Reliability of linear (n, f, k) systems with weighted components

Abstract

The (n,f, k): F(G) system consists of n components and the system fails (works) if and only if there are at least f failed (working) components or at least k consecutive failed (working) components. These system models can be used in electronic equipment, automatic payment systems in banks, and furnace systems. In this paper we introduce and study the (n, f, k):F and (n, f, k): G systems consisting of weighted components. Recursive equations are presented for reliability evaluation of these new models. We also provide some conditions on the weights to represent weighted-(n,f, k) systems as usual (n, f, k) systems.