Strategies for sequential design of experiments and augmentation

The benefits of sequential design of experiments have long been described for both model-based and space-filling designs. However, in our experience, too few practitioners take advantage of the opportunity afforded by this approach to maximize the learning from their experimentation. By obtaining data sequentially, it is possible to learn from the early stages to inform subsequent data collection, minimize wasted resources, and provide answers for a series of objectives for the overall experiment. This paper provides methods and algorithms to create augmented distance-based space-filling designs, using both uniform and non-uniform space-filling strategies, that can be constructed at each stage based on information learned in earlier stages. We illustrate the methods with several examples that involve different initial data, types of space-filing designs and experimental goals.