隨著科技不斷進步與創新，工業產品也逐漸變得複雜與精密。消費者在購買產品時，對於產品品質的要求也變得更為嚴苛。為了達到消費者所需求的品質，生產者在製造產品時，會對製程的要求更加嚴格，如何節省成本及避免造成不必要的浪費，以追求更多的利潤，已是當今生產者所必須重視的問題。
     本研究假設產品的壽命服從Burr XII分配時，在逐步型I區間設限下，計算出壽命績效指標C_L之最大概似估計量並求得其漸近分配。在規格下限L已知的情形下，使用此估計量及兩種拔靴法發展三個檢定程序以判定壽命績效是否達到預定的能力水準。我們會對三種檢定方法的檢定力做模擬比較分析。最後，我們用兩個數值實例說明如何使用本研究所提出的檢定程序。

It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices CL is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Burr XII distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. Two kinds of Bootstrap methods are developed to construct the other two testing procedures. The comparisons of power analysis of three methods are done. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

目錄	I
表目錄	III
圖目錄	VIII
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 設限型式	4
1.3 本文架構	6
第二章 壽命績效指標與其估計	7
2.1 產品的壽命績效指標C_L	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與檢定力	20
3.1 壽命績效指標的檢定演算程序	20
3.2 樣本數大小之決定	25
3.3 檢定力之模擬分析	29
3.4 點估計	35
第四章 模擬與數值實例分析	36
4.1 模擬範例	36
4.2 數值實例	41
第五章  結論與未來研究	47
5.1 結論	47
5.2 未來研究	48
參考文獻	50

表2.1 壽命績效指標C_L值對應之製程良率P_r	12
表4.1 50位關節炎患者的緩解時間(單位：小時)	41
附表 1當形狀參數c=1,規格下限L=0.05,總觀測時間T=1.2，觀測樣本數與觀測次數分別為n=60,m=20,30及n=80,m=30,40、及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.01下，檢定力函數h(c_1 )在0.8(0.025)0.95的數值	52
附表 2當形狀參數c=1,規格下限L=0.05,總觀測時間T=1.2，觀測樣本數與觀測次數分別為n=60,m=20,30及n=80,m=30,40、及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.05下，檢定力函數h(c_1 )在0.8(0.025)0.95的數值	53
附表 3當形狀參數c=1,規格下限L=0.05,總觀測時間T=1.2，觀測樣本數與觀測次數分別為n=60,m=20,30及n=80,m=30,40、及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.1下，檢定力函數h(c_1 )在0.8(0.025)0.95的數值	54
附表 4當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、檢定力1-β=0.75,0.80,0.85、觀測次數m=20,30,40及逐步設限移除率p=0.05,0.075,0.1時，在顯著水準α=0.01、目標值c_0=0.8和實際值c_1=0.825(0.025)0.95下，所需要的最小樣本數	55
附表 5當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、檢定力1-β=0.75,0.80,0.85、觀測次數m=20,30,40及逐步設限移除率p=0.05,0.075,0.1時，在顯著水準α=0.05、目標值c_0=0.8和實際值c_1=0.825(0.025)0.95下，所需要的最小樣本數	56
附表 6當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、檢定力1-β=0.75,0.80,0.85、觀測次數m=20,30,40及逐步設限移除率p=0.05,0.075,0.1時，在顯著水準α=0.10、目標值c_0=0.8和實際值c_1=0.825(0.025)0.95下，所需要的最小樣本數	57
附表 7當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=60、觀測次數m=20,30及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.01下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	58
附表 8當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=60、觀測次數m=20,30及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.05下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	59
附表 9當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=60、觀測次數m=20,30及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.10下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	60
附表 10當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.01下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	61
附表 11當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.05下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	62
附表 12當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，在目標值c_0=0.8和顯著水準α=0.10下，模擬三種不同方法的檢定力在實際值c_1=0.8(0.025)0.95時的數值	63
附表 13當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=60、觀測次數m=20,30及逐步設限移除率p=0.05,0.075,0.1時，模擬三種不同方法的bias在實際值c_1=0.8(0.025)0.95時的數值	64
附表 14當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，模擬三種不同方法的bias在實際值c_1=0.8(0.025)0.95時的數值	65
附表 15當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，模擬三種不同方法的MSE在實際值c_1=0.8(0.025)0.95時的數值	66
附表 16當形狀參數c=1、規格下限L=0.05、總觀測時間T=1.2、觀測樣本數n=80、觀測次數m=30,40及逐步設限移除率p=0.05,0.075,0.1時，模擬三種不同方法的MSE在實際值c_1=0.8(0.025)0.95時的數值	67

圖1.1 逐步型I區間設限圖	5
圖2.1尺度參數k=1,形狀參數c=0.5,1,2,3,5,10時的p.d.f.	8
圖2.2尺度參數k=2,形狀參數c=0.5,1,2,3,5,10時的p.d.f.	8
圖2.3尺度參數k=1,形狀參數c=0.5,1,2,3,5,10時的故障率函數	9
圖2.4尺度參數k=2,形狀參數c=0.5,1,2,3,5,10時的故障率函數	9
圖3.2.1 當α=0.1、1-β=0.75及m=30下，不同的逐步設限移除率p=0.05,0.75,0.1時所需的最小樣本數n	27
圖3.2.2 當α=0.1、1-β=0.75及p=0.05下，不同的觀察次數m=20,30,40時所需的最小樣本數n	28
圖3.2.3 當α=0.1、m=30及p=0.05下，不同的檢定力1-β=0.75,0.8,0.85時所需的最小樣本數n	28
圖3.2.4 當1-β=0.75、m=30及p=0.05下，不同的顯著水準α=0.01,0.05,0.1時所需的最小樣本數n	29
圖3.3.1 當α=0.1、m=5及n=60下，不同的逐步設限移除率p=0.05,0.75,0.1時的檢定力	33
圖3.3.2 當α=0.1、m=30及p=0.05下，不同的樣本數n=60,80時的檢定力	33
圖3.3.3 當α=0.1、n=60及p=0.05下，不同觀察區間個數m=20,30時的檢定力	34
圖3.3.4 當m=30、n=60及p=0.05下，不同的顯著水準α=0.01,0.05,0.1時的檢定力	34
圖4.2 不同c下之p值	43

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