近年來，由於智慧型手機及平板電腦的盛行等等，在產業高度競爭的時代，消費者對於產品品質要求更加嚴格。在實務上，製程能力指標(process capability indices, PCIs)已經被廣泛地用於評估製程的績效，進而不斷地提升產品品質及製程能力。
   本研究假設當產品的壽命服從Rayleigh分配時，在逐步型I區間設限下，求出壽命績效指標C_L之最大概似估計量，並探討其漸近分配與檢定力函數，在規格下限L已知的情形，利用此估計量發展出一個新的假設檢定程序，以判定壽命績效是否達到預定的能力水準。最後，將用兩個數值實例去說明如何使用本研究所提出的檢定程序。

In recent years, due to the prevalence of smart phones and tablet PCs, the consumers require more stringent product quality in the highly competitive commercial market. In practice, process capability indices (PCIs) has been widely used to assess the performance of the process, and then continues to be employed to improve the product quality and process capability.

   This research is focusing on the lifetime of products following the Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index (C_L) based on the progressive type I interval censored sample. The asymptotic distribution of this estimator and the power function are also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit L. Finally, two numerical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

目 錄
第一章  緒論	1
1.1研究動機和目的	1
1.2文獻探討	3
1.2.1 製程能力指標的發展	3
1.2.2 設限樣本	5
1.3 本文架構	7
第二章  Rayleigh分配之壽命績效指標	8
2.1 產品的壽命績效指標與製程良率	8
2.2 壽命績效指標之估計量	11
第三章  壽命績效指標的檢定演算程序	17
3.1 壽命績效指標的檢定演算程序	17
3.2 壽命績效指標檢定程序的檢定力	19
第四章  模擬與數值實例分析	25
4.1 數值實例	25
4.2 模擬例子	28
第五章  結論與未來研究	30
5.1 結論	30
5.2 未來研究方向	31
參考文獻	32
附 錄	34

表目錄	

附表2.1 壽命績效指標C_L值對應之製程良率 	34

附表3.1當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.01下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值	35

附表3.2 當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.05下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值	37

附表3.3 當規格下限L=0.05,總觀測時間T=0.5,設限樣本數m=5(1)8,觀測樣本數n=60(20)100及逐步移除率p=0.05(0.025)0.1時,在目標值c_0=0.8和顯著水準alpha=0.1下, h(c_1)在c_1=0.8,0.825(0.025)0.975檢定力函數的數值	39

圖目錄

圖1.1 逐步型I區間設限圖	7

圖3.1 當alpha=0.1、m=5及p=0.05下，對不同總樣本n=(60,80,100)時的檢定力函數。	22

圖3.2 當alpha=0.1、n=60及p=0.05下，對不同的設限樣本m=(5,6,7,8)時的檢定力函數。	23

圖3.3 當alpha=0.1、n=60及m=5下，對不同的移除率p=(0.05,0.075,0.1)時的檢定力函數。	23

圖3.4 當n=60、m=5及p=0.05下，對不同顯著水準alpha=(0.01,0.05,0.1) 時的檢定力函數。	24

圖3.5 當n=60、m=5,...,20及p=0.05下，對不同顯著水準 alpha=(0.01,0.05,0.1)時的檢定力函數。	24

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