scholarly journals A Simple Repairable System with Warning Device

2015 ◽  
Vol 2015 ◽  
pp. 1-18
Author(s):  
Xiao Zhang ◽  
Lina Guo
Keyword(s):  
Continuous Semigroup ◽  
Semigroup Theory ◽  
Good Condition ◽  
Markov Renewal Process ◽  
Repairable System ◽  
Analysis Method ◽  
Numerical Examples ◽  
Reliability Indices ◽  
Unique Existence ◽  
Warning Device

This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory orC0semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper.

scholarly journals Stability Analysis of a Repairable System with Warning Device and Repairman Vacation

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Yangli Ren ◽  
Lina Guo ◽  
Lingling Zhang
Keyword(s):  
Existence And Uniqueness ◽  
Continuous Semigroup ◽  
Semigroup Theory ◽  
System Dynamic ◽  
Markov Renewal Process ◽  
Repairable System ◽  
Analysis Method ◽  
Reliability Indices ◽  
Dynamic Solution ◽  
Warning Device

This paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and uniqueness as well as regularity of the system dynamic solution are discussed with the functional analysis method. Further, the asymptotic stability, especially the exponential stability of the system dynamic solution, is studied by using the strongly continuous semigroup theory orC0semigroup theory. The reliability indices and some applications (such as the comparisons of indices and profit of systems with and without warning device), as well as numerical examples, are presented at the end of the paper.

scholarly journals Reliability Analysis of 6-Component Star Markov Repairable System with Spatial Dependence

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Liying Wang ◽  
Qing Yang ◽  
Yuran Tian
Keyword(s):  
Spatial Dependence ◽  
Repairable System ◽  
Analysis Method ◽  
Repairable Systems ◽  
Rate Matrix ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Reliability Indices ◽  
Transition Rate Matrix ◽  
Markov Repairable System

Star repairable systems with spatial dependence consist of a center component and several peripheral components. The peripheral components are arranged around the center component, and the performance of each component depends on its spatial “neighbors.” Vector-Markov process is adapted to describe the performance of the system. The state space and transition rate matrix corresponding to the 6-component star Markov repairable system with spatial dependence are presented via probability analysis method. Several reliability indices, such as the availability, the probabilities of visiting the safety, the degradation, the alert, and the failed state sets, are obtained by Laplace transform method and a numerical example is provided to illustrate the results.

scholarly journals The Well-Posedness and Stability Analysis of a Computer Series System

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xing Qiao ◽  
Dan Ma ◽  
Fu Zheng ◽  
Guangtian Zhu
Keyword(s):  
Nonnegative Solution ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
System Model ◽  
Transient Solution ◽  
Reliability Indices ◽  
Unique Existence ◽  
System Operator ◽  
In Series ◽  
The Stability

A repairable computer system model which consists of hardware and software in series is established in this paper. This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view ofc0semigroup theory, we prove the existence of a unique nonnegative solution of the system. Then by analyzing the spectra distribution of the system operator, we deduce that the transient solution of the system strongly converges to the nonnegative steady-state solution which is the eigenvector corresponding to eigenvalue 0 of the system operator. Finally, some reliability indices of the system are provided at the end of the paper with a new method.

Analysis of R-out-of-N repairable systems: the case of phase-type distributions

2004 ◽  
Vol 36 (1) ◽  
pp. 116-138 ◽  
Author(s):  
Yonit Barron ◽  
Esther Frostig ◽  
Benny Levikson
Keyword(s):  
Repairable System ◽  
Repairable Systems ◽  
Regenerative Processes ◽  
Numerical Examples ◽  
Independent Components ◽  
Duality Results ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Two Systems ◽  
Repair Facility

An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R-1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

Reliability Analysis Method on Repairable System with Standby Structure Based on Goal Oriented Methodology

2015 ◽  
Vol 32 (7) ◽  
pp. 2505-2517 ◽  
Author(s):  
Xiao-jian Yi ◽  
B.S. Dhillon ◽  
Jian Shi ◽  
Hui-na Mu ◽  
Hai-ping Dong
Keyword(s):  
Reliability Analysis ◽  
Repairable System ◽  
Analysis Method

scholarly journals Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Fixed Point ◽  
Stationary Solution ◽  
Function Method ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Delayed Feedback ◽  
Competition Model ◽  
Numerical Examples ◽  
Unique Existence ◽  
Lyapunov Function Method

By partly generalizing the Lipschitz condition of existing results to the generalized Lipschitz one, the author utilizes a fixed point theorem, variational method and Lyapunov function method to derive the unique existence of globally asymptotical input-to-state stability of positive stationary solution for Gilpin-Ayala competition model with diffusion and delayed feedback under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of reaction-diffusion Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. And numerical examples illuminate the effectiveness and feasibility of the proposed methods.

