UCLA

Maximin distance designs as an important class of space-filling designs are widely used in computer experiments, yet their constructions are challenging. In this thesis, we develop an efficient procedure to generate maximin Latin hypercube designs, as well as maximin multi-level fractional factorial designs, from existing orthogonal or nearly orthogonal arrays via level permutation and expansion. We show that the distance distributions of the generated designs are closely connected with the distance distributions and generalized word-length patterns of the initial designs. Examples are presented to show that our method outperforms many current prevailing methods. In addition, based on number theory and finite fields, we propose three algebraic methods to construct maximin distance Latin squares, as special Latin hypercube designs. We develop lower bounds on their minimum distances. The resulting Latin squares and related Latin hypercube designs have larger minimum distances than existing ones, and are especially appealing for high-dimensional applications. We show an application of space-filling designs in a combinatorial drug experiment on lung cancer. We compare four types of designs: a 512-run 8-level full factorial design, 80-run random sub-designs, 27-run random sub-designs and a 27-run space-filling three-level sub-design under four types of models: Kriging models, neural networks, linear models and Hill-based nonlinear models. We find that it is the best to adopt space-filling designs fitting Kriging models.