Which runs to skip in two-level factorial designs when not all can be performed

Abstract

When a two-level factorial design allows estimating contrasts that can be considered negligible from scratch, it is possible to omit some runs and later estimate their values by equating to zero the expressions of some of that contrasts. This article presents the combinations of runs to be omitted in 8 and 16 runs two-level factorial designs so that the responses can be estimated in such a way as to produce the least possible impact on the desired properties of the estimated contrasts: low and equal variance and the smallest possible correlation among them.