製程能力指標的改進

Abstract

C* 是一個製程能力的新度量指標，當執行製程時，它同時考慮了製程變異以及目標值與平均數的距離。 當目標值與平均數相等時，C* 即是Cpk。我們利用樣本平均數的定義域分割成三等分的方法，導出 * 的密度函數。在目標值與平均數相等且大於規格上下限中點，以及大樣本假設之下，我們計算了 * 與 pk 的期望值。接著，我們給了改進Cpk 的另一個指標， C**。同時，在目標值與平均數相等且大於規格上下限中點，以及大樣本假設之下，我們也比較了 ** 與 pk 的期望值。 最後，在一個實例中，我們運用複式重複抽樣（bootstrap methods）來比較Cpk 、C*、 C**的信賴區間長度。

A new measure of the process capability, $C^{*}$, that takes into account the distance between the target value and mean as well as the process variation is proposed for assessing the process performance. When the target value is equal to the process mean, $C^{*}$ is the same as Cpk. We derive the density of C* by partitioning the domain of \hat{mu} into three parts. The expected values of $\hat{C}^{*}$ and $\hat{C}_{pk}$ under large sample assumption and mu=T>M, where M is the midpoint of the two specification limits, are accounted. Then, another improvement of Cpk, C**, is proposed. Also, we compare the expected values of $\hat{C}^{**}$ and $\hat{C}_{pk}$ under large sample assumption and mu=T>M. Finally, we apply bootstrap methods to give the confidence intervals for C* and C** and compare their lengths with Cpk in the particular case.