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Semi-Markov Model of a Restorable System with Elementwise Time Redundancy

  • Stochastic Systems
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Abstract

A model that describes the operation of a multi-element restorable system is constructed. After failure, each element of the system remains functionally operable due to an immediately refilled time redundancy. An element is considered to be failed if its restoration time exceeds the time redundancy. In this case, all elements that have a functional link with a failed element are not disconnected. All random variables describing the evolution of the system over time are assumed to have general distributions. This system is studied using the framework of semi-Markov processes with a discrete-continuous state space. The stationary distribution of the embedded Markov chain is found by solving the system of integral equations. Formulas for calculating the stationary availability and mean stationary sojourn times of the system in the operable and failure states are obtained. The stationary characteristics of the system are expressed through the stationary availabilities of its elements and the structural function of the system. An illustrative example of a 3-out-of-4 system is given, and its characteristics are calculated depending on different time redundancies of the elements.

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Acknowledgments

This work was supported by the Ministry of Education and Science of the Russian Federation (state order no. 1.10513.2018/11.12) and by the Russian Foundation for Basic Research, project no. 19-01-00704.

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Authors and Affiliations

  1. Sevastopol State University, Sevastopol, Russia

    A. I. Peschansky

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  1. A. I. Peschansky
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Correspondence to A. I. Peschansky.

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This paper was recommended for publication by V.M. Vishnevskii, a member of the Editorial Board

Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 12, pp. 146–159.

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Peschansky, A.I. Semi-Markov Model of a Restorable System with Elementwise Time Redundancy. Autom Remote Control 80, 2206–2216 (2019). https://doi.org/10.1134/S0005117919120099

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  • DOI: https://doi.org/10.1134/S0005117919120099

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