Abstract
Fractional factorial designs are widely used because of their various merits. Foldover or level permutation are usually used to construct optimal fractional factorial designs. In this paper, a novel method via foldover and level permutation, called quadrupling, is proposed to construct uniform four-level designs with large run sizes. The relationship of uniformity between the initial design and the design obtained by quadrupling is investigated, and new lower bounds of wrap-around \(L_2\)-discrepancy for such designs are obtained. These results provide a theoretical basis for constructing uniform four-level designs with large run sizes by quadrupling successively. Furthermore, the analytic connection between the initial design and the design obtained by quadrupling is presented under generalized minimum aberration criterion.
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Acknowledgements
We thank two referees for constructive comments that lead to significant improvement of this paper. This work was partially supported by the National Natural Science Foundation of China (Nos. 11701213; 11961027; 11871237; 11561025), Research Funding Project for Talents Introduction of Jishou University, Natural Science Foundation of Hunan Province (Nos. 2017JJ2218; 2017JJ3253), Scientific Research Plan Item of Hunan Provincial Department of Education (No. 18A284) and Scientific Research Project of Xiangxi State (Nos. 2018SF5022; 2018SF5023).
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Li, H., Qin, H. Quadrupling: construction of uniform designs with large run sizes. Metrika 83, 527–544 (2020). https://doi.org/10.1007/s00184-019-00741-6
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DOI: https://doi.org/10.1007/s00184-019-00741-6
Keywords
- Level permutation
- Foldover
- Uniform design
- Quadruple design
- Generalized minimum aberration
- Wrap-around \(L_2\)-discrepancy
- Lower bound