部分因子設計會造成因子效應混淆，導致難以掌握因子與反應變數之間的關係。在高斯隨機域的模型假設下，Chang et al.（2018）和 Chang and Cheng（2020）提出了兩個衡量因子效應混淆的指標，分別用來評估類別型因子與連續型因子的效應混淆之嚴重程度，然而這兩個指標與統計性質之間的連結仍然不清楚。在本篇論文中，我們展示了此二指標與因子設計之預測能力有高度相關，並利用數值模擬來觀察低程度混淆的因子設計與預測偏誤和預測變異之關聯。;The existence of effect aliasing in fractional factorial designs makes it difficult to accurately understand the relationship between the factors and the response. For Gaussian random fields, two indices for assessing the degree of severity of effect aliasing have been proposed by Chang et al. (2018) and Chang and Cheng (2020), the former for qualitative factors and the latter for quantitative factors. However, the connection between these two indices and statistical properties remained vague. In this thesis, we show that the two aliasing severity indices are highly correlated with prediction performance of fractional factorial designs. We conduct simulation study to evaluate low-aliasing designs through their prediction bias and prediction variance over the whole experimental region.
