Optimal foldover plans for blocked 2m-k2m-k fractional factorial designs

In many experimental settings, an initial two-level fractional factorial design is run to determine which experimental factors are significant. A follow-up design is then run to further explore relationships such as interactions that might exist between experimental factors. A commonly used follow-up strategy involves the use of a foldover design which is obtained by reversing the signs of one or more columns in the design matrix of the initial design. The full design obtained by joining the runs in the follow-up design to those of the initial design is called the combined design. In this paper we explore the use of the foldover technique as applied to blocked regular fractional factorial designs. In particular, two criteria are suggested for finding optimal foldover plans. The two criteria suggested are a minimum aberration criterion and a maximal rank-minimum aberration criterion as applied to the combined designs which can be obtained by using different foldovers of the initial design. Using these criteria and search methods, optimal foldover plans are obtained for each of the blocked fractional factorial plans given in Sun, Wu and Chen [1997. Optimal blocking schemes for 2n2n and 2n-p2n-p designs. Technometrics 39, 298–307] having nine or fewer factors. Tables containing these optimal foldover plans are given in the Appendix.