近年來，由於科技的進步，許多高科技產品像是平板電腦，手機等等,皆很受消費者歡迎，而消費者對於產品的品質要求則更加嚴格，因此提升產品製程的能力是品管上很重要的工作。在實務上，已經發展了很多種方法來評估產品的品質能力，製程能力指標(process capability indices, PCIs)就是其中一種方法。
     製程能力指標已經被廣泛地用於評估製程的表現績效以及不斷地提升產品品質及製程能力。當產品的壽命服從Gompertz分配時，望大型的壽命績效指標應該是被考慮的。在逐步型I區間設限下，我們求出壽命績效指標之最大概似估計量並求得其漸近分配。在規格下限已知的情形下，我們使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，我們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, consumers are in the pursuit of more stringent product quality requirements for many high-tech products such as tablet, mobile phones, etc. In practice, many researchers have developed a variety of methods to assess the quality of the product and the method of process capability indices (PCIs) is one of them.
Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. When the lifetime of products possesses a Gompertz distribution, the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

目錄
目錄	I
表目錄	III
圖目錄	V
第一章 緒論	1
1.1	研究動機與目的	1
1.2	文獻探討	5
1.3	本文架構	9
第二章 壽命績效指標與其估計	10
2.1	產品的壽命績效指標 	12
2.2	壽命績效指標的估計量	15
第三章 壽命績效指標的檢定演算程序	21
3.1	壽命績效指標的檢定演算程序	21
3.2	壽命績效指標檢定程序的檢定力	23
第四章 數值實例示範	29
第五章 結論與未來研究	37
5.1	結論	37
5.2	未來研究方向	38
參考文獻	39
附錄	42

 
表目錄
表 2.1 壽命績效指標CL值對應之製程良率Pr 	14
表 4.1 被餵食未飽和飲食的老鼠之未罹患腫瘤的天數	29
附表1 當規格下限L=0.05，總觀測時間T=0.5，觀測樣本數n=60、80、100，設限樣本數m=5~8及逐步移除率p=0.05、0.075、0.100時，在目標值c0=0.8和顯著水準alpha=0.01下，檢定力函數 在c1=0.8,0.825(0.025)0.95的數值	42
附表2 當規格下限L=0.05，總觀測時間T=0.5，觀測樣本數n=60、80、100，設限樣本數m=5~8及逐步移除率p=0.05、0.075、0.100時，在目標值c0=0.8和顯著水準alpha=0.05下，檢定力函數 在c1=0.8,0.825(0.025)0.95的數值	44
附表3 當規格下限L=0.05，總觀測時間T=0.5，觀測樣本數n=60、80、100，設限樣本數m=5~8及逐步移除率p=0.05、0.075、0.100時，在目標值c0=0.8和顯著水準alpha=0.1下，檢定力函數 在c1=0.8,0.825(0.025)0.95的數值	46
附表4 當實例一之規格下限L=20，總觀測時間T=175，觀測樣本數n=30，設限樣本數m=5及逐步移除率p=0.05時，在目標值c0=0.8和顯著水準alpha=0.05下，檢定力函數h(c1)在c1=0.8,0.825(0.025)0.95的數值	48
附表5 當實例二之規格下限L=0.035，總觀測時間T=0.8，觀測樣本數n=60，設限樣本數m=8及逐步移除率p=0.1時，在目標值c0=0.9和顯著水準alpha=0.05下，檢定力函數 在c1=0.8,0.825(0.025)0.95的數值	48

 
圖目錄
圖 1.1 逐步型I區間設限圖	4
圖 2.1 雙參數在lambda=1,2時Gompertz分配之機率密度函數圖	11
圖 2.2 雙參數在lambda=1,2時Gompertz分配之故障率函數圖	11
圖 3.1 當alpha=0.1、m=5及p=0.05 之下，對不同總樣本n=(60,80,100)的檢定力	25
圖 3.2 當alpha=0.1、n=60及p=0.05之下，對不同設限樣本m=(5,6,7,8)的檢定力	26
圖 3.3 當alpha=0.1、n=60及m=5之下，對不同移除率p=(0.05,0.075,0.1)的檢定力	27
圖3.4 當n=60、m=5及p=0.05之下，對不同顯著水準alpha=(0.01,0.05,0.1)的檢定力	28
圖 4.1 不同beta_hat下之p-value	31
圖 4.2 當alpha=0.05時，實例1之檢定力	33
圖 4.3 當alpha=0.05時，實例2之檢定力	36

[1] 	Bai, D. S. and Chung, S.W. (1992). Optimal Design of Partially Acceler-ated Life Tests for the Exponential distribution under Type I Censoring. IEEE Trans. Reliability, 41, 400-406. 
[2] 	Balakrishnan, N.; Aggarwala, R. (2000). Progressive Censoring. Theory,Methods and Applications; Birkhauser Publishers: Boston.
[3] 	Boyles, R.A. (1991). The Taguchi capability index, Journal of Quality Technology, 23, 17-26.
[4] 	Chan, L.K., Cheng, S.W. and Spiring, F. A. (1988). A new measure of process capability, Journal of Quality Technology, 20(3), 162-175.
[5] 	Chen, Z. (1998). Joint Estimation for the Parameters of Weibull Distribution. Journal of Statistical Planning and Inference, 66, 113-120.
[6] 	Clement, J.A. (1989). Process capability calculations for non-normal distribution, Quality Progress, 22, 95-100.
[7] 	Spurrier, J. D. and Wei, L. J. (1980). A Test of the Parameter of the Exponential Distribution in the Type I Censoring Case, Journal of the American Statistical Association, 75, 405-409.
[8] 	Juran, J. M. (1974). Journal quality control handbook, (3rd ed), McGraw-Hill, New York.
[9] 	Kane, V. E. (1986). Process capability indices, Journal of Quality Technology, 18, 41-52.
[10] 	Lawless, J. F. (2003). Statistical Models & Methods for Lifetime Data, (2nd ed), New York, John Wiley.
[11] 	Lee, E.T. (1980). Statistical method for survival data analysis. Lifetime Learning Publication, Belmont.
[12] 	Lindsey, J. C. and Ryan, L. M. (1998), Tutorial in biostatistics methods for interval-censored data. Statistics in Medicine, 17, 219–238.
[13] 	Liu, P.H, and Chen, F.L. (2006),Process capability analysis of non-normal process data using the Burr XII distribution, International Journal of advanced Manufacturing Technology,27, 975-984.
[14] 	London, D. (1988). Survival Models, Actex Publications:   Connecticut.
[15] 	Montgomery, D. C. (1985). Introduction to statistical quality control, John Wiley & Sons, New York.
[16] 	Pearn, W. L., Kotz, S. and Johnson, N. L. (1992). Distributional and inferential properties of process capability indices, Journal of Quality Technology, 24(4), 216-233.
[17] 	Pearn, W. L. and Chen, K. S. (1997). Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing, Microelectronics and Reliability, 37(12), 1853-1858.
[18] 	Sun, J. (1997). Regression analysis of interval-censored failure time data, Statistics in Medicine, 16, 497–504.
[19] 	Tong, L. I., Chen, K. T. and Chen, H. T. (2002). Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution, International Journal of Quality & Reliability Management, 19(7), 812-824.
[20] 	Wu, S.J., Lin, Y.P., Chen, Y.J. (2006), Planning step-stress life test with progressively type-I group-censored exponential data, Statistica Neerlandica, 60, 46–56.