Reliability and component importance of a consecutive-k-out-of-n system

Abstract This paper explores the duality between the consecutive- k -out-of- n F and G systems, studies the Birnbaum reliability importance of the components in an i.i.d. system, and reviews the research in uniform treatment of the linear and circular consecutive- k -out-of- n :F systems. Upper and lower bounds for the reliability of a linear consecutive- k -out-of- n system are developed by constructing k -fold series and parallel redundant systems from the linear system.