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.
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.