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研究生(外文):Chia-Han Lu
論文名稱(外文):Construct an Optimal Operation Region for Multi-Response Problems
指導教授(外文):Bernard, C. Jiang
中文關鍵詞:多反應值操作區域二次模型Monte Carlo模擬SUR
外文關鍵詞:multi-responseoperation regionquadratic programmingMonte Carlo SimulationSUR
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由於上述兩個理由,本研究提出一個操作區域,這個區域是考慮同時最佳化多個反應值下,藉由Monte Carlo模擬迴歸係數所建構的。對於每次模擬多個反應值,代入多反應值最佳化方法後,可得到一組新的的操作條件。由於迴歸模型是需同時考慮,所以使用Seemly Unrelated Regression(SUR)方法做迴歸係數估計。在實務上,工程師可以在操作區域中選擇一組操作成本最小的操作條件。

Most manufactured products have multiple quality attributes which are typical of interest to the process engineer, and a common problem encountered in the stage of product development is the selection of a set of operating conditions that achieves overall optimization for the system under investigation. If it is desired to simultaneously optimize several responses variables, then the task is how to locate a compromised optimal solution that is somewhat favorable to all responses.
In a designed experiment, when the observations are subject to error, discrepancies between the fitted response functions and the true response system occur due to inherent variability. To address this problem, the computation of an optimal operation region for operating conditions is suggested. On the other hand, multi-response optimization methods merely give a set of optimal operation conditions, but a field engineer could sometimes be vary hard to implement such conditions in practice.
With the two reasons mentioned above, this study proposes an operation region which considers simultaneous multi-response optimization via Monte Carlo simulations, which repetitively simulate regression coefficients, and the operation region is constructed. For each simulated set of responses, a new optimization factor setting was obtained by using a multi-response optimization approach. It then seems essential to consider the regression model not individually but jointly, so the Seemly Unrelated Regression (SUR) procedure is employed to perform parameter estimation. In practice, the engineer can select a set of operating conditions that has minimal operating cost from the operation region.
At last, this study compares three existing multi-response optimization approaches to construct operation region and evaluate which one is more suitable under different R-square statistic.

第一章 序論1
1.1 動機與目的1
1.2 論文架構4
第二章 文獻探討5
2.1 多反應值的介紹5
2.1.1 多反應值最佳化概念5
2.1.2 處理多反應值時可能遭遇的問題6
2.2 多反應值最佳化方法的介紹6
2.2.1 資料轉換方法(Data Transformation Approach)6
2.2.2 優先排序技巧(Ordering Techniques)8
2.2.3 一般的距離方法(Generalized Distance Approaches)10
2.3 國內其他相關研究12
2.3.1 使用田口方法的S/N比12
2.3.2 使用desirability function13
2.4 結論13
第三章 研究方法14
3.1 Desirability Function Approach14
3.1.1 方法14
3.1.2 實例18
3.1.3 流程圖22
3.2 Del Castillo’s Confidence Regions Approach23
3.2.1 方法23
3.2.2 實例28
3.2.3 流程圖31
3.3 Khuri and Conlon Minimax Approach32
3.3.1 方法32
3.3.2 實例37
3.3.3 流程圖40
3.4 的多變量常態分配與模擬41
3.5 非線性最佳化方法介紹45
3.5.1 非線性規劃概念45
3.5.2 BFGS47
3.5.3 Trust Region49
3.6 模擬方法的流程介紹53
3.7 損失函數56
第四章 模擬結果與最佳操作區域的探討與分析58
4.1 模擬分析58
4.1.1 Khuri and Conlon’s Minimax Approach求最佳操作區域58
4.1.2 Desirability Function Approach求最佳操作區域71
4.1.3 Del Castillo’s Confidence Region Approach求最佳操作區域73
4.1.4 給定反應值規格,求可行解75
4.1.5 利用損失函數QLP求最佳操作條件79
4.2.1 建立不同 迴歸模型的最佳操作區域81
4.2.2 不同 最佳操作區域的探討87
第五章 結論90
附錄1 去除具有線性關係的反應值97
附錄2 Del Castillo方法的二階模型介紹98
附錄3 Khuri’s Approach模擬迴歸係數 的S-Plus程式99
附錄4 Desirability Function模擬迴歸係數 的S-Plus程式104
附錄5 Del Castillo’s Confidence Region Approach模擬迴歸係數 的S-Plus程式109

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