A note on constructing clear compromise plans

The regular two-level fractional factorial designs of n factors and N runs, having resolution IV and allowing experimenters to clearly estimate all main effects and a set of required two-factor interactions (2fi's), are called clear compromise plans. Four classes of clear compromise plans have been discussed in the literature. The general minimum lower order confounding (GMC) is an elaborate criterion, which was proposed to select optimal fractional factorial designs. This paper gives a theory on constructing a set of class three clear compromise plans with 5N∕32+3≤n≤N∕4+1, called partially general minimum lower order confounding (P-GMC) designs. We first prove that each P-GMC design is constructed by a GMC design and two specified columns. Then we study the properties of these designs. For N=32,64 and 128, we illustrate that the P-GMC designs are admissible designs. Furthermore, they all have GMC, except for the P-GMC 213−7 and 223−16 designs.