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Balanced arrays of strength 2l and balanced fractional 2m factorial designs

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Summary

A connection between a balanced fractional 2m factorial design of resolutionV and a balanced array of strength 4 with index set {μ 0,μ 0,μ 1,μ 2,μ 3,μ 4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2m factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ 0,μ 1,μ 2, ⋯,μ 21} provided the information matrixM is nonsingular.

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References

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Authors and Affiliations

  1. Maritime Safety Academy, Hiroshima University, Hiroshima, Japan

    Sumiyasu Yamamoto, Teruhiro Shirakura & Masahide Kuwada

Authors
  1. Sumiyasu Yamamoto
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  2. Teruhiro Shirakura
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  3. Masahide Kuwada
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Yamamoto, S., Shirakura, T. & Kuwada, M. Balanced arrays of strength 2l and balanced fractional 2m factorial designs. Ann Inst Stat Math 27, 143–157 (1975). https://doi.org/10.1007/BF02504632

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  • DOI: https://doi.org/10.1007/BF02504632

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