The objectives of this proposal are to develop new design theories and methodology for factor screening and response surface exploration and to construct efficient factorial and composite designs for practical use. The first part of this proposal studies fractional factorial designs constructed via quaternary codes. These designs often have a complex aliasing structure and a novel approach is introduced for finding defining relations among factors. A general theory is developed for obtaining important design properties such as resolution and wordlength pattern. Novel methods and algorithms are proposed for constructing optimal designs. These designs are shown to have better statistical properties than existing ones in the literature in terms of aberration, resolution and projectivity. The second part studies orthogonal array-based composite designs that consist of a two-level factorial design and a three-level orthogonal array. These composite designs have many desirable features and are effective for factor screening and response surface modeling. They can be used in a single experiment or in a sequential experiment. Efficient composite designs are constructed for practical use and they are shown to be better than central composite designs and other existing designs. This proposal employs a combination of mathematical, coding-theoretical and computational tools to tackle various important issues such as design properties and construction methods.

Experimental design and analysis is an effective and commonly used tool in scientific investigations and industrial applications. Factorial designs are cost-efficient experimental plans for identifying important factors from a pool of variables; response surface designs are crucial for understanding a process or system and building empirical models. Such designs have been successfully used in industrial manufacturing for improving quality and productivity. Recent novel applications include biomedical experiments conducted at UCLA in order to find effective antiviral drug combinations or drug cocktails for treating herpes simplex virus and vesicular stomatitis virus. This proposal aims at developing novel methodology for constructing new efficient factorial and response surface designs. The results of the proposed research can be quickly assimilated into undergraduate and graduate courses on design and analysis of experiments for course enrichment. The proposed methods and designs can be applied in a wide variety of fields of application, including engineering, physical and chemical sciences, medicine and life sciences. The proposed research can lead to better practice in experimentation and help shorten investigation time and reduce experimental cost tremendously.

Project Report

The project developed new design theories and methodology for factor screening and response surface exploration, as well as constructed efficient factorial and composite designs for practical use. A generalized resolution was proposed for choosing orthogonal arrays with qualitative factors. Designs with high resolution were constructed from quaternary codes. Based on level permutation, a general theory and new construction methods were developed for uniform and space-filling fractional factorial designs, as well as for screening quantitative factors. It was shown that generalized minimum aberration designs have good space-filling properties on average in terms of both distance and many uniformity measures. A new class of composite designs was proposed and studied for factor screening and response surface exploration. New efficient factorial and composite designs were constructed and they were successfully applied to drug combination experiments to treat herpes simplex virus type 1. A Hill-based global response surface model was applied to model a 512-run drug combination experiment with three chemicals on lung cancer cells. The results have been presented in major professional conferences and published in top tier statistical and interdisciplinary journals such as Annals of Statistics, Biometrika, JASA, Statistics in Medicine and others. A book chapter, to appear in "Handbook of Design and Analysis of Experiments" in 2015, summarized major developments in nonregular factorial designs and supersaturated designs. Five graduate students and three undergraduate students were supervised by the principal investigator to conduct research. One student obtained her PhD degree and two students obtained their MS degrees.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Gabor J. Szekely
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University of California Los Angeles
Los Angeles
United States
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