A 6-component circular multi-state Markov repairable system with spatial dependence

2015 ◽  
Author(s):  
Liying Wang ◽  
Yuran Tian ◽  
Yongliang Wang ◽  
Baoyou Liu
Keyword(s):  
Spatial Dependence ◽  
Repairable System ◽  
Markov Repairable System

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.

A MARKOV REPAIRABLE SYSTEM INVOLVING AN IMPERFECT SERVICE STATION WITH MULTIPLE VACATIONS

2005 ◽  
Vol 22 (04) ◽  
pp. 555-582 ◽  
Author(s):  
JAU-CHUAN KE ◽  
CHUEN-HORNG LIN
Keyword(s):  
Repairable System ◽  
System Failure ◽  
Service Station ◽  
System Parameters ◽  
Failure Frequency ◽  
The Mean ◽  
Repair Facility ◽  
Markov Repairable System ◽  
Mean Time ◽  
Reliability And Availability

The main purpose of this paper is to study the reliability and availability of a system with M operating devices, m spares, and an imperfect service station that takes vacations. Specifically, once there are no failed devices in the system, the service station takes consecutive vacations until there is at least one failed device upon its return from vacation. The service station may break down and require repair at a repair facility. This paper derives the reliability, the mean time to system failure, the availability, and failure frequency of the K-out-of-M + m system. Numerical simulation of the impacts of system parameters as well as sensitivity analysis for the reliability, the mean time to system failure, the availability and failure frequency is performed.

Research on the model of a multistate aggregated Markov repairable system

2019 ◽  
pp. 1748006X1988765
Author(s):  
Quan Zhang ◽  
Shihang Yu ◽  
Yang Han ◽  
Yanjun Li
Keyword(s):  
System Performance ◽  
The State ◽  
Theory And Practice ◽  
Process Theory ◽  
Repairable System ◽  
Repairable Systems ◽  
Numerical Examples ◽  
Markov Repairable System ◽  
Special Case ◽  
Theoretical Results

In theory and practice, system performance is one of the most important issues. Therefore, a series of indexes has been proposed for evaluating the system performance, such as availability. However, these indexes still cannot meet the variant requirements in the reliability and other fields. The purpose of the article is to develop some theoretical results that may be used in modeling the evolution of system performance. So, based on the aggregated stochastic process theory, some new indexes are introduced and established in Markov repairable systems. In this model, the state space is partitioned into working subset W and failure subset F. The system is regarded as stable if the state of system enters one subset, either W or F, at any instance and sojourns within the subset exceeding a given non-negative threshold [Formula: see text]. Otherwise, the system is regarded as unstable. Under these assumptions, the concepts of point-wise and interval-wise are proposed, and the computation formulae of two types of indexes are derived in the theory. Finally, a special case and a few of numerical examples are given to illustrate the results obtained in the paper.

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