Model-robust factorial designs

In industrial experimentation, experimental designs are frequently constructed to estimate all main effects and a few prespecified interactions. The robust-product-design literature is replete with such examples. A major limitation of this approach is the requirement that the experimenter know which interactions are likely to be active in advance. In this article, we develop a class of balanced designs that can be used for estimation of main effects and any combination of up to g interactions, where g is specified by the user. We view this as an issue of model-robust design: We construct designs that are highly efficient for all models involving main effects and g (or fewer) interactions. We compare the performances of these designs with the standard alternatives from the class of maximum-resolution fractional factorial designs for several criteria. The comparison reveals that the new designs are surprisingly robust to model misspecification, something that is generally not true for maximum-resolution fractional factorial designs. This robustness comes at a price: The new designs are frequently not orthogonal. We demonstrate, however, that the loss of orthogonality is, in general, quite small.