Cyclic SOAs and Moving Window Criteria for Space-Filling Designs

Abstract

Space-filling designs are essential in computer experiments to ensure that design points are well distributed across the input space. Among them, strong orthogonal arrays (SOAs) are widely used for their stratification properties on fixed grids formed by collapsing adjacent factor levels. However, these grids lack flexibility and cannot adapt to local structures. To address this limitation, we introduce a moving window approach that evaluates uniformity over sliding regions across the space. By specifying a window size and selecting a subset of positions, we define a more fine-grained space-filling criterion that generalizes several existing methods. Within this framework, we further propose cyclic SOAs—SOAs that preserve their stratification properties under cyclic shifts of factor levels. These designs exhibit a structural invariance that is particularly useful in settings involving periodicity or level relabeling. We establish their optimality properties and present construction methods, positioning cyclic SOAs as a flexible and robust addition to the space-filling design toolkit.

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