多反應值最佳化的操作區域之建立

Construct an Optimal Operation Region for Multi-Response Problems

呂佳翰(Chia-Han Lu)

指導教授 ： 江行全

元智大學/工程學院/工業工程與管理學系/碩士(2001年)

摘要

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。

關鍵字

多反應值 ； 操作區域 ； 二次模型 ； Monte Carlo模擬 ； SUR

並列摘要

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.

並列關鍵字

multi-response ； operation region ； quadratic programming ； Monte Carlo Simulation ； SUR

參考文獻

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