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Semi-Markov Models
Control of Restorable Systems with Latent Failures
1st Edition - February 2, 2015
Authors: Yuriy E Obzherin, Elena G Boyko
Language: English
Paperback ISBN:9780128022122
9 7 8 - 0 - 1 2 - 8 0 2 2 1 2 - 2
eBook ISBN:9780128024867
9 7 8 - 0 - 1 2 - 8 0 2 4 8 6 - 7
Featuring previously unpublished results, Semi-Markov Models: Control of Restorable Systems with Latent Failures describes valuable methodology which can be used by readers to bu…Read more
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Featuring previously unpublished results, Semi-Markov Models: Control of Restorable Systems with Latent Failures describes valuable methodology which can be used by readers to build mathematical models of a wide class of systems for various applications. In particular, this information can be applied to build models of reliability, queuing systems, and technical control.
Beginning with a brief introduction to the area, the book covers semi-Markov models for different control strategies in one-component systems, defining their stationary characteristics of reliability and efficiency, and utilizing the method of asymptotic phase enlargement developed by V.S. Korolyuk and A.F. Turbin. The work then explores semi-Markov models of latent failures control in two-component systems. Building on these results, solutions are provided for the problems of optimal periodicity of control execution. Finally, the book presents a comparative analysis of analytical and imitational modeling of some one- and two-component systems, before discussing practical applications of the results
Reflects the possibility and effectiveness of this method of modeling systems, such as phase merging algorithms developed by V.S. Korolyuk, A.F. Turbin, A.V. Swishchuk, little covered elsewhere
Focuses on possible applications to engineering control systems
Researchers and students in mathematical modeling, professionals in the field of control of technological processes in instrument making, mechanical engineering, automotive industry and other branches.
Preface
List of Notations and Abbreviations
Introduction
Chapter 1: Preliminaries
Abstract
1.1. Strategies and characteristics of technical control
1.2. Preliminaries on renewal theory
1.3. Preliminaries on semi-Markov processes with arbitrary phase space of states
Chapter 2: Semi-Markov Models of One-Component Systems with Regard to Control of Latent Failures
Abstract
2.1. The system model with component deactivation while control execution
2.2. The System Model Without Component Deactivation While Control Execution
2.3. Approximation of Stationary Characteristics of One-Component System Without Component Deactivation
2.4. The System Model With Component Deactivation and Possibility Of Control Errors
2.5. The System Model With Component Deactivation and Preventive Restoration
Chapter 3: Semi-Markov Models of Two-Component Systems with Regard to Control of Latent Failures
Abstract
3.1. The model of Two-Component serial system with immediate control and restoration
3.2. The model of Two-Component parallel system with immediate control and restoration
3.3. The model of Two-Component serial system with components deactivation while control execution, the distribution of components operating TF is exponential
3.4. The model of Two-Component parallel system with components deactivation while control execution, the distribution of components operating TF is exponential
3.5. Approximation of stationary characteristics of Two-Component serial systems with components deactivation while control execution
Chapter 4: Optimization of Execution Periodicity of Latent Failures Control
Abstract
4.1. Definition of optimal control periodicity for One-Component systems
4.2. Definition of optimal control periodicity for Two-Component systems
Chapter 5: Application and Verification of the Results
Abstract
5.1. Simulation models of systems with regard to latent failures control
5.2. The structure of the automatic decision system for the management of periodicity of latent failures control
Chapter 6: Semi-Markov Models of Systems of Different Function
Abstract
6.1. Semi-Markov model of a queuing system with losses
6.2. The system with cumulative reserve of time
6.3. Two-phase system with a intermediate buffer
6.4. The model of technological cell with nondepreciatory failures
Appendix A: The Solution of the System of Integral Equations (2.24)
Appendix B: The Solution of the System of Integral Equations (2.74)
Appendix C: The Solution of the System of Integral Equation (3.6)
Appendix D: The Solution of the System of Equation (3.34)
References
Index
No. of pages: 212
Language: English
Edition: 1
Published: February 2, 2015
Imprint: Academic Press
Paperback ISBN: 9780128022122
eBook ISBN: 9780128024867
YO
Yuriy E Obzherin
Affiliations and expertise
Head of the Department of Higher Mathematics
Sevastopol State University, Sevastopol, Russia
EB
Elena G Boyko
Affiliations and expertise
Associate Professor, Department of Higher Mathematics
Sevastopol State University, Sevastopol, Russia