Orthogonal designs with branching and nested factors

Abstract

Computer experiments with branching and nested factors are a common class of computer experiments, but it is challenging to construct designs for this type of experiments. In this paper, we define a special type of design called branching orthogonal Latin hypercube design (BOLHD). Such a design has an appealing structure, that is, no matter at each level of a branching factor or the level‐combination of branching factors, the corresponding design points of nested factors form an orthogonal Latin hypercube design (OLHD). This structure makes it a good choice for designing computer experiments with branching and nested factors. We propose several deterministic construction methods when branching factors have the same number of levels. Based on sliced Latin hypercube designs (SLHDs), the proposed methods are easy to operate. Some construction results are tabulated for practical use.