| Fractional factorial designs are commonly used in industrial experiments to identify factors affecting a process. However, it is often impractical to perform the experimental runs of a fractional factorial in a completely random order. In these cases, restrictions on the randomization of the experimental trials are imposed and the design is said to have a split-plot structure. This thesis aims to study both theoretical and applied characteristics of fractional factorial split-plot designs.;For fractional factorial designs, the "goodness" of the design is typically judged by the aberration criterion. Similarly, we rank the fractional factorial split-plot designs using the aberration criterion to find the minimum aberration design. We introduce a new algorithm that constructs the set of all non-isomorphic two-level fractional factorial split-plot designs more efficiently than existing methods. The algorithm is then used to construct a catalog of non-isomorphic 8, 16 and some 32 run fractional factorial split-plot designs ranked by the aberration criterion. We also show how the algorithm can be easily modified to efficiently produce sets of all non-isomorphic fractional factorial designs, where the number of levels is a power of a prime and fractional factorial split-plot designs where the number of levels is a power of a prime.;Next, we take a more theoretical look at fractional factorial split-plot designs. Although the design matrices correspond to fractional factorial design matrices, the randomization structure of the fractional factorial split-plot design is different. We discuss the impact of randomization restrictions on the choice of designs and develop theoretical results. Some of these results are closely related to those available for fractional factorials, while others are more specific to fractional factorial split-plot designs and are more useful in practice. We pay particular attention to the minimum aberration criterion and develop results that allow optimal fractional factorial split-plot designs with many factors to be identified from optimal designs with relatively few factors.;Lastly, the split-plot nature of the design implies that not all factorial effects can be estimated with the same precision. We show how the ability to detect significant effects can influence design selection, particularly when there is more than one non-isomorphic minimum aberration design. We also demonstrate how the split-plot structure simultaneously affects estimation, precision and the use of resources. These issues are discussed using a real industrial experiment from the Statistical Consulting Service at Simon Fraser University. |
