Optimal Foldovers With Column Permutations for Non-Regular Designs
Foldover is a commonly used follow-up strategy in experimental designs. Optimal foldover designs have been developed to maximize the number of aliased pairs of interactions that can be de-aliased. All existing foldover designs were constructed by reversing the sign of columns of the original design. These researchers propose a new methodology by allowing the permutation of columns in foldover. They recently showed that most proposed designs are better than existing results with respect to the minimum aberration criterion. While augmenting a design by a foldover with column permutation may result in a nonregular combined design, this design is able to de-alias a larger number of aliased two-factor interactions. Furthermore, the researchers have demonstrated that they also have more desirable model-robustness properties against model uncertainty. In the current project, the researchers are expanding the existing results from regular designs to nonregular designs. In a regular design, each effect is either fully aliased with or orthogonal to another effect. Nonregular designs allow partial aliasing, and have seen more applications in the past decade.
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