隨著電子產品的消費市場蓬勃發展，人們越加重視產品品質的好壞，而壽命特性常被用來評估電子產品的品質，壽命越長代表品質越好。為了有效衡量品質，製程能力指標為常用的方式，然而許多傳統型的製程能力指標皆須假設其品質特性服從常態分配，但實務上，有些品質特性未必服從常態分配，例如：壽命，若應用傳統製程能力指標來評估壽命績效會造成錯誤的估計，因而壽命績效指標 被提出並建議用來衡量產品壽命的績效表現。
本研究將針對產品壽命服從伽瑪分配與韋伯分配下，以壽命績效指標 為基礎，發展區間估計的方式來進行壽命績效評估，文獻上，當壽命服從伽瑪或韋伯分配，若其形狀參數為已知，已有其估計式抽樣分配之確切形式，可進行區間估計，然而兩分配之參數大多皆為未知的，不易利用傳統抽樣分配法(frequency distribution method)建構精確的信賴區間，因此本研究以貝氏方法結合馬可夫鏈蒙地卡羅(Markov Chain Monte Carlo, MCMC)求得壽命績效指標的可信區間(credible interval)，並將此與過去常見無母數估計的複式抽樣法(Bootstrap resampling method)所建構的信賴區間進行比較與探討，利用涵蓋率(coverage rate)與平均區間寬度(average interval width)等方式評估不同方法建構出的區間表現，模擬結果顯示本研究所發展的馬可夫鏈蒙地卡羅法皆有不錯的表現。此外我們透過兩個應用案例說明產品壽命績效評估之流程，並同時建構一個圖形化使用者介面，藉此協助決策者更容易、更方便應用本研究所發展的方法進行壽命績效評估。

As the consumer market for electronic products flourishes, people pay more attention to the quality of products. And, lifetime is often used to evaluate the quality of electronic products. The longer the lifetime, the better the quality. In order to effectively measure quality, process capability indices (PCIs) are commonly considered to be useful tools. Many traditional PCIs should be applied under the assumption that the quality characteristics are normally distributed. However, in practice, some quality characteristics may not generally possess normal distribution, such as the lifetime of electronic products. A lifetime performance index was therefore proposed and recommended to measure the performance of lifetime.
Based on the lifetime performance index, this study provides procedures for lifetime performance assessment under gamma and Weibull distributions. We can obtain more reliable estimates by interval estimation. When the lifetime follows two distributions and their shape parameters are known, there have exact forms of the sampling distribution of the estimator of respectively so that we can perform interval estimation. However, the parameters of two distributions actually are often unknown and it is not easy to construct an accurate confidence interval using the traditional frequency distribution method. So, in our study we integrate the Markov chain Monte Carlo (MCMC) technique into Bayesian approach to construct credible intervals for . Then, we compare them with the bootstrap confidence intervals in terms of the coverage rates and the average interval widths. The simulation results show that MCMC proposed in our study perform better than bootstrap resampling methods. In addition, we also provide two application cases with a graphical user interface to easily illustrate the procedure of lifetime performance assessment.

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 3
1.3 研究架構 3
第二章 文獻回顧與探討 6
2.1 製程能力指標 6
2.2 壽命績效指標 11
2.3 基於伽瑪分配下之壽命績效指標 13
2.3.1 伽瑪分配與參數估計 13
2.3.2 壽命績效指標與產品壽命合格率 17
2.3.3 壽命績效指標之估計式與信賴區間 18
2.4 基於韋伯分配下之壽命績效指標 20
2.4.1 韋伯分配與參數估計 20
2.4.2 壽命績效指標與產品壽命合格率 24
2.4.3 壽命績效指標之估計式與信賴區間 25
2.5 區間估計方法 28
2.5.1 複式抽樣法 29
2.5.2 貝氏方法 32
2.5.3 馬可夫鏈蒙地卡羅法 33
第三章 基於伽瑪分配下區間估計方法之分析與探討 46
3.1 貝氏區間估計 46
3.1.1 伽瑪分配參數之事後機率分配 46
3.1.2 以馬可夫鏈蒙地卡羅法建構可信區間 50
3.2 形狀參數已知情況下之區間估計 51
3.2.1 模擬環境設定與流程 51
3.2.2 模擬結果分析 54
3.3 雙參數皆未知情況下之區間估計 59
3.3.1 模擬環境設定與流程 59
3.3.2 模擬結果分析 62
第四章 基於韋伯分配下區間估計方法之分析與探討 69
4.1 貝氏區間估計 69
4.1.1 韋伯分配參數之事後機率分配 69
4.2 形狀參數已知情況下之區間估計 72
4.2.1 模擬環境設定與流程 72
4.2.2 模擬結果分析 75
4.3 雙參數皆未知情況下之區間估計 81
4.3.1 模擬環境設定與流程 81
4.3.2 模擬結果分析 84
第五章 圖形化使用者介面與案例分析 93
5.1 圖形化使用者介面操作與說明 93
5.2 案例分析 102
5.2.1 LED燈泡案例 102
5.2.2 TFT-LCD顯示器案例 109
第六章 結論與未來研究方向 117
6.1 結論 117
6.2 未來研究方向 118
參考文獻 120
附錄A 126
附錄B 132

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