基本型製程能力指標（Process Capability Indices, PCIs）不僅被用來評估製程之產出績效，並且是製程管制工具中衡量產品品質的重要技術之一。但基本型製程能力指標之品質特性必需服從常態分配，然而面對非常態製程時，其基本型製程能力指標在計算非常態製程的表現會出現不準確的情況，因此，過去文獻中將基本型製程能力指標利用非常態製程之特徵值加以修正，更有許多學者針對非常態分配之製程提出新的製程能力指標，甚至更進一步針對新的製程能力指標加以比較，但其比較方法參差不齊。本研究首先將過去文獻中針對非常態製程能力指標進行整理及定義，接著，於非常態分配中利用相對偏誤（Relative Bias, RB）進行各指標之分析與比較。針對不同分配參數條件下，將較佳之製程能力指標利用無母數下的複式抽樣法（Bootstrap approach method）建構較佳的製程能力指標之信賴區間，而複式抽樣法下區間估計方法的計算又分為五種不同型態：標準複式法（Standard Bootstrap, SB）、百分位複式法（Percentile Bootstrap, PB）、修正偏差百分位複式法（Biased-Corrected Percentile Bootstrap, BCPB）、t百分位複式法（Percentile-t bootstrap, PT）及加速修正偏差百分位複式法（Biased-Corrected and accelerated percentile bootstrap, BCa）。而後透過電腦模擬求得其涵蓋率（Coverage Rate, CR）及信賴下界平均值（Average Value of Lower Confidence Bound, AVLCB），即可進一步比較各種型態的表現。最後，透過一實際個案，應用本研究之建議進行評估及分析，以供實務上使用之依據。

Process capability indices (PCIs) have been considered as one of practical tools in the field of statistical quality control for measuring process performance and determining whether the process is capable or not. Most research in process capability analysis literature has focused on cases in which the quality characteristic follows the normal distribution. However, an erroneous interpretation of the process’s capability may be occurred when the distribution of the process characteristics is non-normal. To remedy for this, several modified capability indices have been developed for non-normal distributions and investigated. In this thesis, several non-normal capability indices are summarized and compared in terms of relative bias under various non-normal distributions. Then, the well-known non-parametric approach, Bootstrap resampling, is introduced and five types of Bootstrap interval estimation methods, including the standard bootstrap (SB), the percentile bootstrap (PB), the biased corrected percentile bootstrap (BCPB), Percentile-t bootstrap (PT) and Biased-Corrected and accelerated percentile bootstrap (BCa), are applied to construct confidence interval of those better indices. A series of simulations is conducted to calculate the Coverage Rate (CR) and Average Value of Lower Confidence Bound (AVLCB) under various parameters. Finally, an application example is presented for illustration.

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