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Individual Word Length Patterns for Fractional Factorial (Split-Plot) Designs

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Abstract

Fractional factorial (FF) designs are commonly used for factorial experiments in many fields. When some prior knowledge has shown that some factors are more likely to be significant than others, Li, et al. (2015) proposed a new pattern, called the individual word length pattern (IWLP), which, defined on a column of the design matrix, measures the aliasing of the effect assigned to this column and effects involving other factors. In this paper, the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs. As we know, fractional factorial split-plot (FFSP) designs are important both in theory and practice. So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs. The authors propose the IWLP of a factor from the whole-plot (WP), or sub-plot (SP), denoted by the IwWLP and IsWLP respectively, in the FFSP design. The authors further propose combined word length patterns CwWLP and CsWLP, in order to select good designs for different cases. The new criteria CwWLP and CsWLP apply to the situations that the potential important factors are in WP or SP, respectively. Some examples are presented to illustrate the selected designs based on the criteria established here.

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Authors and Affiliations

  1. School of Statistics and Data Science, Qufu Normal University, Qufu, 273165, China

    Xiaoxue Han

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Jianbin Chen

  3. School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin, 300071, China

    Jianfeng Yang & Minqian Liu

Authors
  1. Xiaoxue Han
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  2. Jianbin Chen
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  3. Jianfeng Yang
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  4. Minqian Liu
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Corresponding author

Correspondence to Minqian Liu.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11811033, 11971204, 12101357, 12131001 and 12271270, National Ten Thousand Talents Program of China, Natural Science Foundation of Tianjin under Grant No. 20JCYBJC01050, Natural Science Foundation of Shandong under Grant No. ZR2021QA080, and the 111 Project B20016. The first three authors contributed equally to this work.

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Han, X., Chen, J., Yang, J. et al. Individual Word Length Patterns for Fractional Factorial (Split-Plot) Designs. J Syst Sci Complex 36, 2082–2099 (2023). https://doi.org/10.1007/s11424-023-2023-1

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  • DOI: https://doi.org/10.1007/s11424-023-2023-1

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