Optimal partially replicated parallel-flats designs for 2n1×3n2 mixed factorial experiments

Augmenting additional repeated runs to an unreplicated factorial design provides an economical scheme of obtaining an unbiased estimate for the error variance based on pure replicates. The augmented partially replicated design usually performs satisfactorily in identifying truly active effects regardless of whether the effect sparsity principle holds. Liao and Chai (2009) proposed a set of sufficient conditions for a partially replicated two-level design to be D-optimal over the class of parallel-flats designs. In this article, we generalize their result to the 2n1×3n22n1×3n2 mixed factorial under D-, A- and E-optimality, and include the 2n and 3n symmetric factorials as special cases. In addition, some examples are given to illustrate the main results.