反應六標準差之多品質特性混合實驗最佳化演算法

Abstract

利用實驗設計法(Design of Experiments, DOE)有效率地找出最佳實驗參數組合以降低生產成本或改善品質，為增加產業競爭力的重要手法之一。然而在材料、化工、或食品等產業中，有許多屬於混合實驗(Mixture Experiments)範疇之最佳化設計問題，卻常誤以傳統因子實驗設計之。在混合實驗中，直接影響反應變數的是各混合成分(component)，即各因子(即成分)佔實驗組合總量之比例，而混合實驗之性質與傳統因子實驗差別很大。此外，在科技不斷精進與消費者需求持續提升的情況下，實驗設計之目標往往需要考慮多個品質特性的同時最佳化，但目前僅有文獻提出應用望想函數(desirability function)來處理混合實驗之多品質特性同時最佳化的問題。本研究以Ribardo與Allen[14]所提出改善舊有望想函數未考慮製程平均與變異之缺點的六標準差望想函數(desirability function for achieving six-sigma quality)為依據，提出另一套混合實驗之多個品質特性最佳化的演算法，此六標準差望想函數值並能夠反應六標準差之品質水準。本研究最後以分析新竹某公司所提供之汽車橡膠皮碗之實例，驗證所提演算法之可行性與有效性。

Design of experiments (DOE) is useful in finding the optimal parameter-setting efficiently with low experimental cost. However, in some specific areas, engineers often misuse factorial design on mixture experiments. In mixture experiments, the factor (which is also called component) affects the response by its proportion in all components, but not the actual volume. This is the main difference between factorial design and mixture experiments. In addition, simultaneously optimization of multiple responses is increasingly essential. Therefore, this study proposes a procedure to optimize multi-response in mixture experiments. The desirability function of six-sigma quality introduced by Ribardo and Allen [14] is employed in the proposed procedure. The desirability function considers the estimated mean and variance of response variable and estimate the response under assumptions required in the six-sigma quality. A rubber bowl’s experiment with four components and eleven response variables are utilized to demonstrate the effectiveness of the proposed procedure.