In recent years, the study of reliability properties of consecutive k-out-of-n systems has
attracted a great deal of attention from both theoretical and practical perspectives. In this
paper we consider linear and circular consecutive k-out-of-n systems. It is assumed that
lifetimes of components of the systems are independent but their probability distributions are
non-identical. We study the reliability properties of the residual lifetimes of such systems
under the condition that at least (n− r+ 1), r≤ n, components of the system are operating. We …