Response surface methodology for split-plot designs with categorical factors
Split-plot designs often arise in agriculture and industrial experimentation when some factors are harder to vary than others, leading to randomization restrictions. This has an effect on both the run order and analysis of the experiment. Response surface methodology (RSM) split-plot designs for experiments with quantitative factors have received a lot of coverage in the literature. These designs are not appropriate, however, if categorical factors are also present. Draper and John (1988) and Wu and Ding (1998) explore techniques for adding categorical factors to non-split-plot RSM designs. Building on their initial idea of adding the categorical factor sequentially after taking an initial base design in the quantitative factors, this thesis explores how to add a two-level categorical factor in the split-plot RSM setting. Due to the randomization restrictions, adding a categorical factor in the split-plot setting requires considerably more care, in order to meet basic feasibility requirements and to maintain the structure. We explore four techniques for adding categorical factors and present results on requirements for the feasibility of proposed assignments of the categorical factor. We find that not all methods are appropriate for every base design. Throughout the thesis, we expand upon an example of an RSM split-plot experiment in quantitative factors for a ceramic pipe experiment from Vining and Kowalski (2008), by introducing a hypothetical additional categorical factor at either the whole-plot (hard-to-vary) or split-plot (easy-to-vary) level. We discuss optimal strategies for assigning a factor, conduct some initial exploration of the different response surfaces after perturbations to the data using contour plots, and suggest further avenues for analysis. The thesis culminates in tables of D-optimal designs for the various assignment methods based on an algorithm and computer code written for the various assignment methods.
Statistics, Split-plot, RSM, Categorical factors, Experimental Design