壽命具廣義伽瑪分配之型II 設限階段應力加速壽命試驗的可靠度分析

The Reliability Analysis of Step-Stress Accelerated Life Tests Under Generalized Gamma Lifetime Distributions With Type-II Censoring

張家華(Chia-hua Chang)

指導教授 ： 樊采虹

國立中央大學/理學院/統計研究所/碩士(2012年)

摘要

高可靠度產品在製造過程中經由嚴格控管與要求, 故在正常情況下使用, 需要較長時間才能觀測到失效的時間, 對於此類高靠度的產品必須採用加速壽命試驗來加速產品失效以利分析。本文討論當物件壽命為廣義伽瑪分配時, 在型II 設限計劃中, 物件壽命與應力間具對數線性關係下, 物件壽命分配服從累積暴露模型之階段加速壽命試驗。我們以最大概似法求得模型中參數之最大概似估計和以有母數拔靴法估計參數、可靠度和壽命的標準誤, 並且在正常應力條件下, 物件之平均壽命及可靠度函數之統計推論; 並在主觀先驗分配下由馬可夫鏈蒙地卡羅方法得貝氏估計, 同時比較兩種方法在物件之平均壽命及可靠度函數之統計推論。並以傳統的概似比檢定、AIC 和BIC 方法與貝氏選模中常用的貝氏因子法則, 探討資料配適廣義伽瑪分配與韋伯分配的模型選擇問題。模擬結果顯示, 當樣本資訊不足時, 貝氏分析所得結果優於最大概似方法。在模型選擇中若資料來自韋伯分配, 則配適廣義伽瑪分配並未導致太大的錯誤, 但相反地, 若資料具廣義伽瑪分配而配適韋伯分配模型時, 則結果產生很大的誤差。

關鍵字

階段加速壽命試驗 ； 馬可夫鏈蒙地卡羅方法 ； 有母數拔靴法 ； 廣義伽瑪分配

並列摘要

High reliability products through strictly controlled in the manufacturing process, so their lifetimes are longer under normal environment. Accelerated life test is often useful to observe enough lifetime information of the products. In this thesis, we discuss the step-stress accelerated life testing for the products whose lifetimes are of generalized gamma distribution in which the mean lifetime of each component is a log-linear function of the levels of the stress variables under Type-II censoring scheme with cumulative exposure model. Maximum likelihood estimates are developed for the model parameters with the aid of parametric bootstrap method to estimate the standard errors of the MLEs. Subjective Bayesian inference incorporated with the Markov chain Monte Carlo method is also addressed. We also discuss model fitting issue regarding the generalized gamma distribution andWeibull distribution via different model selection criteria. Simulation study reveals that when the data follow Weibull
distribution but are fitted by generalized gamma distribution, the results are acceptable. On the contrary, fitting the data that actually are generalized gamma distributed by the Weibull distribution may result in considerably inaccurate results.

並列關鍵字

Markov chain Monte Carlo ； step-stress accelerated life testing ； parametric bootstrap method ； generalized gamma

參考文獻

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