Markov Birth–Death Models for Reliability Analysis of Repairable Systems

Abstract
This study investigates the application of Markov birth–death models to the reliability assessment of repairable systems with redundancy operating under constant failure and repair rates. The systems considered are composed of identical units, with the assumption that no further failures occur while the system is in the down state. Mathematical models are developed for various system configurations, and analytical expressions are obtained for key reliability measures, including the stationary availability coefficient, mean time to failure (MTTF), mean time between failures (MTBF), and steady-state probabilities. