應用雙反應曲面分析法於混合實驗多品質特性最佳化之研究

Abstract

工業界在研發新產品或改善產品品質時，常利用實驗設計(Design of Experiments, D.O.E)來規劃實驗及分析實驗數據，以得到最佳因子水準組合。然而，在某些領域（如化學或材料）的實驗中，影響反應變數(response)是各因子在每一實驗組合中所佔之比例，而非各因子之含量多寡，這類特殊的實驗稱為混合實驗(Mixture Experiments)。由於混合實驗之各因子(又稱成份)的比例加總須等於100%，所以可行解區域會比一般實驗設計之維度小，其反應曲面模式也與一般實驗的反應曲面模式不同。此外，產品的品質已非最佳化單一品質特性就能解決，往往需要考慮到多品質特性(multiple response)同時最佳化才行。目前中外文獻已提出一些多品質特性同時最佳化的方法，但是這些方法只限於一般實驗。中外有關混合實驗的文獻，大部分只應用單品質最佳化之案例，至於多品質混合實驗最佳化的問題，國外文獻建議以互償的方式或者使用望想函數找多品質的最佳解，但是其所探討的混合實驗不符合一般性，因此本論文首先利用主成份分析(Principle Component Analysis)或灰色多屬性決策(Grey Multiple Attribute Decision Making)來整合多個品質特性合成單一綜合品質特性，然後發展出一套最佳配方的程序。在成本方面，目前有關最佳化的中外文獻皆沒有討論到最佳配方之成本問題，為了能使新產品更具競爭力，本研究亦將配方之成本納入考量，另發展出一套考量成本之多品質混合實驗演算法。本研究最後透過某公司提供之煞車皮碗的案例，驗證本研究所提出混合實驗最佳化多品質流程確實有效可行。

Design of experiments is often applied in industry to develop new product. However, in some chemical or material experiments, responses are usually affected by factor’s (or component’s) proportion rather than the factor’s quantity. Such experiments are called mixture experiments. Because the proportions of components have to be added to 100%, the dimension of solutions for the optimal factor-quantity combination using the response surface method (RSM) is less than that of the conventional designed experiments. In addition, due to the product design becomes increasingly complicated, more than one quality characteristic must be simultaneously optimized to improve the product quality. Although several procedures for optimizing multi-response process have been developed in recent years, they are appropriate only for the conventional experiments. Only few cases were studied for mixture designs with single response. When more than one response is to be optimized in mixture design, engineers usually determine the optimal component’s proportions from their experiences. However, it is very difficult to decide the optimum component’s proportions. Therefore, this study proposes an optimizing procedure to resolve multi-response problem for mixture designs. This study uses the Grey Multiple Attribute Decision Making (GMADM) or Principle Component Analysis (PCA) to integrate multiple responses into one component’s proportions index, and then develops a procedure for optimizing the composite quality index. Besides, product’s competitiveness is also determined by its manufacturing cost. This study further develops a procedure for obtaining the optimal proportion combination with the manufacture cost. A real case of rubber bowl experiment from a Taiwan’s company is utilized illustrate the effectiveness of the proposed procedure.