Nearly Resolution V Plans on Blocks of Small Size

Abstract

In the present paper we aim at constructing plans (designs) for symmetrical experiments on small blocks such that factorial effects (main effects or interactions) are ‘orthogonal through the block factor’. Specifically, given an initial plan, we derive sufficient conditions on the set of ‘generators’ for a desired change in the relation between a pair of factorial effects in the generated plan—non-orthogonality turning to orthogonality and aliased effects turn into non-aliased. We illustrate the theory with plans for two- and three-level factors on blocks of size four or less, estimating main effects as well as two-factor interactions. The plans constructed have the following features. They are inter-class orthogonal, in the sense that each effect of interest is orthogonal to all effects except the ones in its own class. The sizes of the classes are small, so that amount of non-orthogonality is limited. In particular, in the plans for experiments with three-level factors, most of the main effects are orthogonal to all others.