成本受限下多品質特性之混合實驗最佳化演算法

Abstract

隨著科技的進步及消費者對產品品質之要求增多，使得產品設計日趨複雜，產品之品質已非單一品質特性能決定，而是由多個品質特性所決定。在某些產業中，實驗之反應變數 (response variables) 是受因子間之相對比例調配而成，其因子水準之設定方法不能用傳統之實驗設計 (Design of Experiments, DOE)，而是需要用混合實驗 (Mixture Experiments) 之方法。在混合實驗中，因子稱為成份 (component)，實驗目的在於找出最佳成份比例配方。另外，製造成本對於業者而言是一項相當重要之考量因素，而目前有關實驗設計最佳化的中外文獻中，尚未見到將成本納入考量之實際案例，因此本論文之主要目的是利用反應六標準差品質之望想函數 (desirability function for achieving six-sigma quality) 及雙反應曲面方法 (Dual Response Surface Method, DRSM)，發展出一套具多品質特性混合實驗之最佳化演算法。在成本限制條件下，求出一組可達到最大化產品品質之成份比例，再以最佳配方之總望想值對照其品質水準，建議業者是否需要進行品質改善。最後，本論文以台灣某公司汽車煞車用橡膠皮碗之案例，驗證本論文所提出之多品質特性混合實驗問題之最佳化演算法確實有效。

With the improvement of technology and the increasing demands of the consumer, product design is becoming more and more complicated. The optimization of a single response can no longer satisfy the needs of customers. Therefore, the optimization of multi-responses is increasingly important. In some chemical or material experiments, responses are affected by the proportional relationship of the factors (or components) rather than the quantity of the factors. Such experiments are called mixture experiments. In addition, the manufacturing cost is also a vital condition in determining the optimal proportion of the component. Therefore, this study utilizes the desirability function for achieving six-sigma quality and Dual Response Surface Method (DRSM) to integrate the multi-response into one component’s index, and then to develop a procedure for optimizing the composite quality index under restricted manufacturing costs. A real case study of rubber bowl production from a Taiwan’s automobile company is utilized to illustrate the effectiveness of the proposed procedure.