Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements

The paper presents an approximation algorithm for evaluating cdf of time-to-failure for k-out-of-n systems with shared spare elements. The working and spare elements can have different arbitrary distributions of time-to-failure. Different spare elements can be in different standby modes: cold, hot and warm. The algorithm is based on a universal generating function approach. It is shown that for small k the algorithm outperforms simulation.