In industrial experimentation, time and material costs are often at a premium. In designing an experiment, one needs to balance the desire for sufficient experimental runs to provide adequate data analysis, with the need to conduct a cost-effective experiment. A common compromise is the use of fractional factorial (FF) designs, in which only a fraction of the total possible runs is utilized. After discussing the basic concepts of FF designs, we introduce the fractional factorial split-plot (FFSP) design. Such designs occur frequently, because certain factors are often harder to vary than others, thus imposing randomization restric- tions. This thesis examines two techniques aimed at reducing run size that have not been greatly explored in the FFSP setting — nonregular designs and semifoldover designs. We show that these designs offer competitive alternatives to the more standard regular and full foldover designs and we produce tables of optimal designs in both scenarios.

In industrial experimentation, time and material costs are often at a premium. In designing an experiment, one needs to balance the desire for sufficient experimental runs to provide adequate data analysis, with the need to conduct a cost-effective experiment. A common compromise is the use of fractional factorial (FF) designs, in which only a fraction of the total possible runs is utilized. After discussing the basic concepts of FF designs, we introduce the fractional factorial split-plot (FFSP) design. Such designs occur frequently, because certain factors are often harder to vary than others, thus imposing randomization restric- tions. This thesis examines two techniques aimed at reducing run size that have not been greatly explored in the FFSP setting — nonregular designs and semifoldover designs. We show that these designs offer competitive alternatives to the more standard regular and full foldover designs and we produce tables of optimal designs in both scenarios.

Sequential experimentation is often employed in process optimization wherein a series of small experiments are run successively in order to determine which experimental factor levels are likely to yield a desirable response. Although there currently exists a framework for identifying optimal follow-up designs after an initial experiment has been run, the accepted methods frequently point to multiple designs leaving the practitioner to choose one arbitrarily. In this thesis, we apply preposterior analysis and Bayesian model-averaging to develop a methodology for further discriminating between optimal follow-up designs while controlling for both parameter and model uncertainty.