Reliability models play an important role in the determination of the required generation reserves of a given electric power utility company and of its expected operating cost. Specifically, these models are used to compute the risk of system load loss and the capacity utilization ratios of different units comprising the system. Computation of these indexes usually requires the evaluation of the distribution function of the sum of a large number of discrete random variables with different distributions. Exact methods for computing these distributions prove computationally unfeasible for routine utility operations. This article compares the accuracy of several analytical approximations for computing the required performance indexes. These approximations are (a) the method of cumulants, (b) a distribution fitting procedure, and (c) a large deviation procedure due to Esscher. Application of these procedures to computing the indexes for several representative utility systems shows that Esscher's large deviati...