A Lower Bound to the Measure of Optimality for Main Effect Plans in the Symmetric Factorial Experiments

Abstract

A design d is called D-optimal if it maximizes det(M d ), and is called MS-optimal if it maximizes tr(M d ) and minimizes tr[(M d )2] among those which maximize tr(M d ), where M d stands for the information matrix produced from d under a given model. In this article, we establish a lower bound for tr[(M d )2] with respect to a main effects model, where d is an s-level symmetric orthogonal array of strength at least one. Non isomorphic two level MS-optimal orthogonal arrays of strength one with N = 10, 14, and 18 runs, non isomorphic three level MS-optimal orthogonal arrays of strength one with N = 6, 12, and 15 runs and non isomorphic four level MS-optimal orthogonal arrays of strength one with N = 12 runs are also presented.