Probabilistic sequential methodology for designing a factorial system with multiple responses

This paper addresses the problem of optimizing a factorial system with multiple responses. A heuristic termed probabilistic sequential methodology (PSM) is proposed. The PSM identi® es those designs that maximize the likelihood of satisfying a given set of functional requirements. It is based on sequential experimentation, statistical inference and a probabilistic local search. The PSM comprises three main steps: (1) screening and estimating the main location and dispersion eA ects by applying fractional factorial experiments (FFE) techniques; (2) based on these eA ects, establishing probabilistic measures for diA erent combinations of factorlevels; and (3) constructing a set of candidate designs from which the best solution is selected by applying a heuristic local search. The PSM is attractive when the exact analytic relationship between factor-level combinations and the system’s responses is unknown; when the system involves qualitative factors; and when the number of experiments is limited. The PSM is illustrated by a detailed case study of a Flexible Manufacturing Cell (FMC) design.