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研究生:呂佳翰
研究生(外文):Chia-Han Lu
論文名稱:多反應值最佳化的操作區域之建立
論文名稱(外文):Construct an Optimal Operation Region for Multi-Response Problems
指導教授:江行全江行全引用關係
指導教授(外文):Bernard, C. Jiang
學位類別:碩士
校院名稱:元智大學
系所名稱:工業工程研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:115
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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大多數的產品都有多個品質特性,而這多個品質特性為製程工程師感興趣。在產品發展時常遇到的問題是如何選擇一組操作條件,使得所有的品質特性達到最佳。如果需要同時最佳化多個反應值,則主要的任務是如何找到一組妥協的最佳解,使得這組解對多個反應值都是可行的。
在設計一個實驗時,觀測值容易產生誤差的情形,即配適的反應值方程式與真實的反應值系統之間會產生變異的情況發生,為解決這個問題,計算一組最佳操作區域以求得操作條件範圍是較為建議的。另一方面,多反應值最佳化方法通常產生一組最佳操作條件,但這結果對工程師而言,可能由於製程環境、或是成本的考慮,而無法執行此最佳操作條件組合。
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。
最後,本研究比較3個現有的多反應值最佳化方法,並比較在不同的R-square下,哪一個方法是較被建議使用的。

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最佳操作區域的探討81
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
參考文獻92
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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