太陽能電池中之構造EVA膜其交聯度對其產品效能有極大的影響。本研究對EVA膜進行層壓試驗，再以化學法及DSC法量測其層壓後EVA膜之交聯度，並收集層壓後的交聯度資料。莊惟安 (2014) 建構出一迴歸模型來描述 EVA膜交聯度與層壓時間之間的關係，由模型可推導出EVA膜的最佳層壓時間。然而，影響EVA膜層壓後交聯度之因子，除了層壓時間外，還有層壓溫度等。本文探討了層壓時間與層壓溫度對EVA膜交聯度之關係，以進一步執行其最佳層壓試驗。
    首先，建構一最小極值分配迴歸模型來描述交聯度與層壓溫度及層壓時間之關係，並由此模型推導出層壓溫度與EVA膜最佳層壓時間之關係式。接下來，在給定一層壓溫度下，推導出在此層壓溫度下之最佳層壓時間估計量之漸近變異數，並執行一最佳層壓試驗，使可更準確的估計在給定一層壓溫度下之最佳層壓時間。再來，使用基因演算法求得其最佳樣本比例配置。最後，由模擬分析來探討此試驗設計，由模擬分析結果可知，模擬結果與大樣本理論是相近的，並以全域搜尋與基因演算法所得最佳樣本配置之結果進行比較，得知兩者之相對效率。

With the development of solar power, the degree of crosslinking of EVA sheets has a great influence on the performance of solar module. In this study, lamination tests on EVA sheets are conducted first. And then we use chemical method and differential scanning calorimetry (DSC) method to measure the degree of crosslinking of EVA sheets. Then, a regression model with smallest extreme value distribution was proposed to describe the relationship between the degree of crosslinking of EVA sheets, lamination time, and lamination temperature. Next, we obtain the optimal laminated times with different lamination temperatures. Given fixed lamination temperature, the asymptotic variance of the optimal laminated time was used to perform the optimal design. And the optimal sample allocation was searched by genetic algorithm. Finally, a simulation study further shows that the simulated values are quite close to the asymptotic values when the sample sizes are large enough. And we compare optimal sample allocations based on global search, equal allocation and genetic algorithm by relative efficiency.

目錄
第1章  緒論	1
1.1前言	1
1.2文獻探討	5
1.2.1  EVA膜量測與破壞衰變模型	5
1.2.2 最小極值分配與線性迴歸模型	5
1.2.3 最佳化試驗配置	7
1.2.4 最佳化演算法	8
1.3研究動機及目的	8
1.4研究架構	14
第2章  問題描述	16
第3章  最佳層壓試驗	26
3.1最佳樣本比例配置	26
3.1.1 t ̂_(opt,Chem) 、USL^((1)) 、LSL^((1))之推導	26
3.1.2 t ̂_(opt,DSC) (S) 之推導	28
3.1.3 Avar(t ̂_(opt,DSC) (S)) 之推導	29
3.2基因演算法	33
第四章 層壓試驗分析	38
4.1實例資料分析	38
4.2模擬分析	42
第五章 結論與後續研究	47
附錄	49
參考文獻	54

[1]	Czanderna, A. W. and Pern, F. J. (1996). “Encapsulation of PV modules using ethylene vinyl acetate copolymer as a potent: A critical review,” Solar Energy Materials and Solar Cells, vol. 43, 101-181.

[2]	Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning, reading, MA: Addison Wesley.

[3]	Hirschla, C. and Biebl, M. (2013). “Determining the degree of crosslinking of ethylene vinyl acetate photovoltaic module encapsulates a comparative study,” Solar Energy Materials and Solar Cells, vol. 116, 203-218.

[4]	Jafari, H. and Hashemi, R. (2011). “Optimal designs in a simple linear regression with skew-normal distribution for error term,” Applied Math Mathematics, vol. 1, 65-68.

[5]	Kutner, M., Nachtsheim, N. and Neter, J. (2004). Applied Linear Regression Models, MA:Irwin, Boston.

[6]	Meeker, W. Q. and Escobar, L. A. (1998). Statistical methods for reliability data. New York: John Wiley & Sons.

[7]	Meeker, W. Q., Escobar, L. A. and Lu, C. J. (1998). “Accelerated degration tests: modeling and analysis,” Technometrics, vol. 40, 89-99.

[8]	Meeker, W. Q., Escobar, L. A. and Shi, Y. (2009). “Accelerated destructive degradation test planning,” Technometrics, vol. 51, No.1.

[9]	Meeker, W. Q., Escobar, L. A., Kramer, L. L. and Kugler, D. L. (2003). “Accelerated destructive degration tests: data, models, and analysis,” Mathematical and Statistical Methods in Reliability, vol. 1, 319-337.

[10]	 Ng, H. K. T., Balakrishnan, N. and Chan, P. S. (2006). “Optimal sample size allocation for tests with multiple levels of stress with extreme value regression,” Naval Research Logistics, vol. 54, 237-249.

[11]	 Park, C. and Padgett,W. J. (2005). “Accelerated dradation models for failure based on geometric Brownian motion and Gamma pocess,” Lifetime Data Analysis, vol. 11, 511-527.

[12]	 Peng, L. (1998). “Asymptotically unbiased estimators for the extreme value index,” Statistics & Probability Letter, vol. 38, 107-115. 

[13]	 Stark, W. and Jaunich, M. (2011). “Investigation of ethylene/vinyl acetate copolymer (EVA) by thermal analysis DSC and DMA,” Polymer Testing, vol. 30, 236-242.

[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, vol. 10, 263-276.

[15]	 Tsai, T. R., Lin, C. W., Sung, Y. L., Chou, P. T., Chen, C. L. and Lio, Y. (2012). “Inference from lumen degradation data under wiener diffusion process,” IEEE Transactions on Reliability, vol. 61, 710-718.
	
[16]	 Tseng, S. T., Tsai, C. C. and Balakrishnan, N. (2011). “Optimal sample size allocation for accelerated degradation test based on Wiener process,” 330-343, Chapter 27, Methods and Applications of Statistics in Engineering, Quality Control, and the Physical Sciences, New Jersey, John Wiley & Sons, Hoboken.

[17]	 Wei, L. J. and Ying, Z. (1989). “Linear regression analysis of censored survival data based on rank tests,” Biometrika Trust, vol. 77,  845-851.