製程良率為普遍用於製造業以評估製程產出品質的標準，而製程能力指標(process capability indices, PCIs)為目前業界用來衡量製程產出績效的重要統計工具之一，其中Spk指標能對具雙邊規格之常態分配製程提供精確的良率衡量，其指標值與良率存在一對一的對應關係。然而，Spk指標估計式之求算及抽樣分配相當複雜，以致其精確的信賴區間亦難以求得。此外，在實務上有許多品質特性並非符合常態分配，使得Spk指標在實務應用上受到侷限。
為克服上述問題，本研究基於製程良率指標Spk提出一套通用的製程良率評估流程，探討內容主要分成兩部份，第一部分針對常態製程，以貝氏方法結合馬可夫鏈蒙地卡羅(Markov Chain Monte Carlo, MCMC)建構Spk可信區間，並以涵蓋率及區間寬度評估MCMC所得可信區間之表現，模擬結果證實了MCMC能精確地估計製程良率，為良率估計提供另一種精確又可靠的選擇。而第二部份則針對非常態製程，將非常態資料透過Box-Cox轉換後估計Spk，並進一步分析各種非常態分配下指標估計值的相對偏誤(relative bias)，將此相對偏誤彙整成修正表，供使用者進行後續修正以獲得更準確之估計。最後，本研究建構製程良率評估程序之圖形化使用者介面，針對常態與非常態製程之情境，各應用一個真實案例闡述製程良率分析流程，讓使用者能簡易地進行良率估計與製程能力評估。

Process yield is a standard numerical measure of process performance in manufacturing industry. Process capability indices, closely related to yield, are effective statistical tools for quality assurance. In particular, the yield index Spk can provide an exact measure on the process yield of normal process with two-sided specifications. However, the calculation and sampling distribution of the estimated Spk is mathematically intractable, making the exact confidence interval of Spk difficult to establish. Moreover, in practice, quality characteristic with non-normal distribution are also common, this will restrict the application of Spk.
To overcome the above problem, this paper provide procedures for assessing the process yield based on yield index Spk. For normal processes, we integrate the Markov Chain Monte Carlo (MCMC) technique into Bayesian approach for constructing the credible interval for Spk. The results show that MCMC can provide an accurate and reliable information on assessing the yield. For non-normal processes, we consider the Box-Cox transformation to estimate the yield index, and examine the performance of transformation by relative bias. We also tabulate the relative bias for further adjustment of yield. In addition, we develop a graphical user interface for assessing process yield easily based on Spk and also present two examples for normal and non-normal process to illustrate the applicability of the proposed procedure.

摘要 2
Abstract 3
目錄 4
圖目錄 6
表目錄 8
第一章 緒論 9
1.1 研究背景與動機 9
1.2 研究目的 11
1.3 研究架構 11
第二章 文獻回顧與探討 15
2.1 製程能力指標 15
2.2 製程良率指標之估計式與抽樣分配 18
2.3 製程良率指標之區間估計 20
2.3.1 複式抽樣法 21
2.3.2 廣義信賴區間法 23
2.4 貝氏方法 25
2.5 馬可夫鏈蒙地卡羅法 26
2.5.1 Metropolis-Hastings演算法 27
2.5.2 Gibbs抽樣法 28
2.5.3 適應性拒絕抽樣法 29
2.5.4 適應性拒絕Metropolis抽樣法 31
2.5.5 收斂性評估 34
2.6 Box-Cox轉換法 34
第三章 常態製程之製程良率分析 36
3.1 良率指標之貝氏區間估計 36
3.1.1 常態分配參數之事後機率分配 36
3.1.2 以馬可夫鏈蒙地卡羅法建構可信區間 39
3.2 數值模擬分析與比較 40
3.3 案例分析 48
第四章 非常態製程之製程良率分析 53
4.1 非常態製程與良率指標 53
4.2 非常態製程之良率估計值修正與調整 60
4.3 案例分析 68
第五章 結論與未來研究方向 75
5.1 結論 75
5.2 未來研究方向 76
參考文獻 78
附錄A 82

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