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

Zujun Ou and Hongyi Li ()
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Zujun Ou: Jishou University
Hongyi Li: Jishou University

Statistical Papers, 2021, vol. 62, issue 5, No 17, 2433-2451

Abstract: 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 .

Keywords: Foldover plan; Level permutation; Lower bound; Three-level factorials; Wrap-around $$L_2$$ L 2 -discrepancy; 62K15; 62K99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01194-0

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