scholarly journals Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

2016 ◽  
Vol 04 (08) ◽  
pp. 1585-1591 ◽  
Author(s):  
Abdukerim Haji ◽  
Tursunjan Keyim ◽  
Bilikiz Yunus
Keyword(s):  
Existence And Uniqueness ◽  
Repairable System ◽  
Multiple Vacations ◽  
Dynamic Solution

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.

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.

Optimal sequential preventive maintenance policy for a repairable system with maintenance windows

2019 ◽  
Vol 234 (4) ◽  
pp. 963-977
Author(s):  
Wenke Gao
Keyword(s):  
Preventive Maintenance ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Intensity Function ◽  
Sensitivity Analyses ◽  
Repairable System ◽  
Maintenance Policy ◽  
Catastrophic Failures ◽  
Failure Intensity ◽  
Preventive Maintenance Policy

Optimization of sequential preventive maintenance has been widely studied. However, some issues need further discussion when considering certain real factors. Hence, an sequential preventive maintenance policy for a mono-unit repairable system with maintenance windows is proposed. The load strength and catastrophic failures of a system are considered in the reliability model, and an optimization of the SPM policy is rigorously proven by an analytical method. The existence and uniqueness of the optimal solution with a monotone increasing failure intensity function are presented in detail. The proof of theory indicates that the length of the maintenance window has an upper bound. Finally, a numerical example and some sensitivity analyses are given to illustrate the proposed sequential preventive maintenance policy. Results show that waste may occur when performing the general sequential preventive maintenance policy and may increase along with the length of the maintenance windows.

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.

scholarly journals Well-posedness and Stability of the Repairable System with Three Units and Vacation

2014 ◽  
Vol 2 (1) ◽  
pp. 54-76
Author(s):  
Xiaoshuang Han ◽  
Mingyan Teng ◽  
Ming Fang
Keyword(s):  
Steady State ◽  
Abstract Cauchy Problem ◽  
Steady State Solution ◽  
State Solution ◽  
Repairable System ◽  
Dynamic Solution ◽  
System Operator ◽  
Mean Ergodicity ◽  
System Equations ◽  
The Stability

AbstractThe stability of the repairable system with three units and vacation was investigated by two different methods in this note. The repairable system is described by a set of ordinary differential equation coupled with partial differential equations with initial values and integral boundaries. To apply the theory of positive operator semigroups to discuss the repairable system, the system equations were transformed into an abstract Cauchy problem on some Banach lattice. The system equations have a unique non-negative dynamic solution and positive steady-state solution and dynamic solution strongly converges to steady-state solution were shown on the basis of the detailed spectral analysis of the system operator. Furthermore, the Cesáro mean ergodicity of the semigroupT(t) generated by the system operator was also shown through the irreducibility of the semigroup.

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