A fast recursive algorithm to compute the probability of M-out-of-N events

A simple recursive algorithm is presented to compute the exact probability of occurrence of M or more events out of a possible N events. The algorithm begins by recursively computing the probability of occurrence of exactly M events out of a possible N events. These intermediate results may be quickly summed to obtained the industry standard definition of M or more events out of a possible N events. Performance of the algorithm is on the order of N² in time and 2N in space. This algorithm does not use cut set methodology and consequently is not limited by the combinatorial explosion problem associated with cut set manipulation of the M-out-of-N gate. This algorithm is extremely useful when the exact probability of M-out-of-N is desired, especially in cases where N exceeds limitations of cut set manipulation techniques, and when the M-out-of-N event is statistically independent of other events in the system under consideration