Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

ABSTRACT

Two-level orthogonal arrays of strength 3 permit the study of the main effects and the two-factor interactions of the experimental factors. These arrays are classified into regular and nonregular designs. Good regular designs are available in the literature for large run sizes that are a power of 2. In contrast, good nonregular designs, which have run sizes that are multiples of 8 and are more flexible alternatives to regular designs, are not available for large numbers of runs because their construction is challenging. In this article, we introduce a collection of strength-3 nonregular designs with large run sizes that, to the best of our knowledge, have not been explored before in the design literature. Using theoretical results and algorithmic approaches, we construct nonregular designs with up to 1280 runs. Our designs fill the gaps between the available strength-3 designs with large run sizes and outperform many comparably sized benchmark designs in terms of the aliasing among the two-factor interactions. We show the applicability of our collection of strength-3 designs using an infrared sensor experiment. Supplementary materials for this article are available online.

Keywords:

• Generalized minimum aberration
• Generalized resolution
• Linear permutation
• Orthogonal array
• Two-factor interaction
• Variable neighborhood search

Supplementary Materials

• Supplementary sections.pdf: Proofs; issues with permuting other sets of factors and with 2^{m − p} designs with m − p not a prime number; details of regular designs used; contributions of our theorems and algorithm to construct nonregular designs; tables of two-level strength-3 designs; and, sets of factors for sign switching in the parent designs.

• Programs.zip: Matlab implementation of the VNS algorithm.

Acknowledgments

The authors thank Peter Goos, Eric Schoen, and three referees for their comments that help to improve the presentation of the article. The authors also thank Sidonie Lefebvre for sharing details about the infrared sensor experiment. The research was done while the first author was visiting the Department of Statistics at the University of California, Los Angeles.

Additional information

Funding

Vazquez was financially supported by the Flemish Fund for Scientific Research FWO and Xu was supported by NSF Grant DMS-1407560.