A minimum aberration-type criterion for selecting space-filling designs
受强正交数组的分层正交性启发，提出一种最小偏差型准则，基于设计在各种网格上的分层性质评估空间填充性，用于分类和排序空间填充设计，包括强正交数组和拉丁超立方设计。
Summary Space-filling designs are widely used in computer experiments. Inspired by the stratified orthogonality of strong orthogonal arrays, we propose a criterion of minimum aberration-type for assessing the space-filling properties of designs based on design stratification properties on various grids. A space-filling hierarchy principle is proposed as a basic assumption of the criterion. The new criterion provides a systematic way of classifying and ranking space-filling designs, including various types of strong orthogonal arrays and Latin hypercube designs. Theoretical results and examples are presented to show that strong orthogonal arrays of maximum strength are favourable under the proposed criterion. For strong orthogonal arrays of the same strength, the space-filling criterion can further rank them based on their space-filling patterns.