Construction of orthogonal marginally coupled designs

Marginally coupled designs (MCDs) were first introduced by Deng et al. (Stat Sin 25:1567–1581, 2015), as more economical designs than sliced space-filling designs which are the popular choices for computer experiments with both qualitative and quantitative factors. In an MCD, the design for qualitative factors is an orthogonal array, and the one for quantitative factors is a Latin hypercube design (LHD) with its rows corresponding to each level of any qualitative factor also forming a small LHD. As we know, orthogonality is a popular and important property for evaluating LHDs, but was not considered in existing results on MCDs. In this paper, we propose some approaches to constructing a new class of MCDs with orthogonality. In some cases, the designs for quantitative factors also satisfy the two dimensional space-filling property. Besides, the run sizes of the obtained designs are more flexible than the existing ones.