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.