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.

本文考虑了使用传统设计标准以及纯误差自由度来确定最佳分割图设计（SPD）的问题。如果不允许对整个图和子图方差分量进行适当的方差估计，则最佳SPD几乎没有用。所提出的方法结合了DP优化的多标准版本，以表示在每个设计级别涉及D标准和复制的冲突标准。然后可以获得一组帕累托最优设计，其由关于每个准则的最优设计组成，并且不能就所有准则都被主导。此开发的关键是正交子图设计（OSUBD）的概念，因为此类SPD可以清晰地表示出DP最优性。