Level permutations and factor projections of multiple quadruple designs

Abstract

One of the motivating forces for the current surge of interest in non-regular fractional factorial designs (non-RFrFDs) is that they have partially aliased effects that can be estimated together. Thus, from some estimation perspectives, non-RFrFDs outperform their regular counterparts that have either fully aliased or orthogonal effects. Elsawah (Communications in Mathematics and Statistics 10:623-652, 2022) presented a novel class of four-level non-RFrFDs, called multiple quadruple designs (MQDs), that are attractive from the practical perspective due to their structural and analytical simplicities. Level permutations and factor projections are widely used techniques for improving the eligibility and estimation efficiency of non-RFrFDs that are desirable for factor screening. This paper investigates the potential benefits of level permutations and factor projections for improving the performance of the MQDs in the full-dimension and any low-dimension and constructing new non-isomorphic four-level non-RFrFDs. The results provide theoretical benchmarks and conditions for improving the efficiency of the MQDs and constructing non-isomorphic MQDs. The efficiency is investigated in view of the widely used optimality criteria and modeling performance. The main numerical results show that the generated designs provide good representative points for the experimental domains that help investigators to effectively design and model high-dimensional experiments without prior assumptions about the forms of their underlying models.

Mathematical Subject Classification:

• 62K05
• 62K15

Keywords:

• Aberration
• Distance distribution
• Level permutations
• Multiple quadruple design
• Orthogonality
• Power moment
• Projections
• Uniformity

Acknowledgments

The author thanks the referees, the Associate Editor, and the Editor-in-Chief for constructive comments that lead to significant improvements of this paper. Elsawah greatly appreciates the kind support of Prof. Kai-Tai Fang.

Disclosure statement

There is no conflict of interest.

Additional information

Funding

Elsawah’s work was supported by the UIC Research Grants with No. of (R201912 and R202010); the Curriculum Development and Teaching Enhancement with No. of (UICR0400046-21CTL); the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College with No. of (2022B1212010006); and the Guangdong Higher Education Upgrading Plan (2021–2025) with No. of (UIC R0400001-22).