ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 4. Vol. 25. 2019

DOI: 10.17587/it.25.195-204

V. I. Levin, D. Sc., Professor, e-mail: vilevin@mail.ru, Penza State Technological University, Penza, Russian Federation

Continuous Logic and Analysis of Reliability of Complex Systems. Mathematical Means

In recent years the increasing attention of scientists and designers of technical systems has been acquiring the issues of improving methods for assessing the reliability and safety of these systems, in connection with tasks of increasing the values of these characteristics. The purpose of the article is to develop an automata-logical model of reliability of complex technical systems and corresponding logical methods for evaluating the reliability of such systems, which, unlike known ones, use not the traditional probabilistic reliability indicators, but deterministic logical indicators. In order to achieve this goal, the article suggests using the observed moments of successive failures and recovery of the elements of the technical system as initial data, and as the reliability characteristics of the system itself the moments of successive failures and recovery of this system. In this case, the problem of estimating the reliability of a system is reduced to constructing its mathematical model in the form of automata logical functions expressing the moments of its successive failures and reconstructions through analogous moments of all its elements. This article is the first part of the work in which an automata-logical model designed to calculate the logical function of reliability of complex technical systems is developed in detail. The novelty of the work is the construction of an adequate logical model of the reliability of complex system, which makes it possible to reduce the estimation of reliability of a complex technical system to the calculation of its logical reliability functions. In the process of calculation, the mathematical apparatus of logical determinants is used for the first time, which allows us to solve the complexity problem. In the article the logical model of reliability and methods of its investigation are developed in detail, allowing to introduce new indicators of reliability of complex technical systems that do not require for their evaluation the use of probabilistic methods and initial statistical data on element failures. On the basis of the developed logical model of reliability and methods of its investigation, the problem of constructing an automata system for reliability of systems is solved, which will allow to fulfill practical calculations of complex technical systems by methods of the theory of dynamic automata using the apparatus of logical determinants.
Keywords: complex system, switching process, reliability process, dynamical automaton, binary operator, structure of operator, logical theory of reliability

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