A regular fractional factorial is uniquely determined by its defining relation and it has a simple aliasing structure in that any two effects are either orthogonal or fully aliased. When we have little or no knowledge as for what effects are potentially important, it is appropriate to select designs having minimum aberration. Minimum aberration designs enjoy some desirable model robust properties and therefore can be properly called model robust designs. Regular fractional factorials are well studied and results are abundant in the literature. The same cannot be said of nonregular fractional factorials. Nonregular fractional factorials are given by Plackett-Burman designs, Hadamard matrices, or more generally by orthogonal arrays. Both regular and nonregular designs permit orthogonal estimation of all the main effects. When some interactions are potentially important, the two classes of designs have rather different behaviors. This leads some researchers to study the projection properties of nonregular designs. Despite this important contribution, there has not been a systematic method for assessing and comparing nonregular designs. The broad objective of this project is to extend the theory and methods in regular designs to nonregular designs. This is facilitated by the introduction of J-characteristics, which generalizes the concept of defining relation. The whole project is conducted by focusing on the following research topics: (i) motivate and introduce generalized resolution and minimum aberration criteria, (ii) investigate the hidden projection properties of generalized minimum aberration in terms of estimability and efficiency of designs, (iii) develop a theory of J-characteristics and establish their connections with the projection properties, and (iv) develop, implement, and test efficient computational algorithms for constructing generalized minimum aberration designs.

In many areas of investigations, such as those of Federal Strategic Interest, efficient data collection is one of the key steps for the eventual success of a research project. Well planned experiments ensure relevant and informative data to be collected. Factorial designs provide cost-effective experimental plans that allow a large number of variables to be studied simultaneously and efficiently, and are therefore widely used in industrial experiments for improving the quality of manufactured products and the productivity of manufacturing processes. Factorial designs can be categorized into two classes: regular designs and nonregular designs. Regular designs are well studied and results are abundant in the literature. The same cannot be said of nonregular designs. Two reasons for the scarcity of results on nonregular designs are the lack of general theory and methods, and the associated computational difficulties in data analysis. The broad objective of this project is to develop general theory and methods for studying and constructing nonregular designs. This is achieved by introducing an instrumental concept, called J-characteristics, that is capable of capturing the properties of a design when projected onto lower dimensions. Developing and testing a user-friendly computer package is part of the proposed research. The theory and methods to be developed in the proposed research will shed new light on the study of factorial designs, lead to new economical designs for the experiments in the physical, chemical, and engineering sciences, and promote the application of factorial designs in the areas such as biotechnology and medical research that have huge potential to benefit further from the design methodology.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9971212
Program Officer
John Stufken
Project Start
Project End
Budget Start
1999-06-15
Budget End
2002-05-31
Support Year
Fiscal Year
1999
Total Cost
$97,417
Indirect Cost
Name
University of Memphis
Department
Type
DUNS #
City
Memphis
State
TN
Country
United States
Zip Code
38152