Semi-Markov Model and Phase-Merging Scheme of a Multi-Component System with the Group Instantly Replenished Time Reserve

2019 ◽  
Vol 26 (03) ◽  
pp. 1950014
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M. Sidorov
Keyword(s):  
Markov Model ◽  
High Reliability ◽  
Multicomponent System ◽  
Additional Time ◽  
Time Redundancy ◽  
Reliability Characteristics ◽  
Semi Markov Processes ◽  
Asymptotic Phase ◽  
Multi Component System ◽  
Time Reserve

Time redundancy is a method of increasing the reliability and efficiency of the operation of systems for various purposes. A system with time redundancy provides additional time (a time reserve) for restoring characteristics and synchronizing the work of its individual elements. Time reservation is used in production, energy, gas transportation, information, ergonomic systems and some others. In this paper, based on the theory of semi-Markov processes with a common phase space of states, a semi-Markov model of a multicomponent system with a group instantly replenished time reserve is constructed. The reliability characteristics of the system are determined. To approximate the probability and the average time of failure-free operation of the system in conditions of high reliability, asymptotic phase-merging scheme algorithms are used.

scholarly journals Analysis of reliability of systems with component-wise storages

2018 ◽  
Vol 58 ◽  
pp. 02024 ◽  
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M Sidorov ◽  
Mikhail M Nikitin
Keyword(s):  
Phase Space ◽  
Energy Systems ◽  
Two Component System ◽  
Additional Time ◽  
Component System ◽  
Time Redundancy ◽  
Reliability Characteristics ◽  
Two Component ◽  
Semi Markov Processes ◽  
Time Reserve

Time redundancy is a method of increasing the reliability and efficiency of the operation of systems for various purposes, in particular, energy systems. A system with time redundancy is given additional time (a time reserve) for restoring characteristics. In this paper, based on the theory of semi-Markov processes with a common phase space of states, a semi-Markov model of a two-component system with a component-wise instantly replenished time reserve is constructed. The stationary reliability characteristics of the system under consideration are determined.

scholarly journals Semi-Markov model of a technical system with the component-wise instantly replenished time reserve

2018 ◽  
Vol 224 ◽  
pp. 04008 ◽  
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M. Sidorov ◽  
Sergey N. Fedorenko
Keyword(s):  
Markov Model ◽  
Approximate Determination ◽  
Two Component System ◽  
Additional Time ◽  
Component System ◽  
Time Redundancy ◽  
Two Component ◽  
Technical Systems ◽  
Time Reserve

Time redundancy is one of the methods to increase the reliability and efficiency of technical systems. When it is used, the system is given additional time (a time reserve) for restoring characteristics. In this paper we construct a semi-Markov model of a two-component system with a component-wise instantly replenished time reserve. In this paper we construct a semi-Markov model of a two-component system with a component-wise instantaneous replenishment of the time reserve. For an approximate determination of the stationary characteristics of the reliability of the system, the phase merging scheme algorithm is used.

scholarly journals Semi-Markov model of a multi-component energy system with component-wise storages

2019 ◽  
Vol 139 ◽  
pp. 01065
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M. Sidorov ◽  
Mikhail M. Nikitin
Keyword(s):  
Markov Model ◽  
Energy Systems ◽  
Energy System ◽  
Component System ◽  
Storage Devices ◽  
Time Redundancy ◽  
Multi Component System ◽  
Time Reserve

To increase the reliability and efficiency of the functioning of various purposes systems (in particular, energy systems), time redundancy is used. In this paper, a semi-Markov model of a multi- component system with component-wise storage devices, which are the sources of the time reserve, is constructed. The stationary characteristics of reliability and efficiency of the system under consideration are found. The analysis of the influence of storage capacities on the reliability and efficiency of the system is been.

