Multistate consecutively-connected systems

G. Shanthikumar (ibid., vol.R-36, p.546-550, Dec. 1987) has proposed a system called the consecutively connected system, which is a generalization of the consecutive-k-out-of-n:F system. He gave an O(n²) algorithm for computing the reliability of the consecutively connected system. In the present work, the authors further generalize it by assuming that the components are multistate. They give an O(Kn) algorithm for computing the reliability of the multistate system where K(K<n) is the maximum number of states for a component. They discuss the difficulties of obtaining corresponding algorithms for circular systems and two-way communication, although for two-state components they are able to extend the Shanthikumar algorithm to circular systems