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D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions

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  • Boxin Tang
  • Julie Zhou

Abstract

Theoretical results are derived for finding D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions. The upper bounds of the determinant of the related matrix for D-optimality are obtained. For run sizes 12 and 20, D-optimal orthogonal arrays are found for all requirement sets with three or less two-factor interactions, and all the D-optimal orthogonal arrays except one can be constructed by sequentially collecting columns. Examples are also given for run sizes 36 and 52 to discuss the guidelines to construct D-optimal orthogonal arrays. Copyright Springer-Verlag 2013

Suggested Citation

  • Boxin Tang & Julie Zhou, 2013. "D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 325-337, April.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:3:p:325-337
    DOI: 10.1007/s00184-012-0389-5
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    References listed on IDEAS

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    1. Boxin Tang, 2006. "Orthogonal arrays robust to nonnegligible two-factor interactions," Biometrika, Biometrika Trust, vol. 93(1), pages 137-146, March.
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    Cited by:

    1. EENDEBAK, Pieter T. & SCHOEN, Eric D., 2015. "Two-level designs to estimate all main effects and two-factor interactions," Working Papers 2015019, University of Antwerp, Faculty of Business and Economics.
    2. Yue Yin & Julie Zhou, 2015. "Minimax design criterion for fractional factorial designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 673-685, August.

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