Reliability of consecutive-k-out-of-n:F systems with nonidentical component reliabilities

A system with n components in sequence is a consecutive-k-out-of-n:F system if it fails whenever k consecutive components are failed. Under the supposition that component failures need not be independent and that component failure probabilities need not be equal, a topological formula is presented for the exact system reliability of linear and circular consecutive-k-out-of-n:F networks. The number of terms in the reliability formula is O(n/sup 4/) in the linear case and O(n/sup 5/) in the circular case.>