In this article we investigate two-level split-plot designs where the sub-plots consist of
only two mirror image trials. Assuming third and higher order interactions negligible,
we show that these designs divide the estimated effects into two orthogonal
sub-spaces, separating sub-plot main effects and sub-plot by whole-plot interactions
from the rest. Further we show how to construct split-plot designs of projectivity PZ3.
We also introduce a new class of split-plot designs with mirror image pairs constructed
from non-geometric Plackett–Burman designs. The design properties of such designs
are very appealing with effects of major interest free from full aliasing assuming that
3rd and higher order interactions are negligible