A closer look at de-aliasing effects using an efficient foldover technique

ABSTRACT

Foldover techniques are used to reduce the confounding when some important effects (usually lower order effects) cannot be estimated independently. This article develops an efficient foldover mechanism for symmetric or asymmetric designs, whether regular or nonregular. In this paper, we take the uniformity criteria (UC) as the optimality measures to construct the optimal combined designs (initial design plus its corresponding foldover design) which have better capability of estimating lower order effects. The relationship between any initial design and its combined design is studied. A comparison study between the combined designs via different UC is provided. Equivalence between any combined design and its complementary combined design is investigated, which is a very useful constraint that reduce the search space. Using our results as benchmarks, we can implement a powerful algorithm for constructing optimal combined designs. Our work covers as well as gives results better than recent works of about 20 articles in the last few years as special cases. So this article is a good reference for constructing effective designs.

KEYWORDS:

• Uniformity criteria
• foldover technique
• combined design
• complementary combined design
• optimal combined design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K05
• 62K15

Acknowledgments

The author greatly appreciate helpful suggestions of the two referees and the associate editor that significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the UIC Grant (R201409), the Zhuhai Premier Discipline Grant and the National Natural Science Foundation of China (Nos. 11271147, 11471135, 11471136).