An O(nr/sup k/) algorithm for computing the reliability of consecutive k-out-of-r-from-n:F system

A consecutive k-out-of-r-from-n:F system consists of n linearly or circularly ordered components such that the system fails if and only if there are r consecutive components at least k of which are failed. This paper studies a lower bound for the reliability of a consecutive k-out-of-r-from-n:F system in the more general case when the component probabilities can be different from each other. New recursive equations are proposed, which have time complexity of O(nr/sup k/) for the linear system, and O(nr/sup 2k/) for the circular system.