Abstract: Computer experiments with both qualitative and quantitative input variables occur frequently in many scientific and engineering applications. As a result, how to choose the input settings for such experiments is important for accurate statistical analysis, uncertainty quantification, and decision-making. Sliced Latin hypercube designs were the first systematic approach to address this issue. However, the cost of such designs increases with an increasing number of level combinations of the qualitative factors. To reduce the cost of the run size, marginally coupled designs have been proposed, in which the design for the quantitative factors is a sliced Latin hypercube design with respect to each qualitative factor. The draw- back of such designs is that the corresponding data may not be able to capture the effects between any two (or more) qualitative and quantitative factors. To balance the run size and design efficiency, we propose a new type of design, namely doubly coupled designs. Here the design points for the quantitative factors form a sliced Latin hypercube design with respect to the level of any qualitative factor, and with respect to the level combinations of any two qualitative factors. The proposed designs have a better stratification property between the qualitative and quantitative factors compared with that of marginally coupled designs. Here, we establish the existence of the proposed designs, introduce several construction methods, and examine the properties of the resulting designs.

Key words and phrases: Completely resolvable orthogonal array, sliced Latin hypercube, stratification.