Sliced Latin hypercube designs via orthogonal arrays

• A special class of sliced Latin hypercube design is constructed via both symmetric and asymmetric orthogonal arrays.
• The resulting sliced Latin hypercube designs along with their slices all inherit the r-dimensional uniformity of the parent orthogonal arrays with strength r.
• The construction methods are easy to implement, and the resulting designs are very flexible in run sizes and numbers of factors.

Computer experiments are becoming increasingly popular in studying complex real world systems. A special class of sliced Latin hypercube design is proposed in this paper. Such designs are particularly suitable for computer experiments with both qualitative and quantitative factors, multi-fidelity computer experiments, cross-validation and data pooling. The resulting sliced Latin hypercube designs possess a desirable sliced structure and have an attractive low-dimensional uniformity. Meanwhile within each slice, it is also a Latin hypercube design with the same low-dimensional uniformity. The new sliced Latin hypercube designs can be constructed via both symmetric and asymmetric orthogonal arrays. The same desirable properties are possessed, although the uniformity may be differed. The construction methods are easy to implement, and unlike the existing methods, the resulting designs are very flexible in run sizes and numbers of factors. A detailed comparison with existing designs is made.