Article 4221

Title of the article

AGGREGATION OF STATES OF MARKOV PROCESSES BY MODELING RELIABILITY OF TECHNICAL SYSTEMS

Authors

Boris P. Zelentsov, Doctor of technical sciences, professor, professor of sub-department of higher mathematics, Siberian State University of Telecommunications and Information Sciences (86 Kirov street, Novosibirsk, Russia), E-mail: zelentsovb@mail.ru 

Index UDK

519.217 

DOI

10.21685/2307-4205-2021-2-4 

Abstract

Background. The relevance of the problem of reducing the dimension of systems reliability models is due to the fact that an increase in the number of states causes natural difficulties at all stages of the model implementation, in particular, the need to operate with characteristics of a large dimension. The purpose of the article is a brief overview of approaches to the problem of consolidation of model states based on homogeneous Markov processes in discrete or continuous time, as well as a description of two methods of consolidation that can find application in engineering practice. Materials and methods. These two methods of consolidation of states are based on the reduction of characteristics to the input states of subsets and on the basis of the frequencies of transitions between states and subsets of states. Results. The relationship between the characteristics of the initial system and the enlarged system with a smaller number of states is obtained. The peculiarity of the given methods is that the characteristics of the system, including the reliability measures, are not distorted during the transition to the enlarged model. Conclusions. The methods can be used in engineering practice when modeling the reliability of complex systems in a stationary mode based on Markov processes in discrete and continuous time. 

Key words

aggregation of states, modeling reliability, matrix models of Markov processes in discrete and continuous time 

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Дата создания: 23.09.2021 10:47
Дата обновления: 23.09.2021 12:50