考慮效應邊際準則下的超飽和設計分析

Abstract

在工業實驗的篩選實驗中，通常會考量很多可能會影響結果的因子。此時往往會使用超飽和設計（Supersaturated design）來配置實驗，此設計能夠以較少的實驗樣本個數，找出影響結果的重要因子。本文討論的超飽和設計是考慮二階交互作用下的模型參數個數比實驗樣本個數多的狀況。有鑒於一般分析方法多不考慮效應邊際準則（Functional marginality principle），我們提出三種符合效應邊際準則的方法來分析，並以模擬的方式與常用的向前選取法作比較。Supersaturated designs are usually useful for screening experiments where the goal is to identify the few "active factors" among a potential list of design factors. The advantage of the supersaturated design is that it reduces costs by allowing using a smaller numbers of experimental runs to study many design factors. In this thesis, we consider the analysis of the supersaturated designs when the estimations of two-factor interactions as well as the main effects are of interest. We focus on the case where the number of parameters of the models containing main effects and interaction effects is greater than experimental run sizes. In this thesis we propose three analysis methods which take into account the functional marginality principle on the analysis of supersaturated designs, and compare the results with the forward selection with stimulation.