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

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Abstract

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.

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Authors and Affiliations

  1. LPMC and Institute of Statistics, Nankai University, Tianjin, 300071, China

    Yuna Zhao & Minqian Liu

  2. School of Statistics, Qufu Normal University, Qufu, 273165, China

    Shengli Zhao

Authors
  1. Yuna Zhao
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  2. Shengli Zhao
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  3. Minqian Liu
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Corresponding author

Correspondence to Minqian Liu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11271205, 11371223, 11431006 and 11601244, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20130031110002, the “131” Talents Program of Tianjin, and the Program for Scientific Research Innovation Team in Applied Probability and Statistics of Qufu Normal University under Grant No. 0230518.

This paper was recommended for publication by Editor SHI Jianjun.

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Zhao, Y., Zhao, S. & Liu, M. On Construction of Optimal Two-Level Designs with Multi Block Variables. J Syst Sci Complex 31, 773–786 (2018). https://doi.org/10.1007/s11424-017-6144-2

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  • DOI: https://doi.org/10.1007/s11424-017-6144-2

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