Fasheng Sun

TL;DR: In this paper, the authors propose a method for constructing orthogonal Latin hypercube designs in which all the linear terms are orthogonality not only to each other, but also to the quadratic terms.

TL;DR: In this article, the authors constructed orthogonal LHDs with more flexible run sizes which also have the property that the sum of elementwise product of any three columns is 0.

TL;DR: In this paper, the authors provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing E(f NOD )- and χ 2 -optimal mixed-level SSDs without fully aliasing columns, via equidistant designs and difference matrices.

Abstract: Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-filling properties in terms of distance, uniformity and orthogonality. We show that the new criterion is a function of the pairwise $L_{1}$-distances between the rows, so that the new criterion can be computed at no more cost than a design criterion that ignores projection properties. We develop some theoretical results and show that maximin $L_{1}$-equidistant designs are uniform projection designs. In addition, a class of asymptotically optimal uniform projection designs based on good lattice point sets are constructed. We further illustrate an application of uniform projection designs via a multidrug combination experiment.

TL;DR: In this article, column-orthogonal and nearly column orthogonal designs for computer experiments were constructed by rotating groups of factors of Orthogonal arrays, which supplement the Latin hypercube design in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels.