Two-Level Orthogonal Screening Designs With 24, 28, 32, and 36 Runs

ABSTRACT

The potential of two-level orthogonal designs to fit models with main effects and two-factor interaction effects is commonly assessed through the correlation between contrast vectors involving these effects. We study the complete catalog of nonisomorphic orthogonal two-level 24-run designs involving 3–23 factors and we identify the best few designs in terms of these correlations. By modifying an existing enumeration algorithm, we identify the best few 28-run designs involving 3–14 factors and the best few 36-run designs in 3–18 factors as well. Based on a complete catalog of 7570 designs with 28 runs and 27 factors, we also seek good 28-run designs with more than 14 factors. Finally, starting from a unique 31-factor design in 32 runs that minimizes the maximum correlation among the contrast vectors for main effects and two-factor interactions, we obtain 32-run designs that have low values for this correlation. To demonstrate the added value of our work, we provide a detailed comparison of our designs to the alternatives available in the literature. Supplementary materials for this article are available online.

KEYWORDS:

• G-aberration
• G₂-aberration
• Hadamard matrix
• Orthogonal array
• Plackett–Burman design

Acknowledgments

We are grateful to Dursun Bulutoglu and Kenneth Ryan, who provided details on their results, and to two anonymous referees, whose comments stimulated us to widen the scope of the original submission and to enhance the consistency and clarity of the manuscript.

Funding

This research was financially supported by the Flemish Foundation for Scientific Research FWO.