Sliced space-filling designs with different levels of two-dimensional uniformity

• A new class of sliced space-filling designs are proposed in which the whole design and each slice may have different levels of two-dimensional uniformity for different factors.
• The program for generating these new sliced designs is proposed to randomize a special type of asymmetric orthogonal arrays, called asymmetric balanced sliced orthogonal arrays.
• Several methods are developed to construct such asymmetric balanced sliced orthogonal arrays.
• Simulation study shows that the proposed designs perform well compared with other sliced designs for computer experiments.

We consider sliced computer experiments where priori knowledge suggests that factors may have different levels of importance, and so some factors need to be paid more attention than others. A new class of sliced space-filling designs are proposed to deal with this type of sliced computer experiments, in which the whole design and each slice may have different levels of two-dimensional uniformity for different factors, besides they all achieve maximum stratification in univariate margins. They are generated by elaborately randomizing a special type of asymmetric orthogonal arrays, called asymmetric balanced sliced orthogonal arrays, which can be partitioned into several slices such that each slice is balanced and becomes an asymmetric orthogonal array after some level-collapsing. Several methods are developed to construct such asymmetric balanced sliced orthogonal arrays. Simulation study shows that the proposed designs perform well compared with other sliced designs for computer experiments.