Constructing General Orthogonal Fractional Factorial Split-Plot Designs

Abstract

While the orthogonal design of split-plot fractional factorial experiments has received much attention already, there are still major voids in the literature. First, designs with one or more factors acting at more than two levels have not yet been considered. Second, published work on nonregular fractional factorial split-plot designs was either based only on Plackett–Burman designs, or on small nonregular designs with limited numbers of factors. In this article, we present a novel approach to designing general orthogonal fractional factorial split-plot designs. One key feature of our approach is that it can be used to construct two-level designs as well as designs involving one or more factors with more than two levels. Moreover, the approach can be used to create two-level designs that match or outperform alternative designs in the literature, and to create two-level designs that cannot be constructed using existing methodology. Our new approach involves the use of integer linear programming and mixed integer linear programming, and, for large design problems, it combines integer linear programming with variable neighborhood search. We demonstrate the usefulness of our approach by constructing two-level split-plot designs of 16–96 runs, an 81-run three-level split-plot design, and a 48-run mixed-level split-plot design. Supplementary materials for this article are available online.

• Integer linear programming
• Mixed-level design
• Multi-level design
• Orthogonal array
• Two-level design
• Variable neighborhood search.

ACKNOWLEDGMENTS

The research of the first and third author was supported by the Flemish Fund for Scientific Research FWO. The authors are grateful to Nha Vo-Thanh for the MATLAB codes he developed and for his help when preparing a revised version of this article, and to Pablo Andres Maya Duque for his help with CPLEX. The authors are also grateful to two referees, an associate editor, and the previous editor for their constructive suggestions.