近年來，製程能力指標被製造業廣泛的應用在品質監控方面，以評估製程能力是否合乎水準。但工程師若僅依據指標的點估計值來判斷製程是否符合要求，會因忽略了抽樣誤差而造成不可靠，因此本研究使用區間估計來解釋製程之能力。 本論文使用製程能力指標C_pw來衡量單一製程之製程能力，並以兩個製程能力指標比值C_pw1/C_pw2來比較兩個製程能力之優劣，我們分別利用近似卡方法以及三種拔靴法來建立C_pw與C_pw1/C_pw2之信賴區間，生成常態分配的樣本來做模擬比較，並以覆蓋率高低來判斷不同方法之優劣。 此外，本文也將六標準差的概念與製程能力指標C_pw結合，以衡量目前的製程能力，並說明如何將標準差個數轉換成製程能力指標C_pw。最後，我們提供一個實例說明如何使用製程能力指標C_pw去判定單一製程是否有能力以及比較兩個製程能力之優劣。 In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industry. They are used to assess the ability of a manufacturing process. However, using point estimator for the process capability index is not reliable because sampling errors are ignored. Therefore, the confidence interval approach is used in this study to determine whether the process is capable or not. The process capability index C_pw is used to evaluate the performance of a production process. The ratio of two capability indices C_pw1/C_pw2 is used to compare the performance of capabilities of two production processes. We propose a chi-squared distribution to approximate the distribution of the estimator of the C_pw. Four methods including the approximate chi-squared method and three bootstrap methods are considered to construct the confidence intervals for C_pw and C_pw1/C_pw2 respectively. A simulation comparison of the performance of four methods is done haved on the samples generated from a normal distribution. Moreover, we incorporate the concept of Six Sigma with the process index C_pw. Finally, one example is given to demonstrate how to use the process index C_pw to determine whether if one production process is capable and to determine whether if the capabilities of two production processes are different.
