Uniform row augmented designs with multi-level

Abstract

In many practical applications, follow-up experimental designs are commonly used to explore the relationship between inputs and outputs step by step. As some additional resources become available to the experimenter after the first step, some extra runs may be added in the follow-up stage. The issue of uniform row augmented designs with multi-level is investigated in this paper. The uniformity of row augmented designs with four- or five-level is respectively discussed under the Lee discrepancy, and the lower bounds of Lee discrepancy for row augmented designs are obtained, which can be served as the benchmark for searching uniform row augmented designs. Some numerical examples show that the uniform row augmented designs can be constructed with high efficiency.

Keywords:

• Multi-level design
• Lee discrepancy
• lower bound
• row augmented design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15
• 62K05
• 62K99

Acknowledgment

The authors thank the reviewers for their helpful comments, which have led to improvements in the paper.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11561025, 11701213, 11961027), Hunan Provincial Natural Science Foundation of China (Grant Nos. 2017JJ2218, 2017JJ3253), Scientific Research Plan Item of Hunan Provincial Department of Education (Grant Nos. 18A284, 19A403), Science and Innovation Plan Item of Xiangxi Autonomous Prefecture (Grant Nos. 2018SF5022, 2018SF5023).