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 s...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 B^2-GMC designs for the first time. Experimenters can easily obtain the B^2-GMC designs according to the construction method. Pros of B^2-GMC designs are highlighted in Section 4, and the designs with small run sizes are tabulated in Appendix B for practical use.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11271205,11371223,11431006 and 11601244the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20130031110002+1 种基金the“131”Talents Program of Tianjinthe Program for Scientific Research Innovation Team in Applied Probability and Statistics of Qufu Normal University under Grant No.0230518
文摘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 B^2-GMC designs for the first time. Experimenters can easily obtain the B^2-GMC designs according to the construction method. Pros of B^2-GMC designs are highlighted in Section 4, and the designs with small run sizes are tabulated in Appendix B for practical use.
