A lower bound of average mixture discrepancy for row augmented designs

Abstract

Follow-up experimental designs are frequently employed in a wide range of scientific studies and industries. Lower bounds of average mixture discrepancy for row augmented designs are determined in this paper utilizing the level permutation technique, which is also used to analyse the uniformity of row augmented designs with asymmetrical factorials. Between the row augmented designs and its initial designs or follow-up designs, quantitative relationships of lower bounds of average mixture discrepancy are constructed. Additionally, a proposal is made for the construction algorithm of asymmetrical uniform row augmented designs. Numerical examples indicate that the asymmetrical uniform row augmented designs can be constructed with high efficiency and recommended for use in practice.

Keywords:

• Asymmetrical follow-up design
• average mixture discrepancy
• level permutation
• lower bound
• row augmented design

2020 Mathematics Subject Classifications:

• 62K15
• 62K05
• 62K99

Acknowledgments

The authors would like to thank the editor, the associate editor, and two referees for their comments and suggestions, which helped to improve this paper. We would like to thank Hao Li and Cong Xiang from the College of Finance and Statistics of Hunan University for helpful comments and valuable advice.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant numbers 11961027, 12161040, 12361053], Provincial Natural Science Foundation of Hunan [grant numbers 2021JJ30550, 2023JJ20486), Scientific Research Plan Item of Hunan Provincial Department of Education [grant numbers 22A0355, 22B0613], Plan Item of Hunan Provincial Social Science Achievement Review Committee [grant number XSP2023JJC049].