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This paper presents a method for calculating the reliability of a system depicted by a reliability block diagram, with identically distributed components, in the presence of common-cause failures. To represent common-cause failures, we use the Marshall & Olkin formulation of the multivariate exponential distribution. That is, the components are subject to failure by Poisson failure processes that govern simultaneous failure of a speciflc subset of the components. The method for calculating system relability requires that a procedure exist for determining system reliability from component reliabilities under the statistically-independent-component assumption. The paper includes several examples to illustrate the method and compares the reliability of a system with common-cause failures to a system with statistically-independent components. The examples clearly show that common-cause failure processes as modeled in this paper materially affect system reliability. However, inclusion of common-cause failure processes in the system analysis introduces the problem of estimating the rates of simultaneous failure for multiple components in addition to their individual failure rates.