Monte Carlo simulation of complex system mission reliability

A Monte Carlo methodology for the reliability simulation of highly redundant systems is presented. Two forms of importance sampling, forced transitions and failure biasing, allow large sets of continuous-time Markov equations to be simulated effectively and the results to be plotted as continuous functions of time. A modification of the sampling technique also allows the simulation of both nonhomogeneous Markov processes and of non-Markovian processes involving the replacement of worn parts. A number of benchmark problems are examined. For problems with large numbers of components, Monte Carlo is found to result in decreases in computing times by as much as a factor of 20 from the Runge-Kutta Markov solver employed in the NASA code HARP.