Construction of second-order orthogonal sliced Latin hypercube designs

Sliced Latin hypercube designs are useful for computer experiments with qualitative and quantitative factors, model calibration, cross validation, multi-level function estimation, stochastic optimization and data pooling. Orthogonality and second-order orthogonality are crucial in identifying important inputs. Besides orthogonality, good space-filling properties are also necessary for Latin hypercube designs. In this paper, a construction method for second-order orthogonal sliced Latin hypercube designs is proposed. The constructed designs are further optimized to achieve better space-filling properties. Furthermore, the method is extended to construct nearly orthogonal sliced Latin hypercube designs. The numbers of slices and columns as well as the levels of the resulting designs are more flexible than those obtained by existing methods.