Two-level designs to estimate all main effects and two-factor interactions

Abstract

We study the design of two-level screening experiments with N runs and n factors large enough to estimate a model with all the main effects and all the two-factor interactions, while yet an e ect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two-factor interactions. Orthogonal arrays (OAs) favor main e ect estimation. However, complete enumeration becomes infeasible for cases relevant for practitioners. We develop a partial enumeration procedure for these cases and we establish upper bounds on the D-efficiency of arrays that have not been generated by the partial enumeration. We propose an optimal design procedure that favors main effect estimation as well. Designs created with this procedure have smaller D-efficiencies than D-optimal designs, but standard errors for main effects are improved. Generated OAs for 7{10 factors and 32{72 runs are smaller or have a higher D-efficiency than the smallest OAs from the literature. Designs obtained with the new optimal design procedure or strength-3 OAs (which have main e ects that are not correlated with two-factor interactions) are recommended under effect hierarchy. D-optimal designs are recommended if this assumption is not likely to hold.