指數壽命分佈串聯系統之隱蔽區間資料加速壽命試驗之可靠度分析

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姓名

許琮明(Tsung-Ming Hsu) 查詢紙本館藏

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統計研究所

論文名稱

指數壽命分佈串聯系統之隱蔽區間資料加速壽命試驗之可靠度分析
(Accelerated Life Tests of a Series System with Masked Interval Data Under Exponential Lifetime Distributions)

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摘要(中)

在串聯系統中，當任一物件失效即導致系統失效，但有時某些導致系統失效之物件無從觀測，且只知系統失效時間在某段時間內，而非確切失效的時間，亦即資料為群集隱蔽資料。本文討論在群集隱蔽資料中串聯物件的壽命服從指數分佈，各物件壽命與應力間具對數線性關係及在各階段應力下物件壽命之分配服從累積曝露模型時之階段加速試驗。我們分別以期望值-最大化演算法求得模型中參數之最大概似估計和以母數拔靴法估計其標準誤;以及在主觀先驗分佈下由馬可夫鍊蒙地卡羅方法得貝氏估計，同時比較兩種方法在正常應力條件下，物件與系統之平均壽命及可靠度函數之統計推論。模擬結果顯示，當樣本不是太大時，貝氏分析所得結果似乎優於最大概似方法。

摘要(英)

In this thesis, we consider a system of independent and non-identical components connected in series, each component having a Exponential life time distribution under Type-I group censored. In a series system, the system fails if any of the components fails, and it may only be ascertained that the cause of system failure is due to one of the components in some subset of system components, so called masked data. We discuss the step-stress accelerated life testing in which the mean life time of each component is a log-linear function of the levels of the stress variables. The maximum likelihood estimates via EM algorithm is developed for the model parameters with the aid of parametric bootstrap method to estimate the resulting standard errors when the data are masked. Subjective Bayesian inference incorporated with the Markov chain Monte Carlo method is also addressed. Simulation study shows that the Bayesian analysis provides better results than the likelihood approach not only in parameters estimation but also in reliability inference under normal condition for both the system and components.

關鍵字(中)

★ 隱蔽資料
★ 指數分佈
★ 階段加速試驗
★ 馬可夫鍊蒙地卡羅方法
★ 期望值-最大化演算法
★ 有母數拔靴法

關鍵字(英)

★ EM algorithm
★ parametric bootstrap method
★ Markov chain Monte Carlo method
★ masked data
★ exponential distribution
★ Step-stress accelerated life testing

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 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章型I 設限階段應力加速壽命試驗之對稱隱蔽模型6
2.1 模型介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 對稱隱蔽模型之最大概似估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 對稱隱蔽模型之貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
第三章型I 設限階段應力加速壽命試驗之非對稱隱蔽模型18
3.1 非對稱階段隱蔽機率模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 非對稱物件隱蔽機率模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
第四章數值分析與模擬研究26
4.1 對稱隱蔽模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.1 無隱蔽之群集系統資料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.2 隱蔽發生時之群集系統資料. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1.3 對稱隱蔽模型之舉例闡述. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 非對稱階段隱蔽機率模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1 非對稱階段隱蔽機率模型之模擬研究. . . . . . . . . . . . . . . . . . . . . . 38
4.2.2 非對稱階段隱蔽機率模型之舉例闡述. . . . . . . . . . . . . . . . . . . . . . 42
4.3 非對稱物件隱蔽機率模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.1 非對稱物件隱蔽機率模型之模擬研究. . . . . . . . . . . . . . . . . . . . . . 45
4.3.2 非對稱物件隱蔽機率模型之舉例闡述. . . . . . . . . . . . . . . . . . . . . . 49
第五章結論與展望52
參考文獻53

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2010-6-28

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