Indicator Polynomial Functions and Their Applications in Two-Level Factorial Designs

Abstract

<p>In this thesis, we discuss some properties of indicator polynomial functions. We extend some existing results from regular designs to non-regular designs. More general results which were not obtained even for regular designs are also provided. First, we study indicator polynomial functions with one, two, or three words. Classification of indicator polynomial functions with three words are provided. Second, we consider the connections between resolutions of general two level factorial designs. As special cases of our results, we generalize the results of Draper and Lin [14]. Next, we discuss the indicator polynomial functions of partial fold over design, especially, semifoldover designs. Using the indicator polynomial functions, we examine various possible semifoldover designs. We show that the semifoldover resolution II I.x design obtained by reversing the signs of all the factors can de-alias at least the same number of the main factors as the semifoldover design obtained by reversing the signs of one or more, but not all, the main factors. We also prove that the semifoldover resolution III.x designs can de-alias the same number of two-factor interactions as the corresponding full foldover designs. More general results are also provided. Finally, we present our conclusions and outline possible future work.</p>