非對稱規格區間下指標Cpk"的近似不偏估計量

Abstract

製程能力指標Cpk在製造業中被廣泛的使用來衡量製程表現，但指標Cpk僅以良率為基礎，且與規格目標T互相獨立。因此，指標Cpk在非對稱規格區間下並未考量到製程與規格目標T之間的關係。Pearn 和 Chen (1998)發表了指標Cpk"用以衡量非對稱區間下的製程能力，指標Cpk"相較於其他Cpk的推廣指標要優秀許多。然而，指標Cpk"的估計量 並非不偏估計量。為了解決此問題，我們以曲面擬合的方法將指標Cpk"的估計量Cpk"^ 加入一修正函數cf，使其修正成為近似不偏估計量Cpk"~。此外，我們也以複式抽樣法的方法解決了在修正函數cf裡ξ未知的問題。

Process capability index Cpk has been widely used in the manufacturing industry to provide numerical measures on process performance. For processes having asymmetric tolerances, index Cpk" has considered the relationship of the process centering and the specification limits to provide a measure of the process yield. However, the estimator of index Cpk" is not an unbiased one. Therefore, we apply the curve fitting method to modify the estimator of the index Cpk" to be an approximately unbiased estimator. Furthermore, we use the Bootstrap method to conduct the problem that a parameter ξ is unknown in the correct factor.