第七事業(yè)部質(zhì)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無(wú)Block.第七事業(yè)部質(zhì)量部41.第七事業(yè)部質(zhì)量部42田口設(shè)計(jì)Taguchi DesignTaguchi設(shè)計(jì)思想?yún)?shù)分類：1控制參數(shù)control factors):可以控制的參數(shù)

31、。例如汽缸直徑、單向閥等。2噪聲參數(shù)noise factors：不可控制的參數(shù)。比如，大氣壓力、發(fā)動(dòng)機(jī)轉(zhuǎn)速等。有些參數(shù)不一定完全不可控制，只是由于控制起來(lái)比較困難、本錢很高，不宜控制，所以歸入噪聲參數(shù)指點(diǎn)思想： 尋求使產(chǎn)品性能對(duì)于噪聲不敏感的設(shè)計(jì)，即所謂穩(wěn)健Robust設(shè)計(jì)，這樣有利于獲得性能盡能夠一致的產(chǎn)品TargetTargetTargetTarget.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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類別S/N比品質(zhì)特性控制因子1有有B A2有無(wú)E3無(wú)有D4無(wú)無(wú)C.第七事業(yè)部質(zhì)量部45因子交互作用以及規(guī)劃.第七事業(yè)部質(zhì)量部46RSMResponse Surface Methodology)Response (Original)Centre Point (Added)Axis Point (Added)Fitted curve 1Fitted curve 2Predicted PointOrigina

35、l Point (Observed).第七事業(yè)部質(zhì)量部47.第七事業(yè)部質(zhì)量部48解析度Resolution：Resolution V： 二因子交互作用以及主因子效應(yīng)互不影響Resolution IV：二因子交互作用有混淆，但不與主因子作用混淆Resolution IIV：二因子交互作用與主因子作用有混淆實(shí)驗(yàn)分組(Blocking)實(shí)驗(yàn)次序的隨機(jī)化randomization)-抑制環(huán)境噪聲的影響DOE一些本卷須知做好前期的實(shí)驗(yàn)方案的設(shè)計(jì).第七事業(yè)部質(zhì)量部49質(zhì)量工具Quality Tool控制圖Control Charts-Xbar-R-Xbar-S-Z-MR工序才干Capability Ana

36、lysis)-Normality-Between/Within.第七事業(yè)部質(zhì)量部50均值極差圖(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.第七事業(yè)部質(zhì)量部51Stat Control Charts Variables Charts for subgroups Xbar-S均值方差圖(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.第七事業(yè)部質(zhì)量部52Stat Control Charts Variables Charts for Individuals I-MZ單值挪動(dòng)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.第七事業(yè)部質(zhì)量部53才干分析(Normal)Stat Qu

40、ality Tools Capability Analysis Normal.第七事業(yè)部質(zhì)量部54才干分析(Between/Within)Stat Quality Tools Capability Analysis Between/Within.第七事業(yè)部質(zhì)量部55才干分析( Sixpack )Stat Quality Tools Capability Analysis Between/Within.第七事業(yè)部質(zhì)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)丈量系統(tǒng)分析MSA.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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).第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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. .第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)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.第七事業(yè)部質(zhì)量部65.第七事業(yè)部質(zhì)量部66 Look at the %Study columns for Total Gage R&R and Part-to-Part. The perce