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Effective lower bounds of wrap-around L2-discrepancy on three-level combined designs

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Abstract

How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions. This paper takes the wrap-around L2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    A. M. Elsawah, Jianwei Hu & Hong Qin

  2. Division of Science and Technology, BNU-HKBU United International College, Zhuhai, 519085, China

    A. M. Elsawah

  3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    A. M. Elsawah

Authors
  1. A. M. Elsawah
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  2. Jianwei Hu
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  3. Hong Qin
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Corresponding author

Correspondence to A. M. Elsawah.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11271147, 11471135, 11471136, the UIC Grant R201409, the Zhuhai Premier Discipline Grant, and the Self-Determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE under Grant Nos. CCNU14A05041, CCNU16A02012.

This paper was recommended for publication by Editor TANG Niansheng.

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Elsawah, A.M., Hu, J. & Qin, H. Effective lower bounds of wrap-around L2-discrepancy on three-level combined designs. J Syst Sci Complex 30, 1459–1469 (2017). https://doi.org/10.1007/s11424-017-6036-5

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  • DOI: https://doi.org/10.1007/s11424-017-6036-5

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