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Space-Filling Fractional Factorial Designs

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  • Yong-Dao Zhou
  • Hongquan Xu

Abstract

Fractional factorial designs are widely used in various scientific investigations and industrial applications. Level permutation of factors could alter their geometrical structures and statistical properties. This article studies space-filling properties of fractional factorial designs under two commonly used space-filling measures, discrepancy and maximin distance. When all possible level permutations are considered, the average discrepancy is expressed as a linear combination of generalized word length pattern for fractional factorial designs with any number of levels and any discrepancy defined by a reproducing kernel. Generalized minimum aberration designs are shown to have good space-filling properties on average in terms of both discrepancy and distance. Several novel relationships between distance distribution and generalized word length pattern are derived. It is also shown that level permutations can improve space-filling properties for many existing saturated designs. A two-step construction procedure is proposed and three-, four-, and five-level space-filling fractional factorial designs are obtained. These new designs have better space-filling properties, such as larger distance and lower discrepancy, than existing ones, and are recommended for use in practice. Supplementary materials for this article are available online.

Suggested Citation

  • Yong-Dao Zhou & Hongquan Xu, 2014. "Space-Filling Fractional Factorial Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1134-1144, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1134-1144
    DOI: 10.1080/01621459.2013.873367
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    Cited by:

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    6. Kang Wang & Zujun Ou & Jiaqi Liu & Hongyi Li, 2021. "Uniformity pattern of q-level factorials under mixture discrepancy," Statistical Papers, Springer, vol. 62(4), pages 1777-1793, August.
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    9. A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.
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    11. Liuping Hu & Zujun Ou & Hongyi Li, 2020. "Construction of four-level and mixed-level designs with zero Lee discrepancy," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 129-139, January.
    12. A. M. Elsawah, 2021. "Multiple doubling: a simple effective construction technique for optimal two-level experimental designs," Statistical Papers, Springer, vol. 62(6), pages 2923-2967, December.
    13. Chen, Wen & Qi, Zong-Feng & Zhou, Yong-Dao, 2015. "Constructing uniform designs under mixture discrepancy," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 76-82.
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    15. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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