Consecutive K-Out-of-N Failure Systems: Reliability, Availability, Component Importance, and Multistate Extensions

Abstract

Coherent systems which fail if and only if at least k consecutive components fail are studied, when the components are independent and identically distributed. An expression for the reliability of such systems is derived by examining the waiting time for a run of a certain length using Markov chain techniques. Approximations for systems with large numbers of components are obtained, and measures of component importance are studied. Extensions are made to availability and multistate models.