Generation of Linear Trend-Free Designs for Factorial Experiments

Abstract

The present article deals with generation of designs for factorial experiments (without and with confounding) that permit the estimation of main effects free from linear trend effects present in the experimental units. The proposed method exploits the use of component wise product of vectors to generate linear trend-free for main effects designs for two-level factorials. The procedure of identifying two- and three- factor interactions that are linear trend-free has also been incorporated in the method. The method has also been extended to generate designs for confounded factorial experiments with any number of factors k ( 3) that are linear trend-free for main effects and identify two- and three- factor interactions for which the design is linear/nearly linear trend-free.