伽瑪隨機過程之階段應力加速衰退試驗之貝氏序列可靠度分析

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陳芊卉(Cian-huei Chen) 查詢紙本館藏

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論文名稱

伽瑪隨機過程之階段應力加速衰退試驗之貝氏序列可靠度分析
(A Sequential Bayesian Reliability Analysis under Gamma Step-Stress Accelerated Degradation Process)

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摘要(中)

本文考慮伽瑪隨機過程之階段應力加速衰退試驗(SSADT)之貝氏可靠度分析。在加速因子為溫度之Arrhenius模型下,以主觀先驗分佈經由馬可夫鏈蒙地卡羅方法(MCMC) 得在常溫下產品壽命及可靠度之貝氏推論。另一方面,藉由在類似產品置於正常環境應力水準下之序列衰退試驗中,更新先驗分佈之超參數,以預測產品失效時間之分佈,同時決定測試時間,並以模擬資料驗
證所提方法的可行性和準確性以及貝氏方法之穩健性。

摘要(英)

Degradation analysis is more efficient than the conventional life tests in drawing reliability assessment for high quality products. This thesis aims on the Bayesian approach to the degradation test when the degradation data of different products are collected under higher than normal stress levels via independent gamma processes. Reliability inference of the population under normal condition will be made based on the posterior distribution of the underlying parameters with the aid of Markov chain Monte Carlo method. Further sequentially predictive inference on individual reliability under normal condition is also proposed. Simulation study is presented to show the
appropriateness of the proposed methods, and the robustness of the prior distribution.

關鍵字(中)

★ 階段應力加速衰退試驗
★ 伽瑪隨機過程
★ Arrhenius 模型
★ 馬可夫鏈蒙地卡羅方法
★ 貝氏方法
★ 預測理論

關鍵字(英)

★ Sstep-stress accelerated degradation test
★ gamma process
★ Markov chain Monte Carlo
★ Bayesian approach
★ predictive inference

論文目次

目錄
摘要i
Abstract ii
誌謝iii
目錄v
圖目次vii
表目次x
第一章緒論1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章伽瑪隨機過程之階段應力加速衰退模型5
2.1 試驗與模型介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 正常環境下產品失效時間分佈及其貝氏推論. . . . . . . . . . . . . . . . . . . . . . 9
第三章衰退資料之貝氏序列預測推論14
v
3.1 常溫下類似產品之預測衰退路徑. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 先驗分佈之序列更新. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 動差法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 百分位法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 失效時間之貝氏序列預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 序列預測之試驗時間. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第四章模擬研究22
4.1 模擬資料之可靠度分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 資料分析與貝氏序列預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 試驗時間的選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 先驗分佈之敏感性分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
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

2014-7-22

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