Semi-Markov Models : Control of Restorable Systems with Latent Failures.

Cover -- Title page -- Copyright Page -- Contents -- Preface -- List of Notations and Abbreviations -- Introduction -- Chapter 1 - Preliminaries -- 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 -- 2.1 - The System Model With Component Deactivation While Control Execution -- 2.1.1 - The System Description -- 2.1.2 - Semi-Markov Model Building -- 2.1.3 - Definition of EMC Stationary Distribution -- 2.1.4 - Stationary Characteristics Definition -- 2.2 - The System Model Without Component Deactivation While Control Execution -- 2.2.1 - The System Description -- 2.2.2 - Semi-Markov Model Building -- 2.2.3 - Definition of EMC Stationary Distribution -- 2.2.4 - Stationary Characteristics Definition -- 2.3 - Approximation of Stationary Characteristics of One-Component System Without Component Deactivation -- 2.3.1 - System Description -- 2.3.2 - Semi-Markov Model Building of the Supporting System -- 2.3.3 - Definition of EMC Stationary Distribution for Supporting System -- 2.3.4 - Approximation of the System Stationary Characteristics -- 2.4 - The System Model With Component Deactivation and Possibility of Control Errors -- 2.4.1 - System Description -- 2.4.2 - Semi-Markov Model Building -- 2.4.3 - Definition of EMC Stationary Distribution -- 2.4.4 - System Stationary Characteristics Definition -- 2.5 - The System Model With Component Deactivation and Preventive Restoration -- 2.5.1 - System Description -- 2.5.2 - Semi-Markov model building -- 2.5.3 - Definition of the EMC Stationary Distribution -- 2.5.4 - Definition of the System Stationary Characteristics.

Chapter 3 - Semi-Markov Models of Two-Component Systems with Regard to Control of Latent Failures -- 3.1 - The Model of Two-Component Serial System with Immediate Control and Restoration -- 3.1.1 - System Description -- 3.1.2 - Semi-Markov Model Building -- 3.1.3 - Definition of EMC Stationary Distribution -- 3.1.4 - Stationary Characteristics Definition -- 3.2 - The Model of Two-Component Parallel System with Immediate Control and Restoration -- 3.2.1 - System Description -- 3.2.2 - Definition of System Stationary Characteristics -- 3.3 - The Model of Two-Component Serial System with Components Deactivation while Control Execution, the Distribution of Co... -- 3.3.1 - System Description -- 3.3.2 - Semi-Markov Model Building -- 3.3.3 - Definition of EMC Stationary Distribution -- 3.3.4 - Stationary Characteristics Definition -- 3.4 - The Model of Two-Component Parallel System with Components Deactivation While Control Execution, the Distribution of ... -- 3.4.1 - Definition of EMC Stationary Distribution -- 3.5 - Approximation of Stationary Characteristics of Two-Component Serial Systems with Components Deactivation while Contro... -- 3.5.1 - System Description -- 3.5.2 - Semi-Markov Model Building of the Initial System -- 3.5.3 - Approximation of the Initial Stationary Characteristics -- Chapter 4 - Optimization of Execution Periodicity of Latent Failures Control -- 4.1 - Definition of Optimal Control Periodicity for One-Component Systems -- 4.1.1 - Control Periodicity Optimization for One-Component System with Component Deactivation -- 4.1.2 - Optimal Control Periodicity for One-Component System Without Deactivation -- 4.1.3 - Control Periodicity Optimization for One-Component System with Regard to Component Deactivation and Control Failures -- 4.2 - Definition of Optimal Control Periodicity for Two-Component Systems.

4.2.1 - Control Periodicity Optimization for Two-Component Serial System -- 4.2.2 - Control Periodicity Optimization for Two-Component Parallel System -- Chapter 5 - Application and Verification of the Results -- 5.1 - Simulation Models of Systems with Regard to Latent Failures Control -- 5.1.1 - Comparison of Semi-Markov with Simulation Model in Case of One-Component System -- 5.1.2 - Comparison of Semi-Markov with Simulation Model in Case of Two-Component System -- 5.2 - The Structure of the Automatic Decision System for the Management of Periodicity of Latent Failures Control -- 5.2.1 - Description of ADS CPM of Latent Failures Operation -- 5.2.2 - Passive Industrial Experiment -- Chapter 6 - Semi-Markov Models of Systems of Different Function -- 6.1 - Semi-Markov Model of a Queuing System with Losses -- 6.1.1 - System Description -- 6.1.2 - Semi-Markov Model Building -- 6.1.3 - EMC Stationary Distribution Determination -- 6.1.4 - System Stationary Characteristics Determination -- 6.2 - The System With Cumulative Reserve of Time -- 6.2.1 - System Description -- 6.2.2 - Semi-Markov Model Building -- 6.2.3 - System Characteristics Determination -- 6.3 - Two-phase System With a IntermediateBuffer -- 6.3.1 - System Description -- 6.3.2 - Semi-Markov Model Building -- 6.3.3 - System Stationary Characteristics Approximation -- 6.4 - The Model of Technological Cell With Nondepreciatory Failures -- 6.4.1 - System Description -- 6.4.2 - TC Semi-Markov Model Building -- 6.4.3 - TC Characteristics Determination -- 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.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.