Optimal fractional factorial designs and their construction

Author-Highlights•Optimal symmetrical fractional factorial designs with n runs and m factors of s levels each are constructed.•The minimum moment aberration criterion is used to judge the optimality of the designs.•Some optimal designs are constructed by using generalized Hadamard matrices.•We are able to construct many minimum aberration designs, however, most of them are supersaturated.

Optimal symmetrical fractional factorial designs with nn runs and mm factors of ss levels each are constructed. We consider only designs such that no two factors are aliases. The minimum moment aberration criterion proposed by Xu (2003) is used to judge the optimality of the designs. The minimum moment aberration criterion is equivalent to the popular generalized minimum aberration criterion proposed by Xu and Wu (2001), but the minimum moment criterion is simpler to formulate and employ computationally. Some optimal designs are constructed by using generalized Hadamard matrices.