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 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 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 RELIABILITY ANALYSIS OF A SIMPLE REPAIRABLE SYSTEM

2010 ◽  
Vol 52 (2) ◽  
pp. 203-217
Author(s):  
L. N. GUO ◽  
H. B. XU ◽  
C. GAO ◽  
G. T. ZHU
Keyword(s):  
Steady State ◽  
Semigroup Theory ◽  
Point Of View ◽  
Repairable System ◽  
Dynamic Solution ◽  
Profit Analysis ◽  
Laplace Transform Technique ◽  
System Operator ◽  
Common Technique ◽  
Uniqueness And Existence

AbstractWe consider a new kind of simple repairable system consisting of a repairman with multiple delayed-vacation strategy. A common technique in reliability studies is to substitute the steady-state reliability indexes for instantaneous ones because the dynamic solution of the system is difficult or even impossible to obtain. However, this substitution is not always valid. Therefore, it is important to study the existence, uniqueness and expression for the system’s dynamic solution, and to discuss the system’s stability. The purpose of this paper is threefold: to study the uniqueness and existence of the dynamic solution, and its expression, using C0-semigroup theory; to discuss the exponential stability of the system by analysing the spectral distribution and quasi-compactness of the system operator; to derive some reliability indexes of the system from an eigenfunction point of view, which is different from the traditional Laplace transform technique, and present a profit analysis to determine the optimal vacation time in order to achieve the maximum system profit.

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

Well-Posedness of the Gnedenko System with Multiple Vacations

2012 ◽  
Vol 522 ◽  
pp. 902-909
Author(s):  
Bilikiz Yunus ◽  
Abdukerim Haji
Keyword(s):  
Semigroup Theory ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiple Vacations ◽  
Dynamic Solution ◽  
Multiple Vacation ◽  
Gnedenko System

We investigate the solution of the Gnedenko system with multiple vacation of a repairman. By using-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

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.

scholarly journals Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Z. Pashazadeh Atabakan ◽  
A. Kazemi Nasab ◽  
A. Kılıçman ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Spectral Homotopy Analysis Method

Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

scholarly journals Existence, uniqueness and stability results for semilinear integrodifferential non-local evolution equations with Random impulse

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6615-6626
Author(s):  
B. Radhakrishnan ◽  
M. Tamilarasi ◽  
P. Anukokila
Keyword(s):  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Local Conditions ◽  
Fixed Point Approach ◽  
Non Local ◽  
The Stability ◽  
Random Impulse ◽  
Stability Results

In this paper, authors investigated the existence and uniqueness of random impulsive semilinear integrodifferential evolution equations with non-local conditions in Hilbert spaces. Also the stability results for the same evolution equation has been studied. The results are derived by using the semigroup theory and fixed point approach. An application is provided to illustrate the theory.

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