Nearly orthogonal arrays of strength three

The main effects of a factorial experiment can be estimated with minimum variance and zero bias using orthogonal arrays (OAs) of strength three. However, such arrays require the run size to be a multiple of eight. When the run size is not a multiple of eight, OAs of strength three do not exist. In the presence of non-negligible two-factor interactions, OAs of strength two with minimum G2-aberration are available as variance-optimal designs that have the minimum bias among non-isomorphic OAs of strength two. Such designs only require the run size to be a multiple of four. Best fold-over designs have zero bias and provide the minimum variance among all fold-over designs. We examine the use of nearly orthogonal arrays of strength three for estimating main effects in the presence of nonnegligible two-factor interactions. This provides an approach that is capable of balancing the consideration of variance and bias. Our method is compared with the two existing classes of designs.