Optimal Projective Three-Level Designs for Factor Screening and Interaction Detection
Orthogonal arrays are widely used in industrial experiments for factor screening. Suppose only a few of the factors are important. An orthogonal array can be used not only for screening factors but also for detecting interactions among a subset of active factors. In this article, a set of optimality criteria is proposed to assess the performance of designs for factor screening, pro jection, and interaction detection, and a three-step approach is proposed to search for opti- mal designs. Combinatorial and algorithmic construction methods are proposed for generating new designs. Level permutation methods are used for improving the eligibility and estimation efficiency of the pro jected designs. The techniques are then applied to search for best three-level designs with 18 and 27 runs. Many new, efficient and practically useful nonregular designs are found and their properties discussed.