Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments

Abstract

Latin hypercubes have been frequently used in conducting computer experiments. In this paper, a class of orthogonal Latin hypercubes that preserves orthogonality among columns is proposed. Applying an orthogonal Latin hypercube design to a computer experiment benefits the data analysis in two ways. First, it retains the orthogonality of traditional experimental designs. The estimates of linear effects of all factors are uncorrelated not only with each other, but also with the estimates of all quadratic effects and bilinear interactions. Second, it can facilitate nonparametric fitting procedures, because one can select good space-filling designs within the class of orthogonal Latin hypercubes according to selection criteria.