Fixing Effects and Adding Rows (FEAR) method to estimate factor effects in supersaturated designs constructed from Plackett–Burman designs

Abstract

Two-level supersaturated designs examine more than N SS − 1 factors in N SS experiments, and as a consequence individual factor effect estimation becomes problematic. In this paper, a new method, called the Fixing Effects and Adding Rows (FEAR) method, is proposed to estimate the effects in supersaturated designs more accurately. The FEAR method is based on the idea that too few experiments are executed to estimate the examined factor effects properly, and therefore zero effect rows are added to the model matrix, followed by consecutively fixing the largest estimated effects. The FEAR method is compared with Multiple Linear Regression (MLR) methods, as forward selection and stepwise regression, and with the alternative ridge regression method. A fully simulated, a partially simulated and an experimental data set were used for the evaluation of the methods. It was found that the FEAR method performs better than the earlier applied MLR and ridge regression methods, since the significant main effects are more accurately estimated and because fewer effects are incorrectly considered being either significant or non-significant.