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

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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 \(L_2\)-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 \(L_2\)-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 \(2\le s \le 11\).

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Acknowledgements

The authors greatly appreciate helpful suggestions of Editor-in-Chief and the referees. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11961027, 11701213, 11561025), Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4497), Scientific Research Plan Item of Hunan Provincial Department of Education (Grant Nos. 18A284, 19A403).

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  1. College of Mathematics and Statistics, Jishou University, Jishou, 416000, China

    Zujun Ou & Hongyi Li

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  1. Zujun Ou
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  2. Hongyi Li
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Correspondence to Hongyi Li.

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Ou, Z., Li, H. A new foldover strategy and optimal foldover plans for three-level design. Stat Papers 62, 2433–2451 (2021). https://doi.org/10.1007/s00362-020-01194-0

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