Construction of Asymmetric Nested Orthogonal Arrays
提出了构造非对称嵌套正交阵列的通用方法，能灵活调整运行次数、水平数和强度，生成多种新类型阵列，并给出了小到中等运行规模的实用表格。
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.