Reliability of linear and circular consecutively-connected systems

J.G. Shanthikumar (IEEE Trans. Reliability, vol.R-36, p.546-50, Dec. 1987) proposed a new system structure called the consecutively connected system, which is a generalization of the well-studied consecutive-k-out-of-n:F system. An O(n ²) algorithm was developed for its reliability evaluation. This work studies the structure of the consecutively connected system and provides more efficient algorithms for its reliability evaluation. The complexities of the algorithms are of order O(kn) for linear systems and O(k³n) for circular systems (k <n). The concepts of transmitting capability and receiving capability are introduced