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系統識別號 U0002-1607201411080700
中文論文名稱 二維偏常態破壞衰變模型之貝氏分析
英文論文名稱 A Bayesian Analysis of Bivariate Skew-Normal Destructive Degradation Model
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 102
學期 2
出版年 103
研究生中文姓名 吳易儒
研究生英文姓名 Yi-Lu Wu
學號 601190233
學位類別 碩士
語文別 中文
口試日期 2014-06-24
論文頁數 42頁
口試委員 指導教授-蔡志群
委員-林千代
委員-彭建育
中文關鍵字 貝氏分析  偏常態分配  破壞衰變試驗 
英文關鍵字 Bayesian Analysis  Skew-Normal distribution  Destructive degradation test 
學科別分類 學科別自然科學數學
中文摘要 近年來世界能源逐漸短缺,各國科學家致力於發展再生能源,其中又以太陽能為主要發展重點。然而使用太陽能發電系統時,EVA膜中的材料性能衰變之間會間接影響到太陽能使用功率,且各材料性能衰變之間也會相互影響,故本文將針對各材料性能衰變之間進行進一步的探討。首先,本文中針對EVA膜執行一個破壞衰變試驗,並收集EVA 膜中IR2 與TGA Wt loss 兩種材料性能之衰變資料。接下來,根據資料型態建構出二維偏常態破壞衰變模型,並在假設所有參數為隨機變數之下使用貝氏分析法來估計其模型參數並且進一步推估兩材料性能之間的相關性。最後,本文使用實例資料進行模擬分析得到其參數估計值,並繪出其平均衰變路徑之後可得知其模擬結果落在真值附近之可能性並不低,最後重複執行一百次模擬之後驗證本文中E-M演算法之穩健性,並由模擬結果中得到兩材料性能衰變之間呈現正相關。
英文摘要 With the shortage of energy, scientists are striving to develop the sources of renewable energy. Among these resources, solar energy is currently the most popular, and can provide clean and safe supply of electricity to humans. The power of solar modules is affected indirectly by the decay for the EVA sheet. In this study, the relationship between the material decay for EVA sheet was addressed. Firstly, destructive degradation tests for solar modules are implemented to collect the degradation data for IR2 and TGA Wt loss. Next, a bivariate skew-normal destructive degradation model was constructed to describe the degradation paths of the two material properties. Assuming that all model parameters are random, a Bayesian approach are used to estimate the model parameters, then the correlation between the two material properties can be obtained. The results showed that there is a positive correlation between the decay for two material properties. Finally, a simulation study was carried out to evaluate the performance of the proposed method.
論文目次 1緒論.......................1
1.1前言.......................1
1.2文獻探討.......................5
1.2.1非破壞衰變模型.......................5
1.2.2破壞衰變模型.......................6
1.2.3偏常態分配.......................8
1.2.4貝氏方法.......................10
1.3研究動機與目的.......................11
1.4研究架構.......................15
2問題描述.......................17
3貝氏分析.......................22
3.1先驗分配之決定.......................22
3.2M-H演算法.......................24
4資料分析.......................27
4.1實例資料分析.......................27
4-2模擬分析.......................34
5結論與未來展望.......................37
附錄.......................39
參考文獻.......................41
參考文獻 參考文獻
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[2]Azzalini, A. and Dalla, A. (1996). “The multivariate skew-normal distribution,” Biometrika, 83, 715-726.

[3]Azzalini, A. and Capitanio, A. (1999). “Statistical applications of the multivariate skew normal distribution,” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 61, 579-602.

[4]Boulanger, M. and Escobar, L. A. (1994). “Experimental design for a class of accelerated degradation tests,” Technometrics, 36, 260-272.

[5]Carey, M. B. and Koenig, R. H. (1991). “Reliability assessment based on accelerated degradation,” IEEE Transactions on Reliability, 40, 499-506.

[6]Escobar, L. A., Meeker, W. Q., Kugler, D. L. and Kramer,
L. L. (2003). “Accelerated destructive degradation tests: data, models, and analysis,” Chapter 21 in Mathematical and Statistical Methods in Reliavility, Lindqvist, B. H. and Doksum, K. A., Editors, River Edge, NJ: World Scientific Publishing Company.

[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]Jeng, S. L., Huang, B. Y. and Meeker, W. Q. (2011). “Accelerated destructive degradation tests robust to distribution misspecification,” IEEE Transactions on Reliability, 60, 701-711.

[9]Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data, New York: John Wiley and Sons.

[10]Nelson, W. (1981). “Analysis of performance degradation data from accelerated tests,” IEEE Transactions on Reliability, 30, 149-155.

[11]Peng, C. Y. and Tseng, S. T. (2009). “Mis-specification analysis of linear degradation models,” IEEE Transactions on Reliability, 58, 444-455.

[12]Shi, Y., Meeker, W. Q. and Escobar, L. A. (2009). “Accelerated destructive degradation test planning,” Technometrics, 51, 1-13.

[13]Shi, Y. and Meeker, W. Q. (2012). “Bayesian methods for accelerated destructive degradation test planning,” IEEE Transactions on Reliability, 61, 245-253.

[14]Tsai, C. C., Tseng, S. T., Balakrishnan, N. and Lin, C. T. (2013). “Optimal design for accelerated destructive degradation test,” Quality Technology and Quantitative Management, 10, 263-276.

[15]Yu, H. F. (2003). “Designing an accelerated degradation experiment by optimizing the estimation of the percentile,” Quality and Reliability Engineering International, 19, 197-214.

[16]張家華 (2012) “壽命具廣義伽瑪分配之型 Ⅱ 設限階段應力加速壽命試驗的可靠度分析”,國立中央大學統計研究所碩士論文。

[17]林姿吟 (2013) “偏常態量測誤差模型下之加速破壞衰變試驗”,淡江大學數學研究所碩士論文。
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