A class of optimal robust parameter designs

In robust designs, the control-by-noise interactions are usually considered to be more important than other two-factor interactions. We extend the work on model-robust factorial designs of Li and Nachtsheim (2000) to robust designs, where not all factors are treated equally. A new criterion is proposed to maximize a design's ability to estimate models with at least one control-by-noise interaction. Optimal designs are chosen from the following three groups: regular orthogonal arrays (OAs), non-regular OAs, and balanced designs. Designs with economic run-sizes are constructed algorithmically and are tabulated for practical use.