破壞性物件之加速衰退試驗的貝氏可靠度分析

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姓名

楊國誠(Guo-Cheng Yang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

破壞性物件之加速衰退試驗的貝氏可靠度分析
(A Bayesian reliability analysis of accelerated degradation test for destructive devices)

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摘要(中)

本文考慮在加速破壞性衰退試驗下，假設產品衰退特徵服從對數常態分配，並與應力和
時間的乘積具對數線性關係，藉以進行統計之可靠度推論。所謂衰退特徵值乃產品判定
失效的主要指標及數據，而破壞性試驗是指衰退特徵之測量數據為一次性測量，即破壞
性測量。在推估上，我們利用貝氏理論與馬可夫鏈蒙地卡羅方法來獲得參數之貝氏估計，進而探討在正常應力條件下產品之平均失效時間與其對應之百分位點、失效時間點及可靠度函數之貝氏統計推論，我們也利用預測分配進行產品失效時間之預測。模擬結果顯示，在資訊準確的先驗分配時，即使樣本數不是很大，產品失效時間之貝氏可靠度推論十分準確。

摘要(英)

In this thesis, we consider the accelerated destructive degradation test (ADDT) in which the degradation characteristic is the major indicator of the product failure. We discuss the products whose degradation characteristic is of lognormal distribution with mean being log-linear in the product of the stress level and square root of the observation time. In ADDT, after we measure the degradation characteristics, the products damage. It is called the destructive measure. We use the Bayesian approach with the aid of Markov chain Monte Carlo method to estimate the parameters. Furthermore, we are interested in reliability inferences at the normal stress level, including the mean time to failure, failure time distribution quantiles, failure time piont, and reliability function. We also use the predictive distribution to predict the failure time. From simulation results, when the prior distribution is very informative, the Bayesian approach on ADDT provides accurate reliability inference.

關鍵字(中)

★ 加速破壞性衰退試驗
★ 馬可夫鏈蒙地卡羅方法
★ 預測分配

關鍵字(英)

★ accelerated destructive degradation test
★ Markov chain Monte Carlo
★ predictive distribution

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目次 vi
表目次 vii
第一章緒論 1
1.1 研究動機. . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . 4
1.3 研究方法. . . . . . . . . . . . . 5
第二章對數常態之加速破壞性衰退實驗的貝氏估計 7
2.1 試驗及模型介紹. . . . . . . . . . . . . 7
2.2 貝氏推論. . . . . . . . . . . . . . . .9
2.3 正常狀況下產品失效時間的分配與其相關推論. . .12
第三章模擬研究. . . . . . . . . . . . . . . 19
第四章結論與展望. . . . . . . . . . . . . . 31
參考文獻 33

參考文獻

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[18] 蘇瓔漪(2012). ”串聯系統元件壽命服從韋伯分配下之定應力破壞性加速壽命試驗分析.” 國立中央大學統計研究所碩士論文.

指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2013-7-17

推文