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Split-plot designs with general minimum lower-order confounding

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Abstract

Split-plot designs have been widely used in industrial experiments. Up to now, most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion. Recently, by introducing a new pattern, called aliased effect-number pattern (AENP), Zhang et al. proposed a general minimum lower-order confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory. It is proved that, the GMC criterion selects optimal designs in a more elaborate manner than the existing ones, and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal designs. In this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot designs. Some comparisons of the new criterion with the MA-MSA-FFSP criterion are given, and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    JiaLin Wei, JianFeng Yang & RunChu Zhang

  2. KLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    RunChu Zhang

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100037, China

    Peng Li

  4. School of Sciences, Tianjin University of Commerce, Tianjin, 300134, China

    JiaLin Wei

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  1. JiaLin Wei
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  2. JianFeng Yang
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  3. Peng Li
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  4. RunChu Zhang
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Correspondence to JiaLin Wei.

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Wei, J., Yang, J., Li, P. et al. Split-plot designs with general minimum lower-order confounding. Sci. China Math. 53, 939–952 (2010). https://doi.org/10.1007/s11425-010-0070-2

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  • DOI: https://doi.org/10.1007/s11425-010-0070-2

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