On Construction of Optimal Two-Level Designs with Multi Block Variables

When running an experiment, inhomogeneity of the experimental units may result in poor estimations of treatment effects. Thus, it is desirable to select a good blocked design before running the experiment. Mostly, a single block variable was used in the literature to treat the inhomogeneity for simplicity. However, in practice, the inhomogeneity often comes from multi block variables. Recently, a new criterion called B²-GMC was proposed for two-level regular designs with multi block variables. This paper proposes a systematic theory on constructing some B²-GMC designs for the first time. Experimenters can easily obtain the B²-GMC designs according to the construction method. Pros of B²-GMC designs are highlighted in Section 4, and the designs with small run sizes are tabulated in Appendix B for practical use.