An algorithm for blocking regular fractional factorial 2-level designs with clear two-factor interactions

Abstract

Regular fractional factorial designs with 2-level factors are among the most frequently used experimental plans. In many cases, designs should be blocked for dealing with inhomogeneity of experimental units. At the same time, the research question at hand may imply a focus on specified sets of two-factor interactions, while it is not justified to assume negligibility of other low order effects. An algorithm is provided for blocking a regular fraction into – possibly small – blocks while keeping specified two-factor interactions clear from confounding with main effects or other two-factor interactions. The proposed algorithm is implemented in the R package FrF2 and combines an estimability algorithm by the author with an automated implementation of a recent proposal for blocking fractions by hand.