Construction of mixed-level designs with minimum discrete discrepancy

Liuping Hu, Kashinath Chatterjee, Jianhui Ning and Hong Qin

Statistics & Probability Letters, 2025, vol. 219, issue C

Abstract: Mixed-level designs are widely applicable in various practical fields. In this paper, we introduce new methods for constructing mixed-level designs with minimum discrete discrepancy. Utilizing the minimum discrete discrepancy aberration criterion, we establish a valuable analytical connection between the initial design and the resultant design, demonstrating that a high-quality initial design ensures the quality of the resultant design. Additionally, we derive general lower bounds for the discrete discrepancy, which serve as benchmarks for assessing the uniformity of mixed-level designs. Examples are provided to illustrate the effectiveness of our construction methods and the significance of the newly derived lower bounds.

Keywords: Mixed-level design; Moment aberration; Discrete discrepancy; Lower bound (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110358

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