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The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-Optimal minimal designs have been considered for a variety of mixture models, including Scheffe's linear, quadratic, and cubic models. Usually, these D-Optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-Optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. In this dissertation, extensions of the D-Optimal minimal designs are developed to allow additional interior points in the design space to enable prediction of the entire response surface. First, the extensions of the D-Optimal minimal designs for two commonly used second-degree mixture models are considered. Second, the methodology for adding interior points to general mixture models is generalized. Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. When compared with the standard mixture designs, the proposed extended D-Optimal minimal design provides higher power for the Lack of Fit tests with comparable D-efficiency. / Statistics

The Al₂SiO₅ polymorphs have been examined to provide new insights into their chemical bonding, their crystal chemistry, their equations of state, and the incorporation of water in the form of hydroxyl in their structures. The Al₂SiO₅ polymorphs provide a unique structural assemblage for a crystal chemical examination due to the variation in Al coordination in the structures where Al is in 4-fold, 5-fold, and 6-fold in sillimanite, andalusite, and kyanite, respectively. Consequently, the Al₂SiO₅ polymorphs have been examined with a combination of experimental (high pressure X-ray diffraction and Polarized FTIR spectroscopy) and theoretical (VASP and Crystal 98) methods. An experimental high pressure X-ray diffraction study on andalusite and sillimanite has constrained their equation of state and the pressure derivatives of their bulk modulus with pressure. Additionally, the effect of pressure on the crystal structures has been examined, where the main structural response is compression of the AlO₆ octahedra. Comparatively, compression of the AlO₆ octahedra in andalusite is more anisotropic, while the major direction of axial compressibility in both structures is dependent on the orientation of the AlO6 octahedra. In order to better understand the crystal chemistry of the Al-O and Si-O bonds in the polymorphs, ELF isosurfaces were examined. ELF isosurfaces represent a graphical representation of the localized electron probability density. Six distinct types of ELF isosurfaces were observed in the Al₂SiO₅ polymorphs resulting from differences in the geometry, coordination, and coordinated cation atomic number surrounding the oxygens within the crystal structures. The ELF was also shown to be isostructurally related to electron density difference maps. In a combined experimental and theoretical investigation of the Al₂SiO₅ polymorphs, potential protonation sites within the crystal structures were determined at an atomic level with polarized FTIR spectroscopy and analysis of (3,-3) critical points of the negative Laplacian. The polarized FTIR spectra indicate the orientation of the OH dipole in the three polymorphs and the (3,-3) critical points indicate regions of locally concentrated electron density. Potential protonation sites were determined based on the value of the negative Laplacian, the underbonded nature of the oxygens, and the number of surrounding cations. / Ph. D.

In virtually every buying decision, consumers must make tradeoffs among levels of product attributes. One of the most frequent kinds of tradeoffs is that between price and quality. This research investigates the effects of two controllable variables on price quality trade offs; the price/quality order in which alternatives are presented and whether alternatives outside the range of buyer expectations (outliers) are presented. The level of the final reference point is suggested to mediate order and outliers effects on the dependent variables of evaluation, search length, price-quality choice, and satisfaction. In addition, the effects of order and outliers on buyer-seller relationship quality are examined. A measurement problem precluded determination of final reference point as a mediating variable, but the other effects were as predicted by final reference points. Presenting alternatives in a descending order of price and quality resulted in less search than an ascending order. Primacy effects were evident as the descending order also resulted in choices of higher price and quality than both ascending and random orders. Moderate outliers also resulted in higher price-quality choices than either no outliers or extreme outliers, but only when presented in a descending order. There were no significant effects on evaluation of alternatives. Perceptions of buyer-seller relationship were better when alternatives were presented in an ascending order as compared to a descending order, but were not affected by presenting outliers. Buyer’s satisfaction was lower when an extreme outlier was included in choice set presented in an ascending order. / Ph. D.