The Mrl function of the K-out-of-N system with nonidentical components in the system level

Abstract

A k-out-of-n system is working if at least k of its n components are operating. The system breaks down at the time of the (n-k+1) th component failure. Since all components start working at the same time, this approach leads to a kind of redundancy called active redundancy of n-k components. Important particular cases of k-out-of-n system are parallel and series systems corresponding to k=1 and k=n, respectively. In this paper, we consider the mean residual life (MRL) function of a parallel and k-out-of-n systems consisting of n components having independent and nonidentically distributed lifetimes. We provide new representations of the MRL function for such systems. The MRL functions of systems consisting of components having exponential and power distributed lifetimes are presented. Also we introduce a numerical example to study the effect of increasing the system level and various parameters on the mean residual life of the systems. Further, the relation between the mean residual life for the system and the mean residual life of its components is investigated.