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Optimal additions to and deletions from two‐level orthogonal arrays

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  • Neil A. Butler
  • Victorino M. Ramos

Abstract

Summary. Consider the problem of selecting a two‐level factorial design. It is well known that two‐level orthogonal arrays of strength 4 or more with e extra runs have various optimality properties including generalized Cheng (type 1) optimality when e=1, restricted Cheng (type 1) optimality when e=2 and E‐optimality when 3e5. More general Schur optimality results are derived for more general values of e within the more restricted class of augmented two‐level orthogonal arrays. Similar results are derived for the class of orthogonal arrays with deletions. Examples are used to illustrate the results and in many cases the designs are confirmed to be optimal across all two‐level designs.

Suggested Citation

  • Neil A. Butler & Victorino M. Ramos, 2007. "Optimal additions to and deletions from two‐level orthogonal arrays," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 51-61, February.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:1:p:51-61
    DOI: 10.1111/j.1467-9868.2007.00576.x
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    Cited by:

    1. Butler, Neil A., 2008. "Schur- and E-optimal two-level factorial designs," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 518-527, April.
    2. Roberto Fontana & Fabio Rapallo & Henry P. Wynn, 2022. "Circuits for robust designs," Statistical Papers, Springer, vol. 63(5), pages 1537-1560, October.
    3. Fontana, Roberto & Rapallo, Fabio & Wynn, Henry P., 2022. "Circuits for robust designs," LSE Research Online Documents on Economics 113631, London School of Economics and Political Science, LSE Library.
    4. Roberto Fontana & Fabio Rapallo, 2019. "On the aberrations of mixed level orthogonal arrays with removed runs," Statistical Papers, Springer, vol. 60(2), pages 479-493, April.

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