The improvement of industrial systems' reliability and production quality is a real problem of the modern industry. The automatic systems of technological processes management enable solving this problem. The local technical control constitutes an important part of the system.In spite of the diversity and high level of checkout and measurable instruments， the problem oflatent failures detection and elimination is still significant.
The latent failure is a failure which cannot be detected by standard methods or visually， but by maintenance or special methods of diagnostics only.In this monograph， by the latent failure we refer to one which can be detected during control execution only.
In complex industrial systems， the periodical control is applied. The reason is the difficulty of checHng individual operation of all units and details(components). It means the control is carried out at fixed (in general case random) time periods， which should be optimal for the whole system by ensuring its maximum reliability and efficiency. The problem can be solved by constructing mathematical models of control of restorable systems with latent failures.
The present monograph is dedicated to building such models on the basis of the theory of semi-Markov processes with arbitrary phase state space， as well as to the definition of optimal periodicity of latent failures control. The problems of application of the results obtained are considered.
The authors express deep gratitude to professor V.J. Kopp and professor A.I.Peschansky for valuable comments， contributing to the monograph quality improvement， and to A.I. Kovalenko for the monograph translation into English.
The improvement of industrial systems' reliability and production quality is a real problem of the modern industry. The automatic systems of technological
processes management enable solving this problem. The local technical control constitutes an important part of the system.
In spite of the diversity and high level of checkout and measurable instruments， the problem oflatent failures detection and elimination is still significant.
The latent failure is a failure which cannot be detected by standard methods or visually， but by maintenance or special methods of diagnostics only.
In this monograph， by the latent failure we refer to one which can be detected during control execution only.
In complex industrial systems， the periodical control is applied. The reason is the difficulty of checHng individual operation of all units and details
(components). It means the control is carried out at fixed (in general case random) time periods， which should be optimal for the whole system by ensuring
its maximum reliability and efficiency. The problem can be solved by constructing mathematical models of control of restorable systems with latent failures.
The present monograph is dedicated to building such models on the basis of the theory of semi-Markov processes with arbitrary phase state space， as well as to the definition of optimal periodicity of latent failures control. The problems of application of the results obtained are considered.
The authors express deep gratitude to professor V.J. Kopp and professor A.I.Peschansky for valuable comments， contributing to the monograph quality improvement， and to A.I. Kovalenko for the monograph translation into English.
Preface
List of Notations and Abbreviations
Introduction
1． Preliminaries
1．1 Strategies and Characteristics ofTechnical Control
1．2 Preliminaries on RenewaITheory
1．3 Preliminaries on Semi-Markov Processes with Arbitrary Phase Space of States
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 Modelwith 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
3． Semi-Markov Models ofTwo-Component Systems with Regard to Control of Latent Failures
3．1 The Model ofTwo-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 ofTwo-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 ofTwo-Component Serial System with Components Deactivation While Control Execution， the Distribution of Components Operating TF is Exponential
3．3．1 SystemDescription
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 ofTwo-Component Parallel System with Components Deactivation While Control Execution，the Distribution of Components Operating TF is Exponential
3．4．1 Definition of EMC Stationary Distribution
3．5 Approximation of Stationary Characteristics of Two-Component Serial Systems with Components Deactivation While Control Execution
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
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
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