Optimal Foldovers and Semifolding for Minimum Aberration Even Fractional Factorial Designs

Abstract

Sequential experimentation is one key to the successful use of fractional factorial designs. When one fractional factorial experiment with many factors produces results that, while useful, are not quite conclusive, adding another fraction is often recommended. This article addresses adding another fraction to a resolution IV design containing near the maximal number of factors. We extend the existing literature on foldover designs by presenting general results for identifying the best foldover for resolution IV designs for k factors in n = 2k runs and minimum aberration projections of these designs. We also consider semifolding because follow-up designs with n/2 runs exist that permit estimation of just as many effects of interest as are provided by a regular foldover. The ideas are illustrated for a 15-factor ceramic fiber composite experiment.