A Decision Theoretic Approach to the Design and Analysis of Industrial Experiments — An Application

Abstract

Many of the problems within the domain of classical statistics have been re-examined in recent years from the point of view of Bayesian decision theory. However, a particular area of classical statistics-the design and analysis of experiments-has not been treated in any depth from this viewpoint. The purpose of the paper is to bring decision theory to bear on this class of problems. Specifically, we shall extend previous studies of experimental design models from a Bayesian viewpoint, and focus on cost-effectiveness analysis. In such an analysis, we shall consider explicitly: (a) the probability measure of uncertainty, (b) the economic consequences associated with the decision problem, and (c) the cost and the potential value of the experiment to determine if such an experiment should be conducted to reduce the uncertainty. To demonstrate how this analysis can be used to design and analyze industrial experiments and to aid managers in making decisions, we shall present an actually observed industrial problem.