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Computer-aided unbalanced supersaturated designs involving interactions

Supersaturated designs (SSDs) are defined as fractional factorial designs whose experimental run size is smaller than the number of main effects to be estimated. While most of the literature on SSDs has focused only on main effects designs, the construction and analysis of such designs involving interactions has not been developed to a great extent. In this paper, we propose a backward elimination design-driven optimization (BEDDO) method, with one main goal in mind, to eliminate the factors which are identified to be fully aliased or highly partially aliased with each other in the design. Under the proposed BEDDO method, we implement and combine correlation-based statistical measures taken from classical test theory and design of experiments field, and we also present an optimality criterion which is a modified form of Cronbach's alpha coefficient. In this way, we provide a new class of computer-aided unbalanced SSDs involving interactions, that derive directly from BEDDO optimization.