Reliability and performance evaluation of weighted k-out-of-n:G system consisting of components with discrete lifetimes

Abstract

For the $k$-out-of-$n$ system consisting of components that have different weights, the system is in a good state if the total weight of working components is at least $k$. Such a system is known to be weighted $k$-out-of- $n$:G system. Although the weighted $k$-out-of-$n$ system that has continuously distributed components’ lifetimes has been extensively studied, the discrete weighted $k$-out-of-$n$:G system has not been considered yet. The present paper fills this gap by modeling and analyzing the weighted $k$ -out-of-$n$:G system that consists of discretely distributed components’ lifetimes. In particular, the behavior of the total capacity/weight of the system with respect to the component failures is evaluated. An optimization problem that is concerned with the determination of optimal number of spare components is also formulated by utilizing the mean lost capacity of the system.