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A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

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  • Zujun Ou
  • Hong Qin
  • Xu Cai

Abstract

The objective of this article is to study the issue of employing the uniformity criterion measured by wrap-around L2-discrepancy to assess the optimal foldover plans. For mixed two- and three-level fractional factorials as the original designs, general foldover plan and combined design under a foldover plan are defined, and the equivalence between any foldover plan and its complementary foldover plan is investigated. A lower bound of wrap-around L2-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Suggested Citation

  • Zujun Ou & Hong Qin & Xu Cai, 2014. "A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2274-2285, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2274-2285
    DOI: 10.1080/03610926.2013.776082
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    Cited by:

    1. Zujun Ou & Hongyi Li, 2021. "A new foldover strategy and optimal foldover plans for three-level design," Statistical Papers, Springer, vol. 62(5), pages 2433-2451, October.
    2. Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.

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