Characterizing projected designs: Repeat and mirror-image runs

Two-level designs are useful to examine a large number of factors in an efficient manner. It is typically anticipated that only a few factors will be identified as important ones. The results can then be reanalyzed using a projection of the original design, projected into the space of the factors that matter. An interesting question is how many intrinsically different type of projections are possible from an initial given design. We examine this question here for the Plackett and Burman screening series with N = 12, 20 and 24 runs and projected dimensions k≤5. As a characterization criterion, we look at the number of repeat and mirror-image runs in the projections. The idea can be applied to any two-level design projected into fewer dimensions.