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Student Number 982205005 Author WanJ-Jr Su(蘇岏智) Author's Email Address hellowpdd@hotmail.com Statistics This thesis had been viewed 491 times. Download 286 times. Department Graduate Institute of Statistics Year 2010 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title The relibility analysis of series system with masked data dash generalized gamma distribution Date of Defense 2011-06-09 Page Count 61 Keyword bayesian factor DIC EM algorithm generalized gamma Markov chain Monte Carlo masked data Abstract 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. Table of Content 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

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982205005.pdf Date of Submission 2011-07-15

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