具 Box-Cox 轉換之累進型 I 設限逐步加速指數壽命實驗的可靠度分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：26

、訪客IP：18.221.101.3

姓名

徐聖閎(Sheng-hung Hsu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

具 Box-Cox 轉換之累進型 I 設限逐步加速指數壽命實驗的可靠度分析

相關論文

★ 具Box-Cox轉換之逐步加速壽命實驗的指數推論模型	★ 多元反應變數長期資料之多變量線性混合模型
★ 多重型 I 設限下串聯系統之可靠度分析與最佳化設計	★ 應用累積暴露模式至單調過程之加速衰變模型
★ 串聯系統加速壽命試驗之最佳樣本數配置	★ 破壞性加速衰變試驗之適合度檢定
★ 串聯系統加速壽命試驗之最佳妥協設計	★ 加速破壞性衰變模型之貝氏適合度檢定
★ 加速破壞性衰變模型之最佳實驗配置	★ 累積暴露模式之單調加速衰變試驗
★ 具ED過程之兩因子加速衰退試驗建模研究	★ 逆高斯過程之完整貝氏衰變分析
★ 加速不變原則之偏斜-t過程	★ 花蓮地區地震資料改變點之貝氏模型選擇
★ 颱風降雨量之統計迴歸預測	★ 花蓮地區地震資料之長時期相關性及時間-空間模型之可行性

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

加速壽命實驗為將產品置於較正常使用情況惡劣的環境下，使產品提早損壞以便縮短收集產品失效時間資料的實驗時間，進而分析並預測產品在正常使用狀態下之可靠度。本文中主要討論在物件壽命為一指數分佈單一失效因子之 $k$ 階段累進型 { f I} 設限逐步加速壽命實驗，假設其平均壽命與失效因子之間具有 Box-Cox 轉換之關係時之統計推論。使用的統計方法包括最大概似法、拔靴法和貝氏方法。另外並比較與對數線性模型間之穩健性。

摘要(英)

Accelerated life testing puts the product in the environment which is worse than in normal condition, in order to collect the information of product rapidly, and to use this information to predict the lifetime of product under normal condition. In this thesis, we discuss a k-stage progressive type I censoring step-stress accelerated life testing with single stress variable, when the lifetime of product is of exponential distribution and there is a linear relationship between the lifetime of product and the stress variable under Box-Cox transformation. The maximum likelihood, bootstrap and Bayesian methods are used to make statistical inference and reliability analysis. Model comparsion with the usual log-linear model is also made and it shows that the proposed model is more robust.

關鍵字(中)

★ 最大概似法
★ Box-Cox 轉換
★ 型 I 設限
★ 指數分佈
★ 加速壽命實驗
★ 拔靴法
★ 貝氏方法

關鍵字(英)

★ Maximum likelihood method
★ Box-Cox transformation
★ Type I censoring
★ Exponential distribution
★ Accelerated life testing
★ Bootstrap
★ Bayesian method

論文目次

中文摘要i
英文摘要ii
1 緒論1
1.1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究目的與方法. . . . . . . . . . . . . . . . . . . . . . 4
2 最大概似推論6
2.1 模型假設. . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 最大概似估計. . . . . . . . . . . . . . . . . . . . . . . 9
2.3 區間估計. . . . . . . . . . . . . . . . . . . . . . . . . 14
3 貝氏分析20
3.1 先驗分配. . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 MCMC 演算法. . . . . . . . . . . . . . . . . . . . . . 23
3.3 貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 log-SSALT 模型之貝氏分析. . . . . . . . . . . . . . . 27
4 模擬研究29
4.1 BC-SSALT 模型. . . . . . . . . . . . . . . . . . . . . 29
4.2 log-SSALT 模型. . . . . . . . . . . . . . . . . . . . . . 39
4.3 模型選擇. . . . . . . . . . . . . . . . . . . . . . . . . 46
5 結論50
參考文獻51

