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Multi-level and mixed-level k-circulant supersaturated designs

Author

Listed:
  • K. Chatterjee

    (Visva Bharati University)

  • K. Drosou

    (National Technical University of Athens)

  • S. D. Georgiou

    (RMIT University)

  • C. Koukouvinos

    (National Technical University of Athens)

Abstract

Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the $$E(f_{NOD})$$ E ( f NOD ) -optimality measure of SSDs with general run sizes. This bound is a generalization of existing bounds since it is applicable to both balanced and unbalanced designs. Optimal multi and mixed-level, balanced and nearly balanced SSDs are constructed by applying a k-circulant type methodology. Necessary and sufficient conditions are introduced for the generator vectors, in order to pre-ensure the optimality of the constructed k-circulant SSDs. The provided lower bounds were used to measure the efficiency of the generated designs. The presented methodology leads to a number of new families of improved SSDs, providing tools for directly constructing optimal or nearly-optimal k-circulant designs by just checking the corresponding generator vector.

Suggested Citation

  • K. Chatterjee & K. Drosou & S. D. Georgiou & C. Koukouvinos, 2018. "Multi-level and mixed-level k-circulant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 337-355, April.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:3:d:10.1007_s00184-018-0645-4
    DOI: 10.1007/s00184-018-0645-4
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    References listed on IDEAS

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    1. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 33-53, January.
    2. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    3. Bradley Jones & Dibyen Majumdar, 2014. "Optimal Supersaturated Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1592-1600, December.
    4. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2359-2366, November.
    5. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
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