Construction of Space-Filling Asymmetrical Marginally Coupled Designs

Marginally coupled designs (MCDs) are very suitable for computer experiments with both qualitative and quantitative factors. An MCD consisting of two subdesigns—one for the qualitative factors and the other for the quantitative factors—is said to be symmetrical or asymmetrical when the qualitative factor subdesign is equal-level or mixed-level, respectively. Although symmetrical MCDs have been studied extensively recently, investigations of asymmetrical MCDs are still relatively scarce. In this paper, based on space-filling symmetrical MCDs or space-filling Latin hypercube designs (LHDs), we propose four approaches to constructing a series of space-filling asymmetrical MCDs. The obtained asymmetrical MCDs can inherit the low-dimensional space-filling properties of these symmetrical MCDs or these LHDs. Moreover, the resulting asymmetrical MCDs are flexible in terms of their run sizes. A numerical study is conducted to compare and evaluate the performance of the proposed designs in computer experiments.