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Fractional factorial designs are widely used for designing screeningexperiments. Nonregular fractional factorial designs can have better propertiesthan regular designs, but their construction is challenging. Current researchon the construction of nonregular designs focuses on two-level designs. Weprovide a novel class of multilevel nonregular designs by permuting levels ofregular designs. We develop a theory illustrating how levels can be permutedwithout computer search and accordingly propose a sequential method forconstructing nonregular designs. Compared to regular designs, these nonregulardesigns can provide more accurate estimations on factorial effects and moreefficient screening for experiments with quantitative factors. We furtherexplore the space-filling property of the obtained designs and demonstratetheir superiority.

A Class of Multilevel Nonregular Designs for Studying Quantitative Factors