Space-filling designs for multi-layer nested factors

Abstract This article considers computer experiments where levels for continuous factors are selected in sequential order with the level selected for one factor directly affecting the range of possible levels for the nested factor and, so on, for a finite number of factors. In addition, we assume that the nested relationships between the factors have no closed form solution. We propose an approach for constructing a multilayer nested factor design or multi-NFD for short. This space-filling design approach takes advantage of the maximin criterion and can be analyzed using a standard Gaussian process model. While the multi-NFD approach can be adapted for future computer experiments involving factor relationships of this type, we present results from a particular aerospace computer simulation study.