為研究高可靠度工業產品在正常使用條件下之失效時間，經常將其置於較嚴苛的環境應力中，然後觀察產品品質特性隨時間衰變的過程，稱為加速衰變試驗。加速衰變的品質特性經常是非遞增或非遞減的，所以，品質特性的減量或增量為非負之隨機變數。本文在此一隨機變數為廣義伽瑪分布之假設下，推論在正常使用情形下，有100*P%產品失效的時間，稱之為p分位失效時間，記作t_p。除根據最大概似估計求出 t_p的信賴下界，也應用貝氏方法求得t_p的可信下界。本文以模擬研究上述推論方法之涵蓋機率，結果顯示t_p信賴下界的涵蓋機率在小樣本時無法維持其信賴水準；但是，t_p可信下界之涵蓋機率與信賴水準相近。最後，本文分析一組資料，說明上述推論方法之應用。

In order to study the failure time of industrial product of high reliability under normal situation, we usually observe its quality characteristics (QC) degraded over time under some more severe stress conditions which is called an accelerated degradation test. Because the accelerated degradation QC is often non-increasing or non-decreasing, the QC decrement or increment is a nonnegative random variable. Assume that the random variable is distributed according to a generalized gamma distribution, the p quartile failure time (t_p) is of interest at which 100*p% of products reach the threshold value of QC. In addition to obtaining the confidence lower bound of t_p based on its maximum likelihood estimate, we also find the credible lower bound of t_p . A simulation study is conducted to investigate the performance of the proposed lower bounds. The results show that the coverage probability of the confidence lower bound of t_p is not able to maintain its confidence level, while the credible lower bound of t_p holds well its confidence level. Finally, a real data set is illustrated to demonstrate the application of the proposed lower bounds.

Chhikara R. S. and Folks J. L. (1989). The Inverse Gaussian Distribution: Theory, Methodology and Applications. Marcel Dekker, New York.
Lim H. and Yum B. J. (2011). Optimal design of accelerated degradation tests based on Wiener process models. Journal of Applied Statistics, 38(2), 309-325.
Nelson W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data analysis. John Wiley and Sons, New York.
Park C. and Padgett W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis, 11, 511-527.
Stacy E. W. and Mihram G. A. (1965). Parameter Estimation for a Generalized Gamma Distribution. Technometrics, 7(3), 349-358.
Sturtz S.,Ligges U. and Gelman A. (2005). R2WinBUGS: A Package for Running WinBUGS from R. Journal of Statistical Software,12(3).

Whitmore G. A. and Schenkelberg F. (1997). Modeling accelerated degradation data using Wiener diffusion with a scale transformation. Lifetime Data Analysis, 3, 27-45.
魏郁昇， 「加速衰變測試下p分位失效時間之貝氏估計」 ，國立中央
大學，碩士論文，民國102年。