Some theory for constructing minimum aberration fractional factorial designs

Minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution. Minimum aberration designs for n runs and n/2 less than or equal to m < n factors have previously been constructed using the novel idea of complementary designs. In this paper, an alternative method of construction is developed by relating the wordlength pattern of designs to the so-called 'confounding between experimental runs'. This allows minimum aberration designs to be constructed for n runs and 5n/16 less than or equal to m less than or equal to n/2 factors as well as for n/2 less than or equal to m < n.