Chenlu Shi

Supersaturated Designs for Screening Experiments and Strong Orthogonal Arrays for Computer Experiments

This dissertation centers on supersaturated designs and strong orthogonal arrays, which provide useful plans for screening experiments and computer experiments, respectively.

Supersaturated designs are a good choice for screening experiments. In order to use such designs, a common assumption that all interactions are negligible is made. In this dissertation, this assumption is dropped for the use of supersaturated designs. We propose and study a new class of supersaturated designs, namely foldover supersaturated designs, which allow the active main effects to be identified without making the assumption that two-factor interactions are absent. The E(s2)-optimal foldover supersaturated designs are constructed, and further optimization is also considered for these E(s2)-optimal supersaturated designs.

Strong orthogonal arrays were recently introduced and studied as a class of space-filling designs for computer experiments. This dissertation tackles two important problems that so far have not been addressed in the literature. The first problem is how to develop concrete constructions for strong orthogonal arrays of strength 3. We provide a systematic and comprehensive study on the construction of these arrays, with the aim at better space-filling properties. Besides various characterizing results, three families of arrays of strength 3 are presented. The other important problem is that of design selection for strong orthogonal arrays. We conduct a systematic investigation into this problem with the focus on strong orthogonal arrays of strength 2+ and 2. We first select arrays of strength 2+ by examining their 3-dimensional projections, and then formulate a general framework for the selection of arrays of strength 2 by looking at their 2-dimensional projections. Both theoretical and computational results for arrays are presented.

Keywords: Foldover design; Hadamard matrix; Latin hypercube; regular design; second order saturated design; space-filling design