製程能力指標Cpmk的應用

Abstract

製程能力指標常常被製造業用來評估製程的能力與績效。事實上製程 能力指標是一個容易了解而且又好用的績效評估工具，但是因為製程的參 數是未知的，我們必需由樣本的資料來估計製程的參數才能得到指標的估 計值。由於抽樣的誤差導致指標的估計值會有很大的不確定性。就目前的 狀況而言，大部分都只是以指標的估計值來判斷製程是否達到要求。這種 方法忽略了抽樣誤差所以是一個很不可靠的方法。Cheng(1994)與 Pearn & Chen (1997) 針對指標 Cp,Cpk 與 Cpm提供了一個較為可靠的評估製程 績效的方法，由於指標Cpmk的估計式的分配較為複雜，所以目前為止並沒 有有關指標Cpmk的評估製程績效的方法。本文針對指標 Cpmk 提供了一個 與 Cp,Cpk,Cpm 等三指標類似的方法來評估製程績效。 Process capability indices(PCIs) have been used in manufacturing industries to provide a quantitative measure on process potential and performance.In fact, the formulate for these indices are easy to understand and straightforward to apply.But since,since sample datamust be collected in order to calculate thess indices, a great degree of uncertainty may be introduced into capability assessments due to sampling errors.Currently, most practitioners simply look at the value of the index calculated from the sample data and then make a conclusion on whether the given process meets the capability requirement. This is not reliable since sampling errors are ignored. Cheng(1994) and Pearn andChen (1997) have developed a procedure for using estimators of Cp,Cpk and Cpm for practitioners to use to determine whether a process meets thecapability requirement or not.However,no procedure for Cpmk was given because difficultieswas encountered in calculating the sampling distribution of theestimator of Cpmk. In this paper, we develop a procedure similar to Cp,Cpk and Cpm for the index Cpmk.