Construction of Asymmetric Nested Orthogonal Arrays

Nested orthogonal arrays (NOAs), which consist of a pair of orthogonal arrays with one array nested within the other, are extensively utilized in computer experiments and statistics. They have diverse applications, including data fusion, digital twins, model validation, sequential model evaluation, stochastic programming, chance-constraint problems, nonparametric function estimation, and parameter linking. We propose several general methods for constructing asymmetric NOAs with flexible run sizes, number of levels, and strengths. These methods can generate numerous new classes of NOAs, achieving the maximal number of factors with the minimal run size for both the smaller and larger arrays. A slightly relaxed definition of saturatedness, termed flawless, is introduced for NOAs. Based on the saturated or flawless criteria for the smaller and larger arrays, we classify NOAs into nine types and construct seven new types of NOAs. The newly constructed NOAs with small and moderate run sizes are tabulated for practical use. Supplementary materials for this article are available online.