應用資料包絡分析法與自組性演算法最佳化來自實驗設計之多反應變數

實驗設計(Design of Experiments, DOE)是工業界常用來規劃實驗及找出最佳配方或改善產品∕製程的統計方法，但此法僅能分析單反應之實驗數據，對於具有多個反應之實驗，中外文獻所提出的最佳化方法多以探討田口方法(Taguchi methods)爲主，故本研究針對由DOE 所得的具有多反應之實驗，利用相對效率的概念提出一套最佳化的流程。本研究首先利用資料包絡分析法(Data Envelopment Analysis, DEA)可有效分析多投入多產出之特性，來分析由DOE所得的具有多個反應之實驗數據，將多個反應轉換成一個效率指標，然後再以自組性演算法(Group Method of Data Handling, GMDH)適配出一個效率估計模型，根據此效率估計模型即可求得同時最佳化多反應之最佳配方。本研究方法之優點是可避免應用反應曲面法(Response Surface Method, RSM)或望想函數(desirability function)尋求最佳配方時，必須針對多反應建立多條求解模型才能進行最佳化的缺失。本研究最後以文獻上的四個案例，與新竹科學園區某積體電路公司的一個蝕刻製程實驗，來說明本研究方法之有效性及可行性，由案例的驗證結果顯示出本研究方法確實具實務之應用價值。

關鍵字

多反應變數；實驗設計；資料包絡分析法；自組性演算法；反應曲面法

並列摘要

Design of Experiments (DOE) is often utilized to determine the optimal factor-level combination or enhance product/process quality in industry. However, DOE is used to design and analyze experimental data with a single response. Optimization of multiple responses simultaneously in DOE has received little attention. Therefore, by applying relative efficiency, this work presents an optimization procedure for multiple responses. Given the features of efficiently analyzing multiple inputs and multiple outputs, the relative efficiency of each factor-level combination for an experiment with multiple responses is identified by using Data Envelopment Analysis (DEA). Group Method of Data Handling (GMDH) is then utilized to fit a model for determining the efficiency of various factor-level combinations. An optimal factor-level combination is then determined according to the GMDH model. Through the demonstrated cases, the proposed procedure can effectively optimize multiple responses simultaneously.

並列關鍵字

multiple responses ； design of experiments ； data envelopment analysis ； group method of data handling ； response surface method

參考文獻

Allen, T. T.,Yu, L.(2002).Low-cost response surface methods from simulation optimization.Quality and Reliability Engineering International.18,5-17.

Google Scholar

Ames, A. E.,Mattucci, N.,MacDonald, S.,Szonyi, G.,Hawkins, D. M.(1997).Quality loss functions for optimization across multiple response surfaces.Journal of Quality Technology.29(3),339-346.

Google Scholar

Charnes, A.,Cooper, W. W.,Rhodes, E.(1978).Measuring the efficiency of decision-making units.European Journal of Operational Research.2,429-444.

Google Scholar

Cooper, W. W.,Seiford, L. M.,Tone, K.(2000).Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References, and DEA-Solver Software.Boston:Kluwer Academic Publishers.