具隨機效應與時間尺度之伽瑪加速衰退隨機過程的貝氏可靠度分析

Bayesian Reliability Analysis of Constant-Stress Accelerated Degradation Based on Gamma Process with Random Effect and Time-Scale Transformation

黃雅翎(Ya-ling Huang)

指導教授 ： 樊采虹

國立中央大學/理學院/統計研究所/碩士(2015年)

摘要

加速衰退試驗(accelerated degradation test, ADT)常被用來推估高可靠度產品的可靠度資訊，透過一與壽命具高度相關之品質特徵值(Quality Characteristics, QC)在試驗中隨著時間逐漸衰退的觀測資料建構衰退模型，進而轉換成產品壽命分配以估計產品的可靠度。本文以貝氏方法分析衰退特徵值為具隨機效應的伽瑪隨機過程(Gamma process)之恆定應力加速衰退試驗，其中觀測時間經指數轉換後加速應力與伽瑪隨機過程之形狀參數為對數線性關係，且尺度參數具伽瑪隨機效應。為確認指數轉換之必要性，我們以單一質量和連續型的混合先驗分佈，經馬可夫鏈蒙地卡羅法(MCMC)選擇適當的模型，進而得到正常使用狀態下產品的貝氏可靠度推論。此外並考慮類似產品在正常使用應力下的衰退試驗，以更新先驗分佈之序列預測的方法推估產品的平均失效時間，並在滿足預設的準確度要求下同時決定試驗終止時間。最後利用模擬資料驗證貝氏方法在模型選擇上的效益和準確性，並將本文方法應用至一LED 燈泡亮度衰退實例資料中。

關鍵字

恆定應力加速衰退試 ； 伽碼隨機過程 ； 隨機效應 ； 混合先驗分佈 ； 馬可夫鏈蒙地卡羅法 ； 貝氏理論

並列摘要

Accelerated degradation tests have been widely used to assess the lifetime information of highly reliable products. In this thesis, we apply Bayesian approach to the degradation data collected from quality characteristics of different products under higher than normal stress levels based on random effect gamma process model with time-scale transformation, and a log linear link function for associating the covariates. We consider a mixture prior to identify the parameter of time-scale transformation. An advantage of mixture priors is that it can automatically identify the time-scale transformation in the MCMC procedure. Reliability inference of the failure time distribution under normal use condition will be described through the posterior sample of the underlying parameters
obtained from the MCMC procedure. Sequentially predictive inference on individual reliability under normal condition based on conditional distribution is also proposed. Simulation study is presented to evaluate the performance of the proposed method, and discuss model fitting issue regarding the random effect gamma process model and non-random effect gamma process model via DIC model selection criteria. The proposed method is applied to the LED light intensity data as well.

參考文獻

[1] Abramowitz, M. and Stegun, I. (1972). Handbook of Mathematical Functions: with Formulas,

[2] Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models: Modeling and Statistical

[3] Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis (Second Edition),

[4] Birnbaum, Z. W. and Saunders, S. C. (1969). A new family of life distributions. Journal of

[6] Chaluvadi, V. N. H. (2008). Accelerated life testing of electronic revenue meters, Ph.D. dissertation,