Some theory for constructing minimum aberration fractional factorial designs

Abstract

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 ≤ 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 5 n /16 ≤ m ≤ n /2 factors as well as for n /2 ≤ m < n .