2(n1+n2)-(k1+k2)2(n1+n2)-(k1+k2) Fractional factorial split-plot designs containing clear effects

Whole-plot (WP) factors and sub-plot (SP) factors play different roles in fractional factorial split-plot (FFSP) designs. In this paper, we consider FFSP designs with resolution III or IV from the viewpoint of clear factorial effects, classify two-factor interactions (2FIs) into three types, and give sufficient and necessary conditions for the existence of FFSP designs containing various clear factorial effects, including two types of main effects and three types of 2FIs. The structures of these designs are also shown and illustrated with examples.