Robust multistratum baseline designs

Baseline designs have received considerable attention recently. Most existing methods for finding best baseline designs were developed for completely randomized experiments. How to select baseline designs for experiments under multistratum structures has not been studied in the literature. The purpose of this paper is to fill this gap and extend the use of the baseline design for experiments with complex structures, such as split-plot experiments. A framework for baseline designs under multistratum structures is established and a generalized minimax A-criterion for selecting multistratum baseline designs which are efficient and model robust is proposed. The coordinate-exchange algorithm is applied and robust baseline designs under split-plot, split-split-plot, and block-split-plot structures, which can be constructed via nesting operators repeatedly, are exemplified. A real case study for industrial experiments is provided to demonstrate the application and data analysis of multistratum baseline designs.