製程能力弱度指標的實務應用

Abstract

Greenwich and Jahr-Schaffrath (1995)提出一個製程能力弱度指標（process incapability index）稱為Cpp。事實上，指標Cpp是指標Cpm經由一個簡單的數學轉換而來。指標Cpp之優點為其可以區分出製程的準確性（accuracy）與精確性（precision），而且我們可以很容易得到指標Cpp的優良估計式。指標Cpp是一個簡易而且方便使用的績效評估工具。但是，因為製程的參數是未知而必須由樣本的資料來估計製程的參數，才能得到指標的估計值，所以抽樣的誤差會導致指標估計值有很大的不確定性。如果只根據指標的估計值來判斷製程是否達到要求，會忽略了抽樣誤差所以是一個不可靠的方法。Cheng（1994），以及Pearn與Chen（1997）分別對指標Cp、Cpm、Cpk提供了一些可靠的方法評估製程的績效。本文則針對Cpp提供二個可靠的方法以評估製程的績效。

Greenwich and Jahr-Schaffrath (1995) introduced a new capability index Cpp, a simple transformation of Cpm, which provides an uncojtamianted soparation between information concerning process accuracy and process precision. The formula for Cpp is easy to understand and straightforward to apply. But, since sample data must be collected in order to calculate the index value, a great degree of uncertainty may be introduced into capability assessments due to samplong errors. Currently, practitioners would look at the index value calculated from the sample data then make a conclusion on whether the given process meets the capability requirement. This approach is not reliable since the sampling errors are igmored. In this paper, we take into account the sampling errors and develop a procedure similar to those proposed by Cheng (1994) and Pearn and Chen (1997) using the UMVUE of Cpp, for practitioners to use in determining whether a process meets the capability requirement. The ecisions made using the procedure are, of course, more reliable.