The methods for representing the REE performance characteristics have been considered on the basis of the hyper-random phenomena theory. Mathematical hyper-random models of energy processes in REE were obtained on the basis of the Lagrange equations of the second kind. The forms of representing hyper-random quantities and functions were proposed, and expressions for hyper-random differential equations of the main processes in REE, including electromagnetic, electric, mechanical, and thermal processes, as well as expressions for the reliability indices were obtained. The principle was substantiated according to which any performance (and design) index of REE obtained as a result of designing would represent a set of values lying within the limits determined in accordance with the characteristics of hyper-random functions © 2010 Allerton Press, Inc.