Construction of Orthogonal Designs and Baseline Designs.
In this thesis, we study the construction of designs for computer experiments and also for screening experiments.
We consider the existence and construction of orthogonal designs, which are a useful class of designs for computer experiments. We first establish a non-existence result on orthogonal designs, generalizing an early result on orthogonal Latin hypercubes, and then present some construction results. By computer search, we obtain a collection of orthogonal designs with small run sizes. Using these results and existing methods in the literature, we create a comprehensive catalogue of orthogonal designs for up to 100 runs.
In the rest of the thesis, we study designs for screening experiments. We propose two classes of compromise designs for estimation of main effects using two-level fractional factorial designs under baseline parameterization. Previous work in the area indicates that orthogonal arrays are more efficient than one-factor-at-a-time designs whereas the latter are better than the former in terms of minimizing the bias due to non-negligible interactions.
Using efficiency criteria, we examine a class of compromise designs, which are obtained by adding runs to one-factor-at-a-time designs. A theoretical result is established for the case of adding one run. For adding two or more runs, we develop a complete search algorithm for finding optimal compromise designs. We also investigate another class of compromise designs, which are constructed from orthogonal arrays by changing some ones to zeros in design matrices. We then use a method of complete search for small run sizes to obtain optimal compromise designs. When the complete search is not feasible, we propose an efficient, though incomplete, search algorithm.
Keywords: Computer Experiment; Design Catalogue; Efficiency Criterion; Latin Hypercube; Minimum Aberration; One-factor-at-a-time Design; Orthogonal Array; Rotation Method; Search Algorithm.