具Box-Cox轉換之逐步加速壽命實驗的指數推論模型

Exponential Inference Models for Progressive Step-Stress Life Testing with Box-Cox Transformation

王婉倫(Wan-Lun Wang)

指導教授 ： 樊采虹

國立中央大學/理學院/統計研究所/碩士(2007年)

摘要

為了快速地獲得產品壽命之相關訊息，加速壽命實驗通常被視為一個很有利的工具。本文中我們探討一個k階段的逐步應力加速壽命實驗，此試驗是由M個應力變數之因子水準所設計而成，且觀察值是屬於逐步型一設限分群資料。在此加速壽命實驗中，我們假設對於任何一個應力環境而言，每個受測單位之壽命時間是服從指數分配，且在Box-Cox轉換下，失效率和應力變數之間將以線性方式作連接。再者，對於模式化應力水準改變的影響，累積暴露模型的假設亦成立。古典最大概似方法和基於「馬可夫鏈蒙地卡羅」技術之貝氏方法將被發展來推論模型中所有的參數。數個模擬研究將被實行來示範我們所提出的方法論，同時我們也比較最大概似與貝氏觀點在推論結果上的異同。

關鍵字

最大概似估計 ； 加速壽命實驗 ； 馬可夫鏈蒙地卡羅 ； 貝氏推論 ； 費雪-分數演算法 ； 累積暴露模型

並列摘要

In order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this thesis, we discuss a k-stage step-stress accelerated life-test with M stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box-Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique are developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out.

並列關鍵字

Markov chain Monte Carlo ； Accelerated life-testing ； Fisher-scoring algorithm ； Bayesian inference ； Cumulative exposure model ； Maximum likelihood estimates

參考文獻

Yu, I. T., Wang, Z. H., Cheng, S. W. and Fuh, C. D., 2002. Reliability analysis for pyrotechnics products. J. Chinese Statist. Assoc. 40, 333-360.

Bai, D. S., Kim, M. S. and Lee, S. H., 1989. Optimum simple step-stress accelerated life tests with censoring. IEEE Trans. Reliab. 38, 528-532.

Casella, G. and Berger, R. L., 2002. Statistical Inference. Duxbury, Praci¯c Grove, CA.

Chib, S. and Greenberg, E., 1995. Understanding the Metropolis-Hastings algorithm. Amer. Statist. 49, 327-335.

Gilks, W. R. and Wild, P., 1992. Adaptive rejection sampling for Gibbs sampling. J. Roy. Statist. Soc. Ser. C 41, 337-348.