scholarly journals Network Reliability Modeling Based on a Geometric Counting Process

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 197 ◽  
Author(s):  
Somayeh Zarezadeh ◽  
Somayeh Ashrafi ◽  
Majid Asadi
Keyword(s):  
Network Lifetime ◽  
Counting Process ◽  
Network Reliability ◽  
Stochastic Order ◽  
Reliability Function ◽  
Residual Lifetime ◽  
Reliability Modeling ◽  
Arrival Times ◽  
Network States ◽  
Stochastic Properties

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.

scholarly journals Dynamic Reliability Modeling of Three-State Networks

2014 ◽  
Vol 51 (4) ◽  
pp. 999-1020 ◽  
Author(s):  
S. Ashrafi ◽  
M. Asadi
Keyword(s):  
Network Structure ◽  
Single Step ◽  
Two Dimensional ◽  
Reliability Modeling ◽  
Stochastic Orderings ◽  
Dynamic Reliability ◽  
Network States ◽  
Dynamic Signature ◽  
Stochastic Properties ◽  
Residual Lifetimes

This paper is an investigation into the reliability and stochastic properties of three-state networks. We consider a single-step network consisting of n links and we assume that the links are subject to failure. We assume that the network can be in three states, up (K = 2), partial performance (K = 1), and down (K = 0). Using the concept of the two-dimensional signature, we study the residual lifetimes of the networks under different scenarios on the states and the number of failed links of the network. In the process of doing so, we define variants of the concept of the dynamic signature in a bivariate setting. Then, we obtain signature based mixture representations of the reliability of the residual lifetimes of the network states under the condition that the network is in state K = 2 (or K = 1) and exactly k links in the network have failed. We prove preservation theorems showing that stochastic orderings and dependence between the elements of the dynamic signatures (which relies on the network structure) are preserved by the residual lifetimes of the states of the network (which relies on the network ageing). Various illustrative examples are also provided.

Dynamic Reliability Modeling of Three-State Networks

2014 ◽  
Vol 51 (04) ◽  
pp. 999-1020 ◽  
Author(s):  
S. Ashrafi ◽  
M. Asadi
Keyword(s):  
Network Structure ◽  
Single Step ◽  
Two Dimensional ◽  
Reliability Modeling ◽  
Stochastic Orderings ◽  
Dynamic Reliability ◽  
Network States ◽  
Dynamic Signature ◽  
Stochastic Properties ◽  
Residual Lifetimes

This paper is an investigation into the reliability and stochastic properties of three-state networks. We consider a single-step network consisting of n links and we assume that the links are subject to failure. We assume that the network can be in three states, up (K = 2), partial performance (K = 1), and down (K = 0). Using the concept of the two-dimensional signature, we study the residual lifetimes of the networks under different scenarios on the states and the number of failed links of the network. In the process of doing so, we define variants of the concept of the dynamic signature in a bivariate setting. Then, we obtain signature based mixture representations of the reliability of the residual lifetimes of the network states under the condition that the network is in state K = 2 (or K = 1) and exactly k links in the network have failed. We prove preservation theorems showing that stochastic orderings and dependence between the elements of the dynamic signatures (which relies on the network structure) are preserved by the residual lifetimes of the states of the network (which relies on the network ageing). Various illustrative examples are also provided.

Reliability modeling of coherent systems with shared components based on sequential order statistics

2018 ◽  
Vol 55 (3) ◽  
pp. 845-861
Author(s):  
S. Ashrafi ◽  
S. Zarezadeh ◽  
M. Asadi
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Failure Model ◽  
Coherent Systems ◽  
Sequential Order ◽  
Birth Process ◽  
Reliability Modeling ◽  
Joint Reliability ◽  
Sequential Order Statistics ◽  
Signature Matrix

Abstract In this paper we are concerned with the reliability properties of two coherent systems having shared components. We assume that the components of the systems are two overlapping subsets of a set of n components with lifetimes X1,...,Xn. Further, we assume that the components of the systems fail according to the model of sequential order statistics (which is equivalent, under some mild conditions, to the failure model corresponding to a nonhomogeneous pure-birth process). The joint reliability function of the system lifetimes is expressed as a mixture of the joint reliability functions of the sequential order statistics, where the mixing probabilities are the bivariate signature matrix associated to the structures of systems. We investigate some stochastic orderings and dependency properties of the system lifetimes. We also study conditions under which the joint reliability function of systems with shared components of order m can be equivalently written as the joint reliability function of systems of order n (n>m). In order to illustrate the results, we provide several examples.

Network Blueprint for Maximizing the Lifetime of Smart Devices in Low Power IoT Networks

2021 ◽  
Vol 13 (2) ◽  
pp. 21-38
Author(s):  
Sarwesh P. ◽  
K. Chandrasekaran ◽  
Thamizharasan S.
Keyword(s):  
Network Lifetime ◽  
Network Architecture ◽  
Data Transfer ◽  
Network Reliability ◽  
Smart Devices ◽  
Node Placement ◽  
The Standard Model ◽  
Device Lifetime ◽  
Placement Technique ◽  
Better Than

In the modern communication and computation era, internet of things (IoT) is developing as the key technology that satisfies the requirements of various applications. Prolonging device lifetime and maintaining network reliability is the evident objective for IoT network. Therefore, the authors come up with the network architecture that integrates node placement technique and routing technique. In the architecture, node placement is implemented by varying the density of nodes, by varying battery level of nodes, and by varying transmission range of nodes. Energy efficient and reliable path computation is addressed by routing technique. Therefore, enhancing the features of routing and node placement technique and integrating them together in network architecture can efficiently prolong the network lifetime. From the results, the authors observed that the proposed network architecture prolongs the network lifetime two times better than the standard model and also outperforms EQSR protocol and maintains the reliable data transfer.

A Note on the Mixture Representation of the Conditional Residual Lifetime of a Coherent System

2013 ◽  
Vol 50 (02) ◽  
pp. 475-485 ◽  
Author(s):  
Xiuying Feng ◽  
Shuhong Zhang ◽  
Xiaohu Li
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Reliability Function ◽  
Residual Lifetime ◽  
Coherent System ◽  
Distributed Components ◽  
Residual Lifetimes ◽  
Independent And Identically Distributed

This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

scholarly journals The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2181
Author(s):  
Zhouxia Guo ◽  
Jiandong Zhang ◽  
Rongfang Yan
Keyword(s):  
Reliability Function ◽  
Stochastic Orders ◽  
Residual Lifetime ◽  
Coherent System ◽  
Numerical Examples ◽  
Aging Properties ◽  
Theoretical Results

In this manuscript, we gain a mixture representation for reliability function of the residual lifetime of unfailed components in a coherent system under periodical inspections, given that the number of failed components before time t1 is r(≥0), but the system is still operating at time t1, and the system eventually failed at time t2(>t1). Some aging properties and stochastic orders of the residual lifetime on survival components are also established. Finally, some numerical examples and graphs are given in order to confirm the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document