Abstract
In this paper, we investigate the reliability and stochastic properties of an n-component network under the assumption that the components of the network fail according to a counting process called a geometric counting process (GCP). The paper has two parts. In the first part, we consider a two-state network (with states up and down) and we assume that its components are subjected to failure based on a GCP. Some mixture representations for the network reliability are obtained in terms of signature of the network and the reliability function of the arrival times of the GCP. Several aging and stochastic properties of the network are investigated. The reliabilities of two different networks subjected to the same or different GCPs are compared based on the stochastic order between their signature vectors. The residual lifetime of the network is also assessed where the components fail based on a GCP. The second part of the paper is concerned with three-state networks. We consider a network made up of n components which starts operating at time t = 0 . It is assumed that, at any time t > 0 , the network can be in one of three states up, partial performance or down. The components of the network are subjected to failure on the basis of a GCP, which leads to change of network states. Under these scenarios, we obtain several stochastic and dependency characteristics of the network lifetime. Some illustrative examples and plots are also provided throughout the article.
Highlights
In recent years, there has been a great growth in the use of networks, such as communication networks and computer networks, in human life
We studied the reliability, aging and stochastic characteristics of an n-component network whose components were subjected to failure according to a geometric counting process (GCP)
Some mixture representations of the network reliability were obtained in terms of signature of the network and the reliability functions of the arrival times of the GCP
Summary
There has been a great growth in the use of networks (systems), such as communication networks and computer networks, in human life. The aim of the present paper is to assess the network reliability under the condition that the failure of the components appear according to a recently proposed stochastic process called geometric counting process (GCP). The reliabilities of the lifetimes of the different networks, subjected to the same or different GCPs, are compared based on the stochastic order between the associated signature vectors. We again assume that the components of the network are subjected to failure on the basis of GCP, which results in the change of network states. Under these conditions, we obtain several stochastic and dependency characteristics of the networks based on the two-dimensional signature.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
