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姓名	黃浚為(Chun-wei Huang)  查詢紙本館藏	畢業系所	統計研究所
論文名稱	具共變數之韋能隨機過程衰退試驗貝氏可靠度分析 (A Bayesian Reliability Analysis of Degradation Tests Based on Wiener Process with Covariates)
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摘要(中)	隨著時代科技的進步下, 大部分的產品皆具有高可靠度, 傳統上加速壽命試驗(ALT)已無法精確 評估產品的可靠度, 取而代之的是衰退試驗(DT) 。本文考慮類似產品衰退特徵為具共變數的韋 能過程, 其漂移係數與共變數具不同的線性關係, 在參數具相同共軛先驗分配結構下, 以貝氏方 法可得參數貝氏估計的確切模式, 進而探討類似的新產品在給定共變數條件下, 產品之貝氏可靠 度推論。另一方面, 不同產品間之差異性可能是可忽略的, 也就是其實各產品間不具差異性, 我 們以貝氏模型選擇法則探討不同產品之共變數衰退模型之異同, 以對類似產品進行更精確的可靠 度分析。
摘要(英)	Since most of the products have high reliability as the development of modernized technologies, the traditional ALT fails to evaluate the product reliability and it is replaced by DT. This article concentrates on degradation of covariates of the Wiener process of similar products, the different linear relation between drift coefficients and covariates, the exact mode of coefficients estimation by bayesian methods when coefficients have the same the structure of conjugate prior distribution and furtherly the bayesian reliability inference under the condition of given covariates for these similar new products. On the other hand, the differences between products might be ignored which means the difference may actually not exist. For the more accurate reliabiliy analysis for such similar products, we use the bayesian model selection to discuss the comparison of different covariate degradation models for different products.
關鍵字(中)	★ 衰退試驗 ★ 共變數 ★ 韋能過程 ★ 貝氏理論 ★ 貝氏模型選擇	關鍵字(英)
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 文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 第二章韋能隨機過程中具共變數之貝氏衰退模型6 2.1 模型介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 產品失效時間之分配與其相關推論. . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 剩餘時間之序列預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 第三章貝氏模型選擇18 3.1 具相同衰退特徵之模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 貝氏因子. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 剩餘時間之序列預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 序列預測之停止時間. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 第四章模擬研究24 4.1 模擬資料之可靠度分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 具相同衰退特徵之模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 貝氏模型選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.4 試驗時間之模擬分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 第五章結論與展望38 參考文獻39
參考文獻	[1] Bagdonavicius, V. and Nikulin, M. S. (2002). Accelerated Life Models: Modeling and Statistical Analysis, Chapman & Hall, Boca Raton. [2] Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, Springer Science & Business Media. [3] Chernoff, H. (1961). Sequential tests for the mean of a normal distribution. Proc. Fourth Berkely Symp. Math. Statist. Probab., 1, 79–92. [4] Chhikara, R. S. and Folks, J. L. (1989). The Inverse Gaussian Distribution. Theory, Methodology and Applications, Marcel Dekker: New York. [5] Doksum, K. A. and Hoyland, A. (1992). Models for variable-stress accelerated life testing experiments based on wiener processes and the inverse Gaussian distribution. Technometrics, 34, 74–82. [6] Gertbsbakh, I. B. and Kordonskiy, K. B. (1969). Models of Failure, Springer-Verlag, New York. [7] Jeffreys, H. (1961). Theory of Probability (3rd edition), New York: Oxford University Press. [8] Lawless, J. F. and Cook, R. J. (2007). The Statistical Analysis of Recurrent Events, Springer Science & Business Media. [9] Lawless, J. F. and Crowder, M. (2004). Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Analysis, 10, 213–227. [10] Lu, C. J. and Meeker, W. Q. (1993). Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35, 161–174. [11] Lu, C. J., Meeker, W. Q., and Escobar, L. A. (1996). A comparison of degradation and failure-time analysis methods for estimating a time-to-failure distribution. Statistica Sinica, 6, 531–546. [12] Lu, J. C., Park, J., and Yang, Q. (1997). Statistical inference of a time-to-failure distribution derived from linear degradation data. Technometries, 39, 391–400. [13] Montgomery, D. C., Peck, E. A., and Vining, G. G. (2012). Introduction to Linear Regression Analysis, John Wiley & Sons. [14] Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, Inc., New York. [15] Oliveira, V. R. B. and Colosimo, E. A. (2004). Comparison of methods to estimate the time- to-failure distribution in degradation tests. Quality and Reliability Engineering International , 20, 363–373. [16] Padgett, W. J. and Meredith, A. T. (2004). Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Analysis, 10, 191–206. [17] Park, C. and Padgett, W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Analysis, 11, 511–527. [18] Prabhu, N. U. (1965). Stochastic Processes, Macmillan, New York. [19] Robinson, M. E. and Crowder, M. J. (2000). Bayesian methods for a growth-curve degradation model with repeated measures. Lifetime Data Analysis, 6, 357–374. [20] Tseng, S. T. and Peng, C. Y. (2004). Optimal burn-in policy by using an integrated Wiener process. IEEE Trans. Reliab., 36, 1161–1170. [21] Whitmore, G. A. and Schenkelberg, F. (1997). Modeling accelerated degradation data using Wiener diffusion with a scale transformation. Lifetime Data Analysis, 3, 27–45. [22] Yan, X. (2009). Linear Regression Analysis: Theory and Computing, World Scientific.
指導教授	樊采虹	審核日期	2014-8-12
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