在現今業界中，如何評估製程產出績效以及挑選較佳的合作供應商已是製造商必須正視的重要課題。製程能力指標為業界常用來衡量製程能力的工具，其中非對稱型製程損失指標Le"不僅能有效衡量製程準度與精度，對於目標值不等於規格中心的非對稱允差製程亦能精準量測其製程能力，故本研究將基於Le"對實務上可能發生的情況進行全面的探討。
本研究主要探討的議題分成兩個部分，包含衡量單一製程能力以及比較新舊供應商其製程能力孰優孰劣，並應用抽樣分配法、複式抽樣法、廣義信賴區間法以及貝氏方法結合馬可夫鏈蒙第卡羅(Markov Chain Monte Carlo, MCMC)技巧等區間估計方法建構出單一製程指標Le"以及兩製程損失指標比值與差值之信賴上界，利用模擬的方式從涵蓋率以及指標上界平均值之結果探討各方法的建構表現，分析結果顯示抽樣分配法以及MCMC能夠可靠地估計單一製程能力，而複式抽樣法則是能在以兩製程損失指標比值為基礎的供應商能力比較提供可靠的檢定結果。最後，本研究透過實際案例說明如何應用複式抽樣法於比較新舊供應商其製程能力之議題，令決策者能對於操作流程更加瞭解。

In the current manufacturing industry, how to assess the process output performance and select the better partner supplier is an important issue that manufacturers must face. And the process capability index is a common tool for measuring the process capability. The process loss index with asymmetric tolerances Le" could not only effectively measure the process accuracy and precision, but also precisely measure the process with asymmetric tolerances whose target value is not equal to the midpoint of specification interval. Therefore, this study will conduct the comprehensive investigation for the practical situation based on the index Le".
The topics discussed in this study divided into two parts, including measuring the single process capability and comparing the process capability between original and new suppliers, and then applied the interval estimation methods such as Frequentist Distribution approach (FD approach), Bootstrap method, Generalized Confidence Intervals approach and the Bayesian approach integrated with Markov Chain Monte Carlo (MCMC) technique to construct the Upper Confidence Bound (UCB) of single process index Le", the ratio and difference of two process loss indexes, respectively. Conduct the simulations to evaluate the constructive performance for various methods from the perspective of coverage rate and average value of UCB of index. The simulation results show that FD approach and MCMC could reliably measure the single process capability and Bootstrap method could provide the reliable testing results for the hypothesis testing based on the ratio of two process loss indexes. Finally, the practical case study shows how to apply the Bootstrap method to comparison of process capability between new and original suppliers and make the decision maker more aware of the whole operation process.

致謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 ix
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 4
1.3 研究架構 4
第二章 文獻回顧與探討 7
2.1 製程能力指標 7
2.1.1 良率指標 7
2.1.2 損失指標 9
2.1.3 非對稱型製程損失指標 的估計式及其抽樣分配 12
2.2 製程能力指標之區間估計方法 13
2.2.1 抽樣分配法 14
2.2.2 複式抽樣法 15
2.2.3 廣義信賴區間法 16
2.2.4 貝氏方法 17
2.2.5 馬可夫鏈蒙地卡羅方法 19
2.3 基於製程能力指標之供應商選擇問題 28
第三章 單一製程之製程損失分析 31
3.1 非對稱型損失指標之信賴上界 31
3.1.1 抽樣分配法之信賴上界 31
3.1.2 複式信賴上界 34
3.1.3 廣義信賴上界 36
3.2 非對稱型損失指標之可信上界 38
3.2.1 常態分配參數之事後機率分配 38
3.2.2 以馬可夫鏈蒙地卡羅法建構可信上界 41
3.3 數值模擬分析與比較 42
3.3.1 模擬環境 43
3.3.2 涵蓋率與信賴上界平均值 48
3.3.3 模擬分析之結果 49
第四章 新舊供應商選擇問題之比較程序 63
4.1 檢定方法 63
4.2 模擬分析之結果與比較 73
4.2.1 模擬環境設定 73
4.2.2 涵蓋率表現 79
4.3 案例分析 98
第五章 結論與未來研究方向 103
5.1 結論 103
5.2 未來研究方向 104
參考文獻 106
附錄A 110
附錄B 119

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