設限資料的逐步應力檢測計劃

Planning step-stress test plans based on censored data

周正杰(Cheng-Chieh Chou)

指導教授 ： 林千代

淡江大學/理學院/數學學系博士班/博士(2015年)

https://doi.org/10.6846/TKU.2015.00556

摘要

在型 I 設限和型 I 混合設限計劃下，本論文針對一般性的對數位置尺度(韋伯和對數常態)和指數壽命分佈討論 k 階段逐步應力加速壽命試驗之不等長的應力持續時間。根據累積暴露模型，我們假設一般性的對數位置尺度壽命模式的平均壽命和應力是呈現線性關係，而指數壽命模式的平均壽命和應力是呈現對數線性關係。依據變異數最佳化準則，我們的數值結果顯示指數、韋伯和對數常態分佈的最佳化 k ( ≥ 3 ) 階段逐步應力加速壽命試驗之不等長的應力持續時間，都會縮減為二階段逐步應力加速壽命試驗。利用歸納法，我們更進一步對型 I 設限計劃下的指數壽命模式驗證了此一結果。

關鍵字

加速壽命 ； 設限資料 ； 分佈計算 ； 最大概似估計法 ； 最佳化 ； 可靠度

並列摘要

In this dissertation, we discuss a k-level step-stress accelerated life-testing (ALT) experiment with unequal duration steps. Under the Type-I and Type-I hybrid
censoring schemes, the general log-location-scale and exponential lifetime distributions with mean lives which are a linear function of stress for the former and a
log-linear function of stress for the latter, along with a cumulative exposure model, are considered as the working models. The determination of the optimal unequal duration steps for exponential, Weibull and lognormal distributions are addressed using the variance-optimality criterion. Numerical results show that for the general log-location-scale and exponential distributions, the optimal k-level step-stress ALT model with unequal duration steps reduces just to a 2-level step-stress ALT model when the available data is either Type-I or Type-I hybrid censored data.
Moreover, using the induction argument, we are capable to give a theoretical proof for this result based on a Type-I exponential censored data.

並列關鍵字

accelerated life ； censored data ； distributed computations ； maximum likelihood ； optimization ； reliability

參考文獻

Alhadeed, A. A. and Yang, S. S. (2005). Optimal simple step-stress plan for cumulative

Bai, D. S. and Kim, M. S. (1993). Optimum simple step-stress accelerated life tests for

Bai, D. S., Kim, M. S. and Lee, S. H. (1989). Optimum simple step-stress accelerated life

Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress

Balakrishnan, N. and Kundu, D. (2013). Hybrid censoring: Models, inferential results and applications. Computational Statistics & Data Analysis, 57, 166–209.