An Expository Paper on Optimal Design

ABSTRACT

There are many situations in which the requirements of a standard experimental design do not fit the research requirements of the problem. Three such situations occur when the problem requires unusual resource restrictions, when there are constraints on the design region, and when a nonstandard model is expected to be required to adequately explain the response. This article provides an introduction to optimal design for these types of situations. Optimal designs are computer-generated experiments that are aimed at satisfying specific research problem requirements. We show that the optimal design approach is applicable to any design problem and necessary when there are situations involving resource constraints or nonstandard design regions or models. The mathematical formulations of several design optimality criteria are presented along with examples of optimal design applications.

KEYWORDS:

• A-optimality
• constrained region of experimentation
• D-optimality
• design of experiments
• factorial experiments
• G-optimality
• I-optimality
• response surfaces

Additional information

Notes on contributors

Rachel T. Johnson

Dr. Rachel T. Johnson is an Assistant Professor in the Operations Research Department at the Naval Postgraduate School. She received her B.S. in industrial engineering from Northwestern University and her M.S. and Ph.D. from Arizona State University. Her research and teaching interests are in statistics and operations research with focus in design of experiments. She is a recipient of the Mary G. and Joseph Natrella Scholarship for “leadership, outstanding scholarship and commitment to the pursuit of quality improvement through statistical methods.”

Douglas C. Montgomery

Dr. Douglas C. Montgomery is Regents' Professor of industrial engineering and statistics and Foundation Professor of Engineering at Arizona State University. His research and teaching interests are in industrial statistics. Professor Montgomery is a Fellow of the ASA, a Fellow of the ASQ, a Fellow of the RSS, a Fellow of IIE, a member of the ISI, an academician of the IAQ and has received several teaching and research awards.

Bradley A. Jones

Dr. Bradley A. Jones is the Principal Research Fellow at SAS Institute and a guest professor at the University of Antwerp. He is the inventor of the prediction profile plot, an interactive graph for exploring multidimensional response surfaces. At SAS Institute he is responsible for the design of experiments capabilities in the JMP software package. He is a Fellow of the American Statistical Association and a winner of both the Nelson Award and the Brumbaugh Award.