串聯系統存在隱蔽資料之可靠度分析─以廣義伽瑪分配為例

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蘇岏智(WanJ-Jr Su) 查詢紙本館藏

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統計研究所

論文名稱

串聯系統存在隱蔽資料之可靠度分析─以廣義伽瑪分配為例
(The relibility analysis of series system with masked data dash generalized gamma distribution)

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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停止運作，但有時某些因素導致引發系統失效之物件無從觀測，亦即資料為隱蔽資料。本文討論在不同隱蔽水準時，物件壽命分別具有韋伯分配與廣義伽瑪分配的可靠度之試驗。我們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無母數拔靴法估計參數、可靠度和壽命的標準誤；並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物件與系統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 DIC 和貝氏因子法則探討資料配適廣義伽瑪分配與韋柏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。

摘要(英)

In this thesis, we consider a system of independent and non-identical components connected in series, each component having a Weibull life time distribution under Type-I 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. The maximum likelihood estimates via EM algorithm is developed for the model parameters with the aid of nonparametric bootstrap method to estimate the resulting standard errors of the MLE 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 maximum likelihood approach not only in parameters estimation but also in reliability inference for both the system and components. We also discuss model fitting issue regarding the generalized gamma distribution and Weibull distribution via different model selection criteria.

關鍵字(中)

★ 廣義伽瑪分配
★ 貝氏因子
★ 期望值-最大化演算法
★ 馬卡夫鏈蒙地卡羅演算法
★ 隱蔽資料

關鍵字(英)

★ Markov chain Monte Carlo
★ EM algorithm
★ bayesian factor
★ DIC
★ masked data
★ generalized gamma

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. . . . . . . . . . . . . . . . 3
1.3 研究方法. . . . . . . . . . . . . . . . 4
第二章物件壽命具韋伯分配之串聯系統的壽命試驗6
2.1 模型介紹. . . . . . . . . . . . . . . . 6
2.2 最大概似估計. . . . . . . . . . . . . . 8
2.3 貝氏推論. . . . . . . . . . . . . . . . 13
第三章物件壽命具廣義伽瑪分配之串聯系統的壽命試驗20
3.1 模型介紹與最大概似估計. . . . . . . . . 20
3.2 概似比檢定. . . . . . . . . . . . . . . 23
3.3 貝氏推論. . . . . . . . . . . . . . . . 24
3.4 貝氏模型選擇. . . . . . . . . . . . . . 26
第四章數值分析與模擬研究29
4.1 壽命具韋伯分配之串聯系統模型. . . . . . 29
4.2 壽命具廣義伽瑪分配之串聯系統模型. . . . 33
4.3 模型選擇. . . . . . . . . . . . . . . . 36
第五章結論與展望49
參考文獻50

參考文獻

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2011-7-15

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