Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments

Abstract

Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.