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Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion

Summary: The authors propose a candidate-list-free exchange algorithm that facilitates construction of exact, model-robust, two-level experimental designs. In particular, they investigate two model spaces previously considered in the literature. The first assumes that all main effects and an unknown subset of two-factor interactions are active, but that the experimenter knows the number of active interactions. The second assumes that an unknown subset of the main effects, and all associated two-factor interactions, are active. Previous literature uses two criteria for design construction: first, maximize the number of estimable models; then, differentiate between designs equivalent in estimability by choosing the design with the highest average D-efficiency. The present article proposes a similar strategy that (1) does not impose orthogonality or factor level balance constraints, resulting in generally equal or larger numbers of estimable models, and 2) uses a flexible secondary criterion that maximizes the minimum D-efficiency. The article provides results for many situation of interest, as well as online supplementary material that includes algorithmic details, designs, and MATLAB code.

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  • Topics: Design of Experiments
  • Keywords: D-optimality, Design of experiments (DOE), Optimal design, Robust design, Algorithm
  • Author: Smucker, Bryan J.; del Castillo, Enrique; Rosenberger, James L.;
  • Journal: Technometrics