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

A generalized k-out-of-n system which is denoted by ((n₁,..., n_N),f,k) consists of N 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 if there exist at least f failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n₁= ... = 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.