The goal of this research is a theoretical and practical study of split-plot designs in industrial applications. While split-plot designs maintain many of the fundamental features of industrial experimental design such as effect sparsity, effect hierarchy and effect heredity, the more complicated randomization structure impacts both the design and the analysis of the experiment. Regular and non-regular fractional factorial split-plot designs are studied. In both cases, the fundamental problems considered are (i) defining optimality criteria for split-plot designs in industrial applications; (ii) constructing optimal split-plot designs; and (iii) analysis of split-plot designs. Novel approaches for constructing optimal regular and non-regular fractional factorial split-plot designs will be proposed. To analyze non-regular fractional factorial split-plot designs, new Bayesian variable selection procedures are entertained. Lastly, the connection between split-plot designs and other designs (i.e., compound orthogonal arrays and robust parameter designs) will be addressed.
The design and analysis of experiments have been successfully used in efforts to improve products and processes. They have made important contributions to scientific discovery and innovation and will continue to do so for the foreseeable future. Most recent advancements relate to experiments where the trials are performed as completely randomized designs. However, many industrial processes take place in multiple. This experiment structure induces correlation between observations and a "split-plot" design results. The aim of the proposed research is a theoretical and practical study of the design and analysis of fractional factorial split-plot experiments in industrial applications. The proposed work will develop new techniques for constructing and analyzing such experiments. The potential gains realized by performing an experiment as a split-plot design include more efficient and cost effective designs and increased power to detect some significant effects of interest.
