Reliability of consecutive k-out-of- r-from-n:F system with unequal component probability

摘要

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 k 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 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 explict solution of such general system, which requires O(nr~r) computing tune for linear system and O(nr~(2r)) computing time for circular system.