製程能力指標（Process Capability Indices, PCIs）不僅可量化製程績效以利於評估，並且已廣泛地被運用於衡量產品品質保證。現今製程規格以兩種情形主：對稱公差（Symmetric tolerance）與不對稱公差（Asymmetric tolerance）。然而，過去的文獻主要著重在對稱公差，但假若製程規格為非對稱公差時，則可能會產生製程績效的誤判。因此，本研究探討的主題以非對稱公差為主，並以製程能力指標 作為評估製程績效的依據。而本研究的目的是將過去文獻上針對 所提出的區間估計方法，以及其他統計方法，來建構 之信賴區間。這些區間估計方法包含：兩種型態的抽樣分配法（Sampling distribution approach, SD*與SD）、四種型態的複式抽樣法（Bootstrap approach, SB、PB、BCPB與PT）、廣義信賴區間法（Generalize confidence interval, GCI），以及貝式估計法（Bayesian approach, BA）。本研究透過一連串的電腦模擬，求得各估計方法的涵蓋率（Coverage rate, CR）以及信賴下界平均值（Mean of lower confidence bound, MLCB），即可進一步比較這些估計方法的表現。分析結果顯示，對於估算指標 ，SD*、GCI與BA法相較其他方法具有充分的解釋力，並且也較為精準。最後，本文以實例作為分析與說明，以供實務上使用依據。

Process capability indices provide numerical measures on process performance, which have been widely used as one of practical tools for quality assurance. In manufacturing industries, there are two cases with manufacturing tolerances, one is called symmetric tolerance and the other is called asymmetric tolerance. However, most of researches in the literature are focused on cases while the manufacturing tolerance is symmetric, which have been shown to be inappropriate for evaluating process performance with asymmetric tolerance. Therefore, in this thesis, we focus on asymmetric tolerances and use the index for evaluating process performance. Several available methods for constructing confidence intervals of the index are examined and discussed. These methods include two types of sampling distribution approach (SD*, SD), four types of bootstrap approach (SB, PB, BCPB, PT), generalized confidence interval approach (GCI) and Bayesian approach (BA). A series of simulations is conducted to calculate the coverage rate (CR) and mean of lower confidence bounds (MLCB) under various parameters. The simulation results show that the GCI and BA approaches seem to work very satisfactory. Therefore, these two approaches can be recommended for evaluating process performance with asymmetric tolerances. Finally, an application example is presented for illustration.

致謝 i
中文摘要 ii
Abstract iii
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的 2
1.3研究架構 2
第二章 文獻回顧與探討 4
2.1製程能力指標 4
2.2 製程良率 6
2.3製程能力指標C"pmk 8
2.3.1指標之估計量C^"pmk 8
2.3.2抽樣分配與其相關統計性值 8
2.3.3區間估計 13
2.3.4複式抽樣法 16
2.3.5廣義信賴法 17
2.3.6貝式估計法 18
第三章 製程能力指標 C"pmk之區間估計方法 21
3.1抽樣分配法（Sampling distribution approach） 21
3.2複式抽樣法（Bootstrap approach） 22
3.3廣義信賴區間法（Generalized Confidence Intervals approach） 26
3.4貝式估計法（Bayesian approach） 28
第四章、研究分析與結果 31
4.1 參數設定與執行步驟 31
4.2 涵蓋率之數據分析 37
4.2.1案例一 38
4.2.2案例二 47
4.3信賴下界分析 52
4.3.1案例一 52
4.3.2 案例二 59
第五章、個案分析 63
第六章、結論與未來建議 68
6.1 結論 68
6.2 未來建議 69
參考文獻 70
附錄 74

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