Uniformity pattern of mixed two- and three-level factorials under average projection mixture discrepancy

Abstract

The issue of the projection uniformity of mixed two- and three-level factorials measured by mixture discrepancy is investigated in this paper. The average projection mixture discrepancy is defined to measure the uniformity for low-dimensions projection designs. Moreover, the relationship between uniformity pattern and generalized minimum aberration is established. Two numerical examples are provided to illustrate the theoretical results.

Keywords:

• Average projection mixture discrepancy
• generalized minimum aberration
• lower bound
• mixture discrepancy
• uniformity pattern

MSC:

• 62K15
• 62K05
• 62K99

Acknowledgements

The authors greatly appreciate helpful suggestions of Editor-in-Chief, Associate Editor and the referees.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant numbers 11961027, 11871237, 12161040, 11701213], the Natural Science Foundation of Hunan Provincial [grant numbers 2021JJ30550, 2020JJ4497], Scientific Research Plan Item of Hunan Provincial Department of Education [grant number 19A403]. Discipline Coordination Construction Project of Zhongnan University of Economics and Law [grant number XKHJ202125].