Abstract: Despite the prevalence of space-filling designs in many applications, most of the existing approaches are unsuitable for irregular regions. A new sequential design procedure is introduced for a specific type of irregular region. This procedure constructs designs with desirable space-filling properties and without replacement of design points. Moreover, it provides flexibility on the size of the experiments. Efficient and easy-to-compute unbiased estimators are introduced. The various estimators are compared using a simulation and a data center thermal management example.

Key words and phrases: Adaptive cluster sampling, computer experiment, Latin hypercube design, Rao-Blackwell method, sequential design, space-filling design.