A new look on optimal foldover plans in terms of uniformity criteria

ABSTRACT

In this paper, we develop a new mechanism for finding the optimal foldover plans (OFPs) which is based on the uniformity criteria measured by Lee discrepancy, wrap-around L₂-discrepancy, and centered L₂-discrepancy. For three-level fractional factorials as the original designs, general foldover plans and combined designs are defined, and lower bounds of these three discrepancies of combined designs under general foldover plans are also obtained, which can be used as benchmarks for searching OFPs. Illustrative examples with a comparison study between the foldover plans under these discrepancies are provided. Our results provide a theoretical justification for OFPs of three-level designs in terms of uniformity criteria.

KEYWORDS:

• Combined design
• Complementary foldover plan
• Discrepancy
• Foldover design
• Foldover plan
• Lower bound
• Uniformity criterion

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K05
• 62K15

Acknowledgments

The authors greatly appreciate helpful suggestions of the referees and the editor that greatly improved the article.

Funding

This work was partially supported by the National Natural Science Foundation of China (No. 11271147, 11471135, 11471136), the UIC Grant (No. R201409), the Zhuhai Premier Discipline Grant.