Network Reliability Modeling Under Stochastic Process of Component Failures
The concept of D-spectrum is a useful tool to investigate the reliability and stochastic properties of networks. In this paper, we consider a network consisting of components (links or nodes), and assume that the network has two states: up, and down. We study the D-spectrum-based reliability of the network under the assumption that the components are subject to failure according to a counting process. Mixture representation of the reliability of the network lifetime is given in terms of the reliability functions of arrival times. It is shown that, when the D-spectra of two networks are stochastically ordered, then under some conditions the lifetimes of two networks are also stochastically ordered. Under the special case when the process of the failure of the components is a nonhomogeneous Poisson process, we arrive at a mixture representation for the reliability function of the network lifetime, and explore several stochastic and aging properties of the network lifetime under different scenarios. The failure rate of the network lifetime and its asymptotic behavior is investigated. D-spectrum based representation theorems are also given on the basis of the stochastic precedence concept.
d-spectrum stochastic ordering nonhomogeneous poisson process stochastic precedence increasing failure rate record values system signature two-state networks