A semi-markov model for clinical trials

1965 ◽  
Vol 2 (02) ◽  
pp. 269-285 ◽  
Author(s):  
George H. Weiss ◽  
Marvin Zelen
Keyword(s):  
Clinical Trials ◽  
Probability Distribution ◽  
Acute Leukemia ◽  
Markov Model ◽  
Markov Models ◽  
Transition Probabilities ◽  
State Transitions ◽  
Semi Markov Processes ◽  
Absorbing States ◽  
Epidemic Diseases

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

scholarly journals Analyzing the Improved Software Reliability Based on the Markov Model by Considering Error propagation

2018 ◽  
Vol 7 (2.32) ◽  
pp. 91
Author(s):  
Dr S. Srinivasa Rao ◽  
D Sowjanya ◽  
CH Dileep Chowdary ◽  
M Harika
Keyword(s):  
Markov Model ◽  
Reliability Analysis ◽  
Software Reliability ◽  
Error Propagation ◽  
High Reliability ◽  
Transformation Techniques ◽  
Model Driven ◽  
Model Based ◽  
Estimate Reliability ◽  
Analysis Design

In the software reliability analysis we proposed an approach, which is named as Model Driven Development method. This is a modelling and model transformation techniques. The Markov model used in reliability fields is modified to adapt to error propagation behaviors of components. The Markov model has been used for results of reliability analysis. Markov model which means that that future or upcoming states depend only on the present state not on the events that occurred before it to ensure high reliability of this software is to estimate reliability accurately in the developing phase. Then a study on the transformation between model based on Architecture & Analysis Design Language (AADL) and Markov model has been done. By considering all these a model based software reliability analysis approach is proposed. 

scholarly journals Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

2020 ◽  
pp. 713-720
Author(s):  
Shirin Kordnoori ◽  
Hamidreza Mostafaei ◽  
Shaghayegh Kordnoori ◽  
Mohammadmohsen Ostadrahimi
Keyword(s):  
Monte Carlo ◽  
Markov Model ◽  
Markov Processes ◽  
Network Traffic ◽  
Markov Models ◽  
Transition Probabilities ◽  
Simulation Method ◽  
Monte Carlo Algorithm ◽  
Statistical Characteristics ◽  
Semi Markov Processes

Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.

A semi-markov model for clinical trials

1965 ◽  
Vol 2 (2) ◽  
pp. 269-285 ◽  
Author(s):  
George H. Weiss ◽  
Marvin Zelen
Keyword(s):  
Clinical Trials ◽  
Probability Distribution ◽  
Acute Leukemia ◽  
Markov Model ◽  
Markov Models ◽  
Transition Probabilities ◽  
State Transitions ◽  
Semi Markov Processes ◽  
Absorbing States ◽  
Epidemic Diseases

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

scholarly journals Optimization of the maintenance planning of a multi-component system

2018 ◽  
Vol 200 ◽  
pp. 00011
Author(s):  
Issam Mallouk ◽  
Badr Abou El Majd ◽  
Yves Sallez
Keyword(s):  
High Reliability ◽  
Maintenance Planning ◽  
Multi Objective Optimization ◽  
Maintenance Policy ◽  
Swarm Optimization ◽  
Multiobjective Particle Swarm Optimization ◽  
Maintenance Policies ◽  
The Cost ◽  
The Mathematical Model ◽  
Multi Component System

The vehicle’s maintenance costs, uptime and security are the most important goals for owners and transport companies, but these goals are conflictual and the major cause for delays is related to the maintenance policies. The main objective of transporters is to respond properly to their customer’s demands. In order to deal with this competitiveness, transport companies are working to improve the management of their fleets by focusing in particular on vehicle maintenance, which impact the vehicles uptime, and generate the most important cost. In addition, a vehicle maintenance policy aims to avoid failures and keep the vehicle up and safe. This objective is reached by ensuring a high reliability; otherwise, an unexpected failure of a component can cause vehicle down and can affect the entire sub-system while generating costs. In this paper, we propose a new maintenance policy based on multi-objective optimization. This problem is solved using the Speed-Constrained Multiobjective Particle Swarm Optimization (SMPSO) for an instance of 18 components and 20 vehicles. First, we give an overview of the existing techniques used for vehicle’s maintenance policy, then we present the mathematical model that describes the cost of maintenance and the level of safety. Numerical experiments are presented to demonstrate the efficiency of our approach.

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