使用Cpmk指標對兩個製程能力作比較

Comparing the Capability of two Processes by Using Cpmk Index.

梁梅莒(Mei-Chu Liang)

指導教授 ： 吳淑妃

淡江大學/管理學院/統計學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00830

摘要

近年來，製程能力指標已被多數品管工程師廣泛地應用在品質管制方面，以評估製程是否合乎能力水準。然而這些品管工程師通常只是簡單地利用樣本觀察值的資料來計算其製程能力指標的估計值，並且直接以此估計值來判斷製程是否符合能力水準，這樣的處理方式其實是不恰當的。因為此估計值是由點估計所得到的單一數值，能提供給我們的資訊較少，所以並無法評估此估計值的精確度。但是在區間估計中，則以點估計的標準誤來建立區間估計值的範圍，亦即將標準誤的衡量一起納入區間估計中。
在本文中，為了比較兩個製程表現之差異，我們關心的是兩個製程之製程能力指標Cpmk之比值和差異。在點估計方面，分別比較自然估計法、拔靴法和摺刀法之偏差與均方差的表現；在區間估計方面，我們利用Boyles(1991)法、三個拔靴法和摺刀法來建立兩個製程之製程能力指標Cpmk比值之信賴區間。並利用Chen and Hsu(1995)之漸近常態分配法、三個拔靴法和摺刀法來建立兩個製程之製程能力指標Cpmk差異之信賴區間。我們使用常態分配所產生的樣本分別對不同方法作模擬比較，並以覆蓋率高低來判斷不同方法之優劣。最後，我們給一個實例示範如何使用製程能力指標Cpmk去比較兩個製程能力之優劣。

關鍵字

製程能力指標 ； 拔靴法抽樣 ； 摺刀法抽樣 ； 常態母體 ； 重複抽樣

並列摘要

In recent years, Process Capability Indices (PCIs) have been applied in the quality control by most practitioners, to evaluate the capability of a production process. However, the approach of these practitioners usually simply look at the index value calculated from the given sample and then making a decision on whether the given process is capable or not is intuitively reasonable but not reliable because sampling errors are ignored. Therefore, the confidence interval approach should be provided to decide whether the production process is capable or not.
For comparing two processes, we consider to estimates the ratio and the difference of two capability indices Cpmk. For point estimation, the bias and the mean square error (MSE) of the given point estimation method are simulated and compared. With respect to the confidence interval estimation, we use the Boyles(1991) method, three bootstrap methods, and the Jackknife method to construct the confidence interval of the ratio of two Cpmk indices. Furthermore, we use the Chen and Hsu’s(1995) method, three bootstrap methods, and the Jackknife method to estimate the difference of two Cpmk indices. The samples generated from normal distribution are used for simulation study and the performance of all methods based the highest average probability are evaluated. At least, one example is given to demonstrate how to compare two processes by using all proposed methods.

並列關鍵字

Process Capability Indices ； Bootstrap Sampling ； Jackknife Sampling ； Normal Populations ； re-sampling

參考文獻

21. Kotz, S. and Johnson, N.L. (1995).Comment on：Percentage of units within specification limits assocated with given values of Cpk and Cpm (by Chan LK and Tang JH). Commun. Statist.

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