Most procedures labeled "Empirical Bayes" that are in use at present are frequentist rather than Bayesian; although often the motivation for employing Empirical Bayes procedures is the conceptual or the computational difficulty of the analogous Bayes procedures. This research broadens the Empirical Bayes framework and then examines the comparative behaviors of the several methodologies with respect their performance and their feasibility. Theoretical results defining conditions of superiority for Empirical Bayes methods will be sought. Empirical results from simulations and theoretical results for properties of Empirical Bayes estimators will be applied to reliability theory. Statistical analyses draw on models or on prior information and expert opinion to set the framework for analyzing data. In certain circumstances the data itself can be used to determine the framework as well as be analyzed within the framework. Procedures of this type are called "Empirical Bayes;" and these can be viewed in some sense as a hybrid of model-based (frequentist) and prior information-based (Bayesian) procedures. This research will investigate the circumstances under which each class of procedures is significantly superior to the others for applications in reliability testing and estimation.
