ACTIVE REDUNDANCY ALLOCATION FOR COHERENT SYSTEMS WITH INDEPENDENT AND HETEROGENEOUS COMPONENTS

2018 ◽  
Vol 34 (1) ◽  
pp. 72-91 ◽  
Author(s):  
Rui Fang ◽  
Xiaohu Li
Keyword(s):  
Sufficient Conditions ◽  
Coherent Systems ◽  
Minimal Path ◽  
Redundancy Allocation ◽  
Numerical Examples ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Minimal Path Sets ◽  
Theoretical Results

This paper studies the allocation of active redundancies to coherent systems on the context that the base and redundancy components have mutual independent lifetimes. For systems with two symmetric components and systems with one component's minimal cut sets (minimal path sets) covering those of another, we derive sufficient conditions to compare the resultant system lifetimes. Some numerical examples are also presented to illustrate the theoretical results.

On inactivity times of failed components of coherent system under double monitoring

2021 ◽  
pp. 1-18
Author(s):  
Zhouxia Guo ◽  
Jiandong Zhang ◽  
Rongfang Yan
Keyword(s):  
Sufficient Conditions ◽  
Reliability Function ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Behavior ◽  
Numerical Examples ◽  
Comparison Results ◽  
Aging Properties ◽  
Theoretical Results

Abstract This article discusses the stochastic behavior and reliability properties for the inactivity times of failed components in coherent systems under double monitoring. A mixture representation of reliability function is obtained for the inactivity times of failed components, and some stochastic comparison results are also established. Furthermore, some sufficient conditions are developed in terms of the aging properties of the inactivity times of failed components. Finally, some numerical examples are presented to illustrate the theoretical results.

scholarly journals Some new results on stochastic comparisons of coherent systems using signatures

2020 ◽  
Vol 57 (1) ◽  
pp. 156-173
Author(s):  
Ebrahim Amini-Seresht ◽  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Sufficient Conditions ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Numerical Examples ◽  
Distributed Components ◽  
Signature Vector ◽  
Theoretical Results ◽  
Independent And Identically Distributed

AbstractWe consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.

Two-terminal Reliability Analysis for Time-evolving and Predictable Delay-tolerant Networks

2020 ◽  
Vol 13 (2) ◽  
pp. 236-250
Author(s):  
Gaurav Khanna ◽  
Sanjay K. Chaturvedi ◽  
Sieteng Soh
Keyword(s):  
Network Reliability ◽  
Dynamic Networks ◽  
Dynamic Network ◽  
Delay Tolerant Networks ◽  
Minimal Path ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Terminal Reliability ◽  
Delay Tolerant ◽  
Minimal Path Sets

Background: Several techniques are available to evaluate the two-terminal reliability (2TR) of static networks; however, the advent of dynamic networks in recent past, e.g., Delay Tolerant Networks (DTNs), has made this task extremely challenging due to their peculiar characteristics with an associated disruptive operational environment. Recently, a Cartesian product-based method has been proposed to enumerate time-stamped-minimal path sets (TS-MPS)-a precursor to compute the 2TR of such networks. However, it cannot be used to generate time-stamped-minimal cut sets (TS-MCS). TS-MCS cannot only be used as an alternative to generate 2TR but also to compute other unexplored reliability metrics in DTNs, e.g., the weakest link. Objective: To propose a novel approach to enumerate both TS-MPS and TS-MCS of a dynamic network, thereby computing the 2TR of such networks. Methods: The proposed technique converts the time aggregated graph model of a dynamic network into a Line Graph (LG) while maintaining the time-varying graph’s node reachability information. This LG is used thereafter to generate TS-MCS as well as TS-MPS to compute 2TR of the network. Results: The DTN examples are presented to show the efficacy and salient features of our algorithm to obtain 2TR of such networks. Conclusion: The terminologies and techniques used for studying/analyzing network reliability of static networks can be extended to dynamic networks as well, e.g., the notion of minimal path sets to TS-MPS or minimal cut sets to TS-MCS, to assess their network reliability-a potential area of furthering network reliability research.

Stochastic comparisons of coherent systems under different random environments

2018 ◽  
Vol 55 (2) ◽  
pp. 459-472 ◽  
Author(s):  
Ebrahim Amini-Seresht ◽  
Yiying Zhang ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Random Environments ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Numerical Examples ◽  
Reversed Hazard Rate ◽  
Collaborative Environment ◽  
Theoretical Results

Abstract For many practical situations in reliability engineering, components in the system are usually dependent since they generally work in a collaborative environment. In this paper we build sufficient conditions for comparing two coherent systems under different random environments in the sense of the usual stochastic, hazard rate, reversed hazard rate, and likelihood ratio orders. Applications and numerical examples are provided to illustrate all the theoretical results established here.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

ON RELATIVE AGING COMPARISONS OF COHERENT SYSTEMS WITH IDENTICALLY DISTRIBUTED COMPONENTS

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Neeraj Misra
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Stochastic Orders ◽  
Coherent System ◽  
Coherent Systems ◽  
Cumulative Hazard ◽  
Numerical Examples ◽  
Distributed Components ◽  
Rate Functions ◽  
Important Notion

The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.

scholarly journals Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chunqing Wu ◽  
Shengming Fan ◽  
Patricia J. Y. Wong
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Studies ◽  
Patchy Environment ◽  
Predator Prey ◽  
Numerical Examples ◽  
Predator Prey Model ◽  
Prey Model ◽  
Dispersal Corridors ◽  
Predator Prey Models ◽  
Theoretical Results

We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey models. By comparing the two permanence criteria, we discuss the effects of dispersal corridors on the permanence of the predator-prey model. It is found that the dispersion of the prey from one patch to another is helpful to the permanence of the prey if the population growth of the prey is density dependent; however, this dispersion of the prey could be disadvantageous or advantageous to the permanence of the predator. Five numerical examples are presented to confirm the theoretical results obtained and to illustrate the effects of dispersal corridors on the permanence of the predator-prey model.

On transform orders for largest claim amounts

2021 ◽  
Vol 58 (4) ◽  
pp. 1064-1085
Author(s):  
Yiying Zhang
Keyword(s):  
Lower Bound ◽  
Sufficient Conditions ◽  
Claim Amount ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Numerical Examples ◽  
Comparison Results ◽  
Convex Transform Order ◽  
Star Order ◽  
Theoretical Results

AbstractThis paper investigates the ordering properties of largest claim amounts in heterogeneous insurance portfolios in the sense of some transform orders, including the convex transform order and the star order. It is shown that the largest claim amount from a set of independent and heterogeneous exponential claims is more skewed than that from a set of independent and homogeneous exponential claims in the sense of the convex transform order. As a result, a lower bound for the coefficient of variation of the largest claim amount is established without any restrictions on the parameters of the distributions of claim severities. Furthermore, sufficient conditions are presented to compare the skewness of the largest claim amounts from two sets of independent multiple-outlier scaled claims according to the star order. Some comparison results are also developed for the multiple-outlier proportional hazard rates claims. Numerical examples are presented to illustrate these theoretical results.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

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