應用灰色系統理論於重覆性實驗計畫中受限資料之分析

Abstract

工業界常需利用實驗計畫法(Design of Experiments)來研發或改善產品，但在實驗進行中，有時會發生一些狀況而無法蒐集到完整的實驗數據，例如：為了加快產品上市，在實驗進行到一定程度後便得結束實驗進行分析；或是因為實驗儀器的限制、實驗中突然斷電等。在這些狀況下只能蒐集到一定範圍內的數據，此類數據稱之為『受限資料』（censored data）。由於受限資料所包含的因子資訊較少，因此無法以傳統的實驗計畫法做分析。目前文獻中所提出受限資料方面的分析方法，多是利用迴歸分析等統計方法構建模式來估計受限資料，這些方法使用上皆需要嚴謹的統計假設與繁雜的計算，使得不具太多統計背景的工程人員難以運用；後來雖然有些學者提出以不需統計假設的類神經網路方法來分析重覆性實驗計畫之受限資料，但是其網路的架構需要以試誤法決定，使得分析過於繁瑣。因此本研究之主要目的乃是針對重覆性傳統實驗計畫和田口方法中單一受限資料提出一套決定最佳因子水準組合的方法。本方法是利用灰色預測法（grey prediction method）對每一因子水準組合下的受限觀測值做預測，再將這些預測值與未受限之觀測值合併後視為完整數據。最後分別以傳統實驗計畫分析法與田口方法來找出顯著因子及決定最佳因子水準組合。本研究最後並以實例來說明所提之受限資料分析法的有效性及可行性

Design of Experiment (DOE) has been extensively adopted to improve the efficiency of new product design and manufacturing process development in industry. However, only part of the designed experiments can be completed due to some uncontrollable causes such as cost and time limitations, and power damage during the experiment. Under such circumstances, the incomplete data obtained from the experiment are referred to as censored data. Because the censored data contains less information, the standard analysis method cannot be applied to the censored data and the analysis more difficult. Conventional approaches for analyzing censored data are computationally complicated and often demand statistical assumptions on data such as normality assumption. This study proposes a procedure to analyze the censored data from repetitious experiments using the gray system theory. The proposed procedure does not need any statistical assumption and is less conceptual and computational complicated than the existing methods. Two cases, one traditional experiment with typeⅡ censored and Taguchi experiment with typeⅠcensored, are utilized to demonstrate its effectiveness.