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.

A growing trend in engineering and science is to use multiple computer codes with different levels of accuracy to study the same complex system. Strategies are needed to combine the simulation results obtained at different levels of accuracy to produce an efficient surrogate model for prediction. In this paper, we propose an integral model to borrow as much information as possible from the low-accuracy experiment.We ignore the Markov property assumed before and model the high-accuracy experiment based on an integral form of the low-accuracy experiment. The proposed model is more general thus better predictions are expected. Two explicit forms of some matrices and vectors used in our predictions are given. The effectiveness of the proposed model is illustrated with several examples.