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A new foldover strategy and optimal foldover plans for three-level design

Author

Listed:
  • Zujun Ou

    (Jishou University)

  • Hongyi Li

    (Jishou University)

Abstract

The foldover is a useful technique in construction of factorial designs. It is also a standard follow-up strategy discussed in many textbooks by adding a second fraction called a foldover design. In this paper uniformity criterion measured by the wrap-around $$L_2$$ L 2 -discrepancy is used to further distinguish the optimal foldover plan for three-level designs. For three-level fractional factorials as the original designs, a new foldover strategy is provided based on level permutation of each factor, which vastly enlarge the full foldover space. Some theoretical properties of the defined foldover plans are obtained, a tighter lower bound of the wrap-around $$L_2$$ L 2 -discrepancy of combined designs is also provided, which can be used as a benchmark for searching optimal foldover plans. For illustration of our theoretical results and comparison with the existing results, a catalog of optimal foldover plans of the new strategy for uniform initial designs with s three-level factors is tabulated, where $$2\le s \le 11$$ 2 ≤ s ≤ 11 .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01194-0
    DOI: 10.1007/s00362-020-01194-0
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    References listed on IDEAS

    as
    1. Zujun Ou & Hong Qin, 2019. "Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy," Statistical Papers, Springer, vol. 60(5), pages 1699-1716, October.
    2. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2005. "Choice of optimal initial designs in sequential experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 127-135, April.
    3. 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.
    4. Zujun Ou & Hong Qin & Kashinath Chatterjee, 2017. "Some new lower bounds to various discrepancies on combined designs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3244-3254, April.
    5. Ai, Mingyao & Hickernell, Fred J. & Lin, Dennis K.J., 2008. "Optimal foldover plans for regular s-level fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 896-903, May.
    6. Zujun Ou & Kashinath Chatterjee & Hong Qin, 2011. "Lower bounds of various discrepancies on combined designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 109-119, July.
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