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.