Exact reliability formula for consecutive-k-out-of-n:F systems with homogeneous Markov dependence

A direct, exact method for computing the reliability for a consecutive-k-out-of-n:F system with homogeneous Markov dependence is presented. This method calculates the reliability for a consecutive-k-out-n:F system where the probability that any component i fails depends upon, and only upon, the state of the component (i-1).>