A Shock Model Based Approach to Network Reliability

TL;DR

This paper introduces a new t-signature model for analyzing network reliability under shock-induced failures, deriving explicit reliability formulas and exploring aging properties with practical examples.

Contribution

It presents a novel t-signature concept for shock models and provides explicit reliability formulas under non-homogeneous Poisson shock processes.

Findings

Explicit reliability formulas derived for shock models

Network lifetime exhibits specific aging properties

Examples illustrate practical applications of the model

Abstract

We consider a network consisting of $n$ components (links or nodes) and assume that the network has two states, up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each shock may lead to the component failures. Under some assumptions on the shock occurrences, we present a new variant of the notion of signature which we call it t-signature. Then t-signature based mixture representations for the reliability function of the network are obtained. Several stochastic properties of the network lifetime are investigated. In particular, under the assumption that the number of failures at each shock follows a binomial distribution and the process of shocks is non-homogeneous Poisson process, explicit form of the network reliability is derived and its aging properties are explored. Several examples are also provided