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.

abstract: During the initial stages of experimentation, there are usually a large number of factors to be investigated. Fractional factorial (2^(k-p)) designs are particularly useful during this initial phase of experimental work. These experiments often referred to as screening experiments help reduce the large number of factors to a smaller set. The 16 run regular fractional factorial designs for six, seven and eight factors are in common usage. These designs allow clear estimation of all main effects when the three-factor and higher order interactions are negligible, but all two-factor interactions are aliased with each other making estimation of these effects problematic without additional runs. Alternatively, certain nonregular designs called no-confounding (NC) designs by Jones and Montgomery (Jones & Montgomery, Alternatives to resolution IV screening designs in 16 runs, 2010) partially confound the main effects with the two-factor interactions but do not completely confound any two-factor interactions with each other. The NC designs are useful for independently estimating main effects and two-factor interactions without additional runs. While several methods have been suggested for the analysis of data from nonregular designs, stepwise regression is familiar to practitioners, available in commercial software, and is widely used in practice. Given that an NC design has been run, the performance of stepwise regression for model selection is unknown. In this dissertation I present a comprehensive simulation study evaluating stepwise regression for analyzing both regular fractional factorial and NC designs. Next, the projection properties of the six, seven and eight factor NC designs are studied. Studying the projection properties of these designs allows the development of analysis methods to analyze these designs. Lastly the designs and projection properties of 9 to 14 factor NC designs onto three and four factors are presented. Certain recommendations are made on analysis methods for these designs as well. / Dissertation/Thesis / Ph.D. Industrial Engineering 2012