Post-Stage Search Property of the 12-run Plackett-Burman Design

So far, the Plackett-Burman (PB) designs have been considered as saturated non-regular fractional factorial designs for screening purposes. Since introduction of the hidden projection of PB's by Wang and Wu (1995), the estimation capability of such projections onto a subset of factors has been investigated by many researchers. In this paper, by considering the search and estimation capability of a design, we introduce the post-stage search designs, using sparsity principle of factorial effects. That is, by the post-stage property of a design, we mean the capability of such a design in searching and estimating possible nonzero 3-factorial interactions along with estimation of the general mean, main effects and active 2-factor interaction effects, identified in the pre-stage. We show that a 12-runs PB projections onto 4 and 5 factors are post-stage search designs.