Computing the Signature of a Generalized k-Out-of-n System

Abstract

A generalized k-out-of-n system which is denoted by ((n(1), ... , n(N)), f, k) consists N of modules ordered in a line or a circle, and the ith module is composed of n(i) components in parallel. (n(i) >= 1, i = 1, ... , N). The system fails iff there exist at least failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n(1) = ... = n(N) = n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components.