Uniform sliced Latin hypercube designs

Sliced Latin hypercube designs (SLHDs) achieve maximum stratification in each dimension, but neither the full designs nor their slices can guarantee a good uniformity over the experimental region. Although the uniformity of the full SLHD and that of its slices are related, there is no one-to-one correspondence between them. In this paper, we propose a new uniformity measure for SLHDs by combining the two kinds of uniformity. Based on such a combined uniformity measure, the obtained uniform SLHDs have the design points evenly spread over the experimental region not only for the whole designs but also for their slices. Numerical simulation shows the effectiveness of the proposed uniform SLHDs for computer experiments with both quantitative and qualitative factors.