Building some bridges among various experimental designs

Abstract

Designing their experiments is the significant problem that experimenters face. Maximin distance designs, supersaturated designs, minimum aberration designs, uniform designs, minimum moment designs and orthogonal arrays are arguably the most exceedingly used designs for many real-life experiments. From different perspectives, several criteria have been proposed for constructing these designs for investigating quantitative or qualitative factors. Each of those criteria has its pros and cons and thus an optimal criterion does not exist, which may confuse investigators searching for a suitable criterion for their experiment. Some logical questions are now arising, such as are these designs consistent, can an optimal design via a specific criterion perform well based on another criterion and can an optimal design for screening quantitative factors be optimal for qualitative factors? Through theoretical justifications, this paper tries to answer these interesting questions by building some bridges among these designs. Some conditions under which these designs agree with each other are discussed. These bridges can be used to select a suitable criterion for studying some hard problems effectively, such as detection of (combinatorial/geometrical) non-isomorphism among designs and construction of optimal designs. Benchmarks for reducing the computational complexity are given.