姓名 |
莊翔宇(Hsiang-yu Chuang)
查詢紙本館藏 |
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統計研究所 |
論文名稱 |
壽命具韋伯分佈之電火工品加速失效模型的可靠度分析 (Accelerated Failure Tests of Electro-Explosive Devices Under Weibull Lifetime Distributions)
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摘要(中) |
本文假設電火工品壽命服從韋伯分佈,電火工品為高可靠度的產品,由於成本昂貴以致於在試驗上通常樣本數不會太大,對於此類高靠度的產品必須採用加速失效試驗來加速產品失效以利分析,假設韋伯分佈中尺度參數與加速應力存在對數線性關係,我們使用最大概似與貝氏方法,探討在正常應力下電火工品的期望壽命與可靠度函數之統計推論。在貝氏分析中,本文將失效機率之先驗分佈轉換為模型中參數之先驗分佈,並分別考慮以動差和眾數來決定先驗分佈之超參數,由馬可夫鏈蒙地卡羅方法得貝氏估計。模擬結果顯示,貝氏方法所得結果優於最大概似方法。考慮在貝氏方法下,若先驗訊息較不確定時,以眾數方法所決定的先驗分佈所得結果較佳。另外我們也考慮電火工品之貝氏零失效可靠度示範實驗,以產品是否達到預期之標準,求得實驗所需之最小樣本數與最短試驗時間之組合。
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摘要(英) |
Due to the high reliability and high testing cost of electro-explosive devices, we consider an accelerated failure experiment in which the lifetime following a Weibull distribution with scale parameter being related to the accelerated variable. We use the maximum likelihood and Bayesian approaches to develop statistical inference on the mean-time-to-failure (MTTF) and reliability under normal condition. In the Bayesian approach, we convert the prior information from the success probability to the prior distribution of the underlying parameters and use the moments and mode to determine hyperparameters of the prior distributions, respectively. Markov chain Monte Carlo method is applied to derive the Bayesian inference.
Simulation study shows that the Bayesian approach performs better than the ML approach, especially when there only few failures or zero failures. In Bayesian approach, using mode to determine the prior outperforms using the moments. On the other hand, a Bayesian zero-failure reliability demonstration test is also conducted to design composition of the minimum sample size and the shortest experiment time subject to certain specified reliability criterion.
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關鍵字(中) |
★ 馬可夫鏈蒙地卡羅方法 ★ 零失效可靠度示範實驗 ★ 韋伯分佈 ★ 高可靠度 ★ 先驗分佈 ★ 加速失效試驗 |
關鍵字(英) |
★ Bayesian approach ★ Markov chain Monte Carlo method ★ accelerated experiment ★ high reliability ★ Weibull distribution ★ Bayesian zero-failure reliability demonstration |
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. . . . . . . . . . . . . . . . . . . 5
第二章模型及方法7
2.1 加速失效實驗之統計模型. . . . . . . . . . . . 7
2.2 最大概似推論. . . . . . . . . . . . . . . . . 9
2.3 貝氏推論. . . . . . . . . . . . . . . . . . . 12
2.3.1 先驗分佈之決定. . . . . . . . . . . . . . . 13
2.3.2 後驗分佈. . . . . . . . . . . . . . . . . . 16
第三章電火工品之貝氏零失效可靠度示範實驗20
3.1 模型與方法. . . . . . . . . . . . . . . . . . 20
3.2 最小樣本數或實驗時間之決定. . . . . . . . . . 21
第四章數值分析與模擬研究25
4.1 非零失效模擬資料之可靠度分析. . . . . . . . . 25
4.2 高可靠度產品模擬資料之可靠度分析. . . . . . . 30
4.3 模擬實例之可靠度分析. . . . . . . . . . . . . 35
4.4 貝氏零失效可靠度示範實驗之模擬. . . . . . . . 40
第五章結論與展望44
參考文獻45
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參考文獻 |
[1] Balaban, H. (1975). “Reliability demonstration: Purposes practices,and value.” Proceedings of the 1975 Annual Reliability and Maintainability Symposium, Washington,D. C.. 246-248.
[2] Beger, J.O. and Sun, D. (1993). “Bayesian analysis for the Poly-Weibull distribution.”Journal of the American Statistical Association , 88, 1412-1418.
[3] Bonis, A.J. (1966). “Bayesian reliability demonstration plans.” Reliability and Maintainability
Conference, 5, 861-870.
[4] Hastings, W.K. (1970). “Monte Carlo sampling methods using Markov chains and their application.” Biometrika, 57, 97-109.
[5] Martz, H.F. andWaller, R.A. (1979). “A Bayesian zero-failure (BAZE) reliability demonstration testing procedure.” Journal of Quality Technology, 11, 128-138.
[6] Meeker, W.Q. and Escobar, L.A. (1998). Statistical Methods for Reliability Data.Wiley, NewYork.
[7] Fan, T.H., Balakrishnan, N. and Chang, C.C. (2009). “The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing.” Journal of Statistical Computation and Simulation, 79, 1143-1154.
[8] Fan, T.H. and Chang, C.C. (2009). “A Bayesian zero-failure reliability demonstration test of high quality electro-explosive Devices.” Quality and Reliability Engineering International, 25, 913-920.
[9] 傅承德、俞一唐、王仁和和鄭少為(2002). ”電火工品產品的可靠度分析.” 中國統計學報, 第40 卷, 第3 期, 333-360 頁.
[10] 張曉冉、胡文傑、夏茂輝和溫艷清(2006). ”Weibull 分布下只有一個失效數據的多層Bayes 分析.” 燕山大學學報, 第30 卷, 480-486 頁.
[11] 劉海濤和張志華(2008). ”威布爾分布無失效數據的Bayes 可靠性分析.” 系統工程理論與實踐, 第11 期, 103-108 頁.
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指導教授 |
樊采虹(Tsai-hung Fan)
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審核日期 |
2011-7-15 |
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