An O(n) algorithm to compute the reliability of consecutive k-out-of-r-fcom-n :F system under the condition of r < 2k

A consecutive k-out-of-r-from-n :F system consists of n ordered components such that the system fails if and only if there are r consecutive components at least of which are failed. Such systems arise in quality -control problems and inspection procedures as well as in radar detection. This paper studies the reliability of a linear consecutive k-out-of-r-from-n :F system in the general case when the component probabilities can be different from each other. New recursive equation is derived for explicit solution of such general system, which required O(n) computing time. The results of some computational experiments are also described.