子裝成一箱。此兩批分別由兩廠交貨之同規格之筒子紗,強度之規格為平均數μ0=2.40牛頓,1廠之製程管制記錄顯示其強度之標準差σ1=0.3315牛頓,2廠之製程管制記錄顯示其標準差σ2=0.3112牛頓。
抽樣單位的技術特性:從兩批棉紗中,分別隨機抽取10箱及12箱,而後從每箱內隨機抽取一個,在每個筒子上距離末端約5m處取約50cm的一段試驗紗進行試驗。測得之數據分別為X11,X12,..........,X1n11及X21,X22,..........,X2n21如下所示,以牛頓為單位測出每段試驗紗的強度。
1廠 2.297 2.133 2.582 1.885 1.949 1.986 2.362 1.642 2.040 2.915
2廠 2.286 2.327 2.388 3.172 3.158 2.751 2.222 2.367 2.247 2.512 2.104 2.707 ? One Sample T (一組樣本的檢定及信賴區間) 檢定
H0:???0
Vs. H1:???0
H0:???0
H0:???0
H1:???0 H1:???0
雙邊 單邊:右邊
單邊:左邊
檢定統計量:T?1.雙邊情形:
X??0sn若∣t∣>tα/2,則拒收H0:μ=μ0或以顯著水準的大小判定 P-Value=P[∣t∣>T]
2.單邊情形(右邊): 若t>tα,則拒收H0:μ=μ0或以顯著水準的大小判定
P-Value=P[t>T]
3.單邊情形(左邊): 若t<-tα,則拒收H0:μ=μ0或以顯著水準的大小判定
P-Value=P[t
雙邊信賴區間: (X?(t?2?sn),X?(t?2?s單邊信賴區間: (X?(t??s
n))
n),?)或(??,X?(t??sn))
One-Sample T-Test and CI(一組樣本的檢定及信賴區間): 1廠 Test of mu = 2.4 vs. mu < 2.4(檢定H:0??2.4 vs. H:1??2.4)
snVariable N Mean StDev SE Mean 1廠 10 2.179 0.371 0.117
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T?X??0=(2.179-2.4)/0.117=-1.88,P=P[t
Variable 95.0% Upper Bound T P 1廠 2.394 -1.88 0.046
t Boxplot of 1廠
Boxplot of 1紅(with Ho and 95% t-confidence interval for the mean)[_X]Ho95%μ的信賴區間 2.02.53.01紅
? Two-Sample T-Test and CI(兩組樣本的檢定及信賴區間) 檢定
H:0?1??2
H:0?1??2
H:0?1??2
Vs. H:1?1??2
雙邊
H:1?1??2 H:1?1??2
單邊:右邊 單邊:左邊
1.雙邊情形: 若∣t(n1+n2-2)∣>tα/2,則拒收H0:μ1-μ2=0或以顯著水準的大小判定P-Value=P[∣t(n1+n2-2)∣>t0]
2.單邊情形(右邊): 若t(n1+n2-2)> tα,則拒收H0:μ1-μ2=0或以顯著水準的大小判定
P-Value=P[t(n1+n2-2)>t0]
3.單邊情形(左邊): 若t(n1+n2-2)<- tα,則拒收H0:μ1-μ2=0或以顯著水準的大小判定
P-Value=P[t(n1+n2-2)
Two-Sample T-Test and CI(兩組樣本的檢定及信賴區間): 1廠, 2廠 N Mean StDev SE Mean
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1廠 10 2.179 0.371 0.12 2廠 12 2.520 0.355 0.10 Difference = mu 1廠- mu 2廠
T?(X1?X2)sd=(2.179-2.520)/0.362=-2.20 Estimate for difference: -0.341
95% CI for difference: (-0.665, -0.017)
T-Test of difference = 0 (vs not =): T-Value = -2.20 P-Value = 0.040 DF = 20 Both use Pooled StDev = 0.362
Boxplots of 1廠, 2廠
Boxplots of 1紅 and 2紅(means are indicated by solid circles)3.12.62.11.61紅2紅 6.4 Gage R&R研究
如第七篇計量值的量測系統分析,將數據轉換成下面的結構,MINITAB的Quality Tools>GAGE R&R STUDY即可處理得下面的結果
370
量測值 作業員別 零件別
? X?R法
零件別 作業員別 量測值 分析法 變異數分析法 平均數-全距分析法
371
Gage R&R (Xbar/R) for MEASUREMENTComponents of Variation100Gage name:Date of study:Reported by:Tolerance:Misc:變異數分量 %Contribution %Study Var 6.846.836.82Response by PART依零件別 Percent50標準差法 0Gage R&RRepeatReprodPart-to-Part6.816.80PART 1 2 3 4 5 6 7 8 910R Chart by OPERATOR0.015ABCResponse by OPERATORSample RangeR 管制圖 UCL=0.013186.846.836.820.0100.0050.000依檢驗員 R=0.004033LCL=06.816.80OPERATORABCXbar Chart by OPERATOR6.84ABCOPERATOR*PART InteractionXbar 管制圖 Mean=6.823LCL=6.8156.846.836.826.81OPERATORA B C Sample Mean6.826.816.80Average6.83UCL=6.830檢驗員與零件 1 2 3 4 5 6 7 8 910PART交互影響 ? ANOVA法
Gage R&R (ANOVA) for MEASUREMENTComponents of Variation100Gage name:Date of study:Reported by:Tolerance:Misc:變異數分量 %Contribution %Study Var 6.846.836.82By PART依零件別 Percent50標準差法 0Gage R&RRepeatReprodPart-to-Part6.816.80PART 1 2 3 4 5 6 7 8 910R Chart by OPERATOR0.015ABCBy OPERATORSample RangeR 管制圖 UCL=0.013186.846.836.82依檢驗員 0.0100.0050.0000R=0.004033LCL=06.816.80OPERATORABCXbar Chart by OPERATOR6.84ABCOPERATOR*PART InteractionXbar 管制圖 Mean=6.823LCL=6.8156.846.836.826.81OPERATORA B C Sample Mean6.826.816.800Average6.83UCL=6.830檢驗員與零件 1 2 3 4 5 6 7 8 910PART交互影響
372
MINITAB 在SPC上的应用



