Doctor of Philosophy, The Ohio State University, 2006, Statistics

The problems of combinatorial and geometric equivalence of symmetric factorial experiments, as well as characterization and ranking of two-level Split-plot and Split-lot designs are considered. Two fractional factorial symmetric designs with qualitative factors are said to be combinatorially equivalent if one can be obtained from the other by reordering the runs, relabeling the factors and relabeling factor levels. If the only permissible relabeling of factors levels is reversal of symbols, geometric equivalence is obtained. Existing criteria for detecting combinatorial and geometric equivalence or non-equivalence of symmetric factorial designs are described and evaluated via computer algorithms. Some new necessary and sufficient criteria for both types of equivalence are presented. All results generalize to designs with factors having different number of levels. A characterization method for two-level Split-plot and Split-lot designs based on nonregular fractional factorial designs is given. As an application, a new ranking method is proposed for general two-level Split-plot and Split-lot designs which suggests that existing ranking criteria overlook some aspects of the designs.

Committee: Angela Dean (Advisor) Subjects: Statistics

Doctor of Philosophy, The Ohio State University, 2003, Industrial and Systems Engineering

This dissertation re-examines some of the most basic design of experiment methods with respect to their ability to achieve intuitive objectives. For example, it provides probably the first comprehensive evaluation of the ability of standard screening approaches to correctly tell which factors have important effects on average outputs. Also, the dissertation examines the prediction errors that users of so-called mixture experimental design and qualitative response surface methods can achieve. In practical situations, the derived "decision support" information can tell the user in advance whether the number of runs used is adequate for the experimenter's needs and provide a basis for selecting one method over another when alternatives are presented. Also, the dissertation clarifies, perhaps for the first time, the potentially serious prediction error issues associated with the methods that have been proposed for response surface investigation when some factors are qualitative. In addition to developing comprehensive computational studies of existing methods, new methods are proposed with potentially important advantages. For example, the dissertation provides some of the first unbalanced screening experimental plans relevant to cases in which some combinations of settings have far higher costs than other combinations. For situations in which some factors are mixture components, e.g., %CO2, %Ar, %N, and other factors are process variables, the dissertation provides some of the first economically relevant experimental plans offering potentially substantial reductions in prediction errors. Also, the dissertation provides the first truly advisable experimental designs for many response surface cases in which some variables are qualitative. All new methods are derived from optimization formulations or "improvement systems design problems". In each case, the intent is to design the method using the objective or objectives that most directly describe the purpose of the impro (open full item for complete abstract)

Committee: Theodore Allen (Advisor) Subjects:

Doctor of Philosophy, The Ohio State University, 1983, Graduate School

Committee: Not Provided (Other) Subjects: Statistics