Mathematical Sciences: Studies in Optimal and Efficient Design of Experiments

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This research is on the construction of factorial experimental designs which are robust against time trends and where errors are more generally correlated. The problems include (i) optimal and efficient block and row-column designs for comparing treatments when the observations are autocorrelated, (ii) optimal and efficient designs for estimating or predicting a response surface over a region for correlated errors and (iii) systematic methods of generating fractional factorial designs to meet specific experimental needs with as few runs as possible. This research is in a subfield of statistics called experimental design which involves the development of plans for allocating resources efficiently. This work will extend the current theory on experimental design to more appropriately accommodate experiments in which data is collected over a period of time, rather than all at the same time.