在科技進步迅速的時代，製造業者為了能提高消費者對於產品的購買意願，產品品質的提升以達到消費者所需求的品質水準是品管上很重要的課題。在實務上，製程能力指標(process capability indices, PCIs)已被廣泛地應用在評估製程績效與潛能(potential capability)之評估上，進而不斷地提升產品品質及製程能力。本研究假設觀測到的產品壽命服從Fréchet分配，在逐步型II設限且給定規格下限L下，使用最大概似估計量和貝氏估計量的兩種方式對壽命績效指標做估計，並建構出壽命績效指標的兩種信賴下界，使用此下界來檢定壽命績效指標是否達到預定的能力水準。在不同設限下，我們對兩種檢定方法做模擬比較，結果顯示貝氏方法有較好的表現。最後，我們用兩個數值實例說明如何使用本研究提出的檢定程序。

In modern emerging market, it’s very important that manufacturers improve the quality of products in terms of lifetime performance in order to reach high quality standards of demanding customers. In practical world, process capability indices (PCIs) have been widely used to assess the performance of the process and potential capability.
This research is focusing on the lifetime performance index of products following a Fréchet distribution under progressive type II censoring. The maximum likelihood estimator and bayesian estimator for the lifetime performance index   are used to develop the hypothesis testing for   based on a credible interval in the condition of know lower specification limit (L) to determine whether the product performance adheres to the required level. Finally, two practical examples are given to illustrate the proposed the testing algorithmic procedure to determine whether the process is capable.

目錄
目錄 I
表目錄 III
圖目錄 IV
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻探討 3
1.2.1 製程能力指標之發展 3
1.2.2 設限樣本 5
1.3 本文架構 7
第二章 Fréchet分配壽命績效指標與其估計 8
2.1 產品的壽命績效指標 10
2.2 壽命績效指標的估計量 13
第三章 壽命績效指標的檢定演算程序 16
3.1 壽命績效指標的檢定演算程序 16
3.2 覆蓋率的蒙地卡羅模擬與其模擬值的比較 20
第四章 數值範例 33
4.1 數值實例 33
4.2 模擬範例 38
第五章 結論與未來研究 43
5.1 結論 43
5.2 未來研究 44
參考文獻 45

表目錄
表2.1 壽命績效指標 值對應之製程良率 12
表3.1 壽命績效指標 使用MLE與貝氏估計量之覆蓋率和SMSE(括號內)26
表3.1(續) 壽命績效指標 使用MLE與貝氏估計量之覆蓋率和SMSE(括號內) 27
表3.1(續) 壽命績效指標 使用MLE與貝氏估計量之覆蓋率和SMSE(括號內) 28
表3.2 壽命績效指標 之MLE與貝氏估計量之風險值	29
表3.2(續) 壽命績效指標 之MLE與貝氏估計量之風險值 30
表3.3 壽命績效指標 使用MLE與貝氏估計量之標準偏誤 31
表3.3(續) 壽命績效指標 使用MLE與貝氏估計量之標準偏誤	32
表4.1 台灣北區20年之單日最大總雨量(單位:米)	33
表4.2 設限計劃 下北區之單日最大總雨量(單位:米) 36
表4.3 設限計劃 下北區之單日最大總雨量(單位:米) 37
表4.4 Fréchet分配之模擬逐步型II設限樣本 39
表4.5 模擬Fréchet分配之逐步型II設限樣本設限計劃 41

圖目錄
圖1.1 逐步型II設限圖 6
圖2.1 雙參數在 時Fréchet分配之機率密度函數圖 9
圖2.2 雙參數在 時Fréchet分配之故障率函數圖	9
圖4.1 不同 下之p-value 35

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