應用主成份分析與資料包絡法最佳化具多品質特性之混合實驗設計

Abstract

工業界常利用實驗設計（Design of Experiments, DOE）或田口方法(Taguchi Methods)來設計和規劃實驗，並分析實驗數據以找出製程參數之最佳配方。但是，現今有許多產業，如：化工、食品工業、材料、醫療等，其製程之反應變數（response variables）並非受到因子之絕對數量所影響，而是與各成份所佔總含量之百分比(proportion)有關，這類的產業並不適用於傳統的實驗設計，而是屬於混合實驗（Mixture Experiments）之範疇。在混合實驗中，因子稱為成份（component），此類實驗受到各成份比例加總等於一之限制，實驗的目的在於找出最佳之成份比例；此外，隨著科技進步、消費者對產品品質特性的要求既多元且多樣，多品質特性最佳化的問題很重要。因此本論文之主要目的是利用主成份分析(Principle Components Analysis, PCA)、資料包絡法（Data Envelopment Analysis, DEA）及自組性演算法（Group Method of Data Handling, GMDH），在成本限制條件下，發展出一套具多品質特性混合實驗之最佳化演算法。本研究最後分別以新竹某公司所提供之混合實驗及另一公司所提供之汽車煞車用橡膠皮碗之案例，驗證本論文所提出之最佳化多品質特性混合實驗問題之演算法確實有效。

In some mixture experiments, such as chemical or material experiments, the responses of the experiments are affected by the proportional relationship among the factors (or components) rather than the quantities of the factors. Hence, the conventional design of experiments (DOE) techniques is not appropriate for the mixture experiments. Moreover, with the rapid improvement of the manufacturing technologies and the increasing demands from the consumers, product design is becoming more and more complicated. Optimization of a single response can no longer satisfy the needs of customers. Therefore, this study first utilizes Principle Components Analysis (PCA) and Data Envelopment Analysis (DEA) to integrate the multiple responses into a composite index, and then employs Group Method of Data Handling (GMDH) to develop a procedure to optimize the composite index under the restricted proportion of components. A real case of rubber bowl production from a Taiwanese automobile company is utilized to demonstrate the effectiveness of the proposed procedure.