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In systems of parallel components, the system reliability function Rp(t) is usually defined as the probability that not all the parallel components fail in a time interval t, given that all the components are operating at the beginning of the interval. This definition implies that if there is one component which operates throughout the whole interval in question, then the system reliability is perfect. Consider the system S which always requires M > 1 components to do its job. It is obvious that the system is not reliable if there are only k, 1 Â¿ k < M, components working in the time interval t. The conventional reliability function Rp(t) is then insufficient for studying the reliability of the system S. A generalized reliability function Rr,n(t) is presented in this paper, and it is shown that the conventional reliability function Rp(t) is a special case of the generalized reliability function Rr,n(t). The practical application of this generalized reliability function is also discussed.