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There are several instances where the classical method of triple-modular redundancy (TMR) reliability modeling may provide predictions which are inadequate. It is shown that for even simple networks such as those exhibiting fan-in and fan-out, classical methods may predict a reliability that is higher than or lower than the actual reliability. Furthermore, the classical method gives no hint as to whether the predicted number is high or low. As a solution to this problem, a method of partitioning an arbitrary network into cells such that faults in a cell are independent of faults in other cells is proposed. An algorithm is then given to calculate the reliability of any such cell, by considering only the structure of the interconnections within the cells. The value of the reliability found is exact if TMR is assumed to be a coherent system. An approximation to the algorithm is also described; this can be used to find a lower bound to the reliability without extensive calculation.