參考文獻

[1] Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
[2] Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models: Modeling and Statistical Analysis, Chapman & Hall, Boca Raton, Florida.
[3] Bai, D.S., Kim, M.S. and Lee, S.H. (1989). Optimum simple step-stress accelerated life tests with censoring. IEEE Transactions on Reliability, 38, 528-532.
[4] Balakrishnan, N. and Han, D. (2008). Optimal step-stress testing for progressively type-I censored data from exponential distribution. Journal of Statistical Planning and Inference. In press.
[5] Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. 2nd Ed. Springer, New York.
[6] Box, George E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society Series B, 26, 211–246.
[7] Casella, G. and Berger, R.L. (2002). Statistical Inference. 2nd Ed. Duxbury, Pacific Grove, CA.
[8] Casella, G. and George, E. (1992). Explaining the Gibbs sampler. The American Statistician, 46, 167-174.
[9] Chib, S. and Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335.
[10] Cohen, A. C. (1963). Progressively censored samples in life testing. Technometrics, 5, 327-339
[11] Efron, B. (1979). Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7, 1–26.
[12] Fan T.H., Wang W.L. and Balakrishnanb, N. (2008). Exponential progressive step-stress life-testing with link function based on Box-Cox transformation. Journal of Statistical Planning and Inference, 138, 2340-2354.
[13] Fisher, R.A. (1956). Statistical Methods and Scientific Inference. Oliver and Boyd, Edinburgh.
[14] Geman, S. and D. Geman (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-724.
[15] Gilks, W.R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Journal of the Royal Statistical Society Series C, 41, 337-348.
[16] Hastings, W.K. (1970). Monte-Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
[17] Jeffreys, H. (1961). Theory of Probability. 3rd Ed. Oxford University Press, Oxford.
[18] Khamis, I.H. (1997). Optimum m-step, step-stress test with k stress variables. Communications in Statistics - Simulation and Computation, 26, 1301-1313.
[19] Meeker, W.Q. and Escobar, L.A. (1998). Statistical Methods for Reliability Data, John Wiley & Sons, New York.
[20] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A.H. and Teller, E.(1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.
[21] Nelson, W. (1980). Accelerated life testing - step-stress models and data analysis. IEEE Transactions on Reliability, 29, 103-108.
[22] Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, John Wiley & Sons, New York.
[23] Osborne, M. R. (1992). Fisher's method of scoring. International Statistical Review / Revue Internationale de Statistique, 60, 99-117.
[24] Patel, M. N. and Gajjar, A. V. (1990). Progressively censored samples from geometric distribution. The Aligarh Journal of Statistics, 10, 1–8.
[25] Robert, C.P. (2001). The Bayesian Choice: from decision-theoretic foundations to computational implementation. 2nd Ed. Springer, New York.
[26] Ross, S.M. (2006). Simulation. 4th Ed, Academic press, USA.
[27] Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
[28] van Dorp, J.R., Mazzuchi T.A., Fornell G.E. and Pollock, L.R. (1996). A Bayes approach to step-stress accelerated life testing. IEEE Transactions on Reliability, 45, 491-498.
[29] van Dorp, J.R. and Mazzuchi, T.A. (2004). A general Bayes exponential inference model for accelerated life testing. Journal of Statistical Planning and Inference, 119, 55-74.
[30] Wu, S.J. and Chang, C.T. (2003). Inference in the Pareto distribution based on progressive type II censoring with random removals. Journal of Applied Statistics, 30, 163-172.
[31] Wu, S.J., Lin, Y.P. and Chen, Y.J. (2006). Planning step-stress life test with progressively type I group-censored exponential data. Statist. Neerlandica, 60, 46-56.
[32] Zhao, W. and Elsayed, E.A. (2005). A general accelerated life model for step-stress testing. IIE Transactions, 37, 1059-1069.

指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2008-10-11

推文