Abstract
We propose an approach for constructing a new class of space-filling designs, called asymmetric nested lattice samples. As a stepping stone to the proposed approach, we introduce two methods for generating asymmetric nested orthogonal arrays. We then present an elaborate randomization method to shuffle the levels of an asymmetric nested orthogonal array to produce a pair of asymmetric nested lattice samples. The constructed designs have a desirable nested structure, possess attractive space-filling properties, and allow different axes to be divided at different scales of fineness. For multifidelity computer experiments, sequential evaluations, and multistep functional fitting and linking parameters, the asymmetric feature is appealing for situations where some factors are believed to be more important or deserve more attention than others. The proposed designs are also useful in problems where different factors, by nature, require dividing their axes at different levels of fineness. © 2014 American Statistical Association and the American Society for Quality TECHNOMETRICS.