An Algorithm to Determine the Reliability of a Complex System

The method most often suggested for determining the reliability of a system is to construct a reliability network, enumerate from the network all mutually exclusive working states of the system, calculate the probability of occurrence of each working state, and sum these probabilities. For a complex system this is not a practical method for there is a very large number of working states. Esary and Proschan suggest a lower bound approximation to reliability that requires the enumeration of a much smaller set of system states. These states are called minimal cuts. An algorithm is presented to determine the set of minimal cuts and thus calculate a lower bound to system reliability. The algorithm is intended for digital-computer implementation and computational times are provided.