A system with n elements in sequence is called a consecutive-k-out-of-n:F system if it fails whenever k consecutive elements are failed. Consecutive-k-out-of-n:F systems can be used to model belt conveyor systems, telecommunication systems, oil pipeline systems, street lighting and others. This paper presents formulas and algorithms for the reliability of consecutive-k-out-of-n:F systems with identical and nonidentical elements.
