製程能力指標（Process Capability Indices, PCIs）為製程產出提供一個數值的衡量方法，用來協助業界評估製程產出的品質水準，以及是否能夠符合消費者的要求。然而，傳統的製程能力指標大多需假設製程產出為常態分配，但實務上並非所有製程產出都能符合常態分配假設，因此在此情況下若使用常態假設的製程能力指標可能會導致錯估而造成誤判。為解決此缺失，許多學者紛紛提出非常態型的製程能力指標以用來評估製程產出不符合常態分配的情況。本研究首先整理出過去文獻中所提出的七種非常態型製程能力指標，包含指標Cjkp、Cs、Csm、Cpc、CNpk、Cpk(WV)及Cpk(WSD)。接著，在多種非常態分配(例如：Gamma、Weibull、Lognormal、Chi-square分配)利用兩種比較準則來探討這七種非常態製程能力指標的表現，藉由各種不同分配的參數設定，進而評選出較能適切反應製程能力的非常態製程能力指標(包含指標 Cpk(WSD)、Cpk(WV) 及 CNpk)。經由篩選後，進一步利用三種無母數的複式抽樣方法(Bootstrap resampling method)建構指標之信賴區間。並透過模擬方式計算其涵蓋率(Coverage rate, CR)以及信賴下界平均值(Average value of lower confidence bound)，以比較及評估三種區間估計方法的表現。最後透過實例分析及探討以提供決策者在評估非常態製程之產出績效的參考依據。

Process capability indices (PCIs) are used to provide numerical measures on process performance and determine whether a production process is capable of producing products within a specified tolerance. Even cases of process data with normally distributed are very common in practical situations, cases of process data with non-normal distributions are also occurred in the manufacturing industry. Unfortunately, when the distribution of a process characteristic is non-normal, the actual product quality may be misrepresented if we measure the process performance by conventional PCIs and the practitioners might make incorrect decisions. In order to deal with this problem, many non-normal process capability indices have been developed. In this thesis, we first review seven non-normal PCIs including Cjkp, Cs, Csm, Cpc, CNpk, Cpk(WV) and Cpk(WSD) indices and compare their performance for measuring process capability under various non-normal distributions. The comparative rules include the concept of matched Cpk (MCpk) and the corresponding fraction of non-conforming items. The results indicate that three indices, Cpk(WSD), Cpk(WV) and CNpk, have the better achievement to evaluate process performance for non-normal distributions. Next, the nonparametric bootstrap resampling methods (SB, PB and BCPB methods) are applied to establish the confidence interval of these three non-normal capability indices under four non-normal distributions (Gamma, Weibull, Lognormal and Chi-square distributions). A simulation study is conducted to compare the accuracy of these three bootstrap methods in terms of coverage rate and the average value of lower confidence bound. Finally, an application example is presented for illustration.

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