The Selection of Power Supply Mode Based on Reliability's Social Costs

2013 ◽  
Vol 805-806 ◽  
pp. 772-778
Author(s):  
Rui Li ◽  
Yi Ming Hou ◽  
Hui Jun Yan ◽  
Shi Hong Miao ◽  
Hao Xu ◽  
...  
Keyword(s):  
Power Supply ◽  
Cost Benefit ◽  
Social Costs ◽  
Analysis Method ◽  
Full Account ◽  
Reliability Indices ◽  
Supply Mode ◽  
Power Supply Mode ◽  
Suitable Power ◽  
Selection Of

Selecting the power supply mode for important power consumers involves two aspects of reliability and economy. Combining with the power system reliability analysis method and taking full account of each component failure mode and their combination patterns, this paper embarks from the reality, accurately calculated the reliability indices of these power supply modes by minimal-cut sets, and then used the reliability indices to estimate the power losses of the users, finally used the theory of reliability cost-benefit and took the minimizing social costs that consist of reliability costs and outage losses as the goal to compare and analyze the reliability cost and the users outage losses under different power supply modes, obtained the suitable power supply mode for different important level of users.

Diffusive wave-absorbing control: example of the boundary stabilization of a thin flexible beam

2011 ◽  
Vol 18 (11) ◽  
pp. 1708-1721 ◽  
Author(s):  
Gérard Montseny
Keyword(s):  
Continuous Semigroup ◽  
Semigroup Theory ◽  
Flexible Beam ◽  
Convolution Operators ◽  
Controlled System ◽  
Reflected Waves ◽  
Output State ◽  
Finite Dimensional ◽  
Euler Bernoulli Beam ◽  
The Ideal

In this paper we deal with the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Such controls are based upon the reduction of reflected waves and involve long memory non-rational convolution operators resulting from specific properties of the system. These operators are reformulated under so-called diffusive input–output state-space realizations, which allow us to represent the global closed-loop system under the abstract form d X/d t = A X with A the infinitesimal generator of a continuous semigroup. So, well-posedness and stability of the controlled system result from classical semigroup theory. Finite-dimensional approximations of the diffusive realizations are then studied, with the aim of providing implementable controls close to the ideal ones. Finally, significant numerical simulations are presented.

Form-Finding Analysis of Tensioned Fabric Structures Using Nonlinear Analysis Method

2011 ◽  
Vol 243-249 ◽  
pp. 1429-1434 ◽  
Author(s):  
Hooi Min Yee ◽  
Jae Yeol Kim ◽  
Ong Chong Yong
Keyword(s):  
Nonlinear Analysis ◽  
Minimal Surfaces ◽  
Stress Pattern ◽  
Classical Solutions ◽  
Analysis Method ◽  
Form Finding ◽  
Numerical Examples ◽  
Fabric Structure ◽  
Fabric Structures ◽  
Form Finding Analysis

Nonlinear analysis method is one of the earliest methods proposed for form-finding analysis of tensioned fabric structures. However due to some inherent weaknesses, the method has not been fully developed. In this paper, computational strategies for form-finding analysis of tensioned fabric structure using the nonlinear analysis method has been proposed. For the purpose of verification, form-finding analysis on numerical examples of tensioned fabric structures in the form of minimal surfaces Catenoid, Helicoid, Scherk and Enneper have been carried out. Both the obtained shape and pre-stress pattern have been checked with classical solutions for the above minimal surfaces for verification of the effectiveness of the proposed computational strategies.

The well-Posedness of a Two-Unit Standby Redundant Electronic Equipment System

2013 ◽  
Vol 325-326 ◽  
pp. 315-318
Author(s):  
Xing Qiao ◽  
Yan Wang ◽  
Dan Ma ◽  
Zhuang Liu
Keyword(s):  
Steady State ◽  
Electronic Equipment ◽  
Time Dependent ◽  
Well Posedness ◽  
Reliability Study ◽  
Reliability Indices ◽  
Unique Existence ◽  
Human Failure ◽  
Time Dependent Solution ◽  
Equipment System

In this paper, we deal with a two-unit standby redundant electronic equipment system under human failure. In reliability study, it is ordinary to substitute the steady-state reliability indices for dynamic ones because the time-dependent solution is difficult to get. But this replacement should be based on some conditions in general. Therefore it is important to study the unique existence and the expression of the dynamic solution and it is the same with its stability.

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