DP Pareto optimal balanced orthogonal subplot designs. Issue 4 (3rd July 2020) - Wulff, Shaun S.; Cao, Yongtao; Robinson, Timothy J.
ABSTRACT: This paper considers the problem of identifying optimal Split-Plot Designs (SPDs) using traditional design criteria along with pure error degrees of freedom. An optimal SPD is of little use if it does not allow for suitable variance estimation of the whole plot and subplot variance components. The proposed approach incorporates a multi-criterion version of DP-optimality to represent the conflicting criteria involving the D-criterion and the replication at each design level. A set of Pareto optimal designs can then be obtained that consists of the optimal design with respect to each criterion and which cannot be dominated with respect to all the criteria. Key to this development is the notion of Orthogonal Subplot Designs (OSUBD) since this class of SPDs leads to a clear representation of DP-optimality. A number of common SPD design scenarios are provided to demonstrate the approach and to highlight the benefits of using the proposed multi-objective criterion.