Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy

Zujun Ou and Hong Qin ()
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Zujun Ou: Jishou University
Hong Qin: Central China Normal University

Statistical Papers, 2019, vol. 60, issue 5, No 13, 1699-1716

Abstract: Abstract Literatures reveal that foldover is a useful technique in construction of factorial designs. The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around $$L_2$$ L 2 -discrepancy to assess the optimal foldover plans for asymmetric fractional factorials. A general foldover strategy and combined design under a foldover plan are developed for asymmetric fractional factorials, some theoretical properties on the equivalence between the defined foldover plan and its complementary foldover plan are discussed. A new lower bound for the wrap-around $$L_2$$ L 2 -discrepancy of combined designs 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.

Keywords: Asymmetric fractional factorial; Combined design; Foldover plan; Lower bound; Wrap-around $$L_2$$ L 2 -discrepancy; 62K15; 62K05; 62K99 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-017-0892-x

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