All Times ET
Keywords: Computer experiments, Bush construction type II method, Galois fields, Latin hypercube designs,Orthogonal array
Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among techniques used in the development of computer experiments but also helpful whenever interest is on designing some traditional experiments. Design construction for computer experiments has become a novel area especially in Nigeria and Africa at large since it is more about experimental planning rather than modelling aspect in which some progress has been documented. The Bush Construction Type II method was used in this study 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 experiments. The OALHD was used in this research as a Latin hypercube design constructed based on orthogonal arrays in order to achieve better space-filling properties that would otherwise not be accomplished by a random Latin hypercube design (LHD). Orthogonal Array (N, m) LHD were constructed at parameter values of OA (N, m) = (216, 8) and (343, 9). This study is an improvement on the early paper that employed Bush Construction Type I method to achieve an OALHD of the strength of two 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 (216, 8) LHD and OA (343, 9) LHD constructed possessed better space-filling properties and they achieve uniformity in each dimension of the designed variables. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a traditional or a computer experiment on real life situations and can be used to improve the study design in biomedical research. A program was written using MATLAB 2016 computer package to implement the construction of OALHDs in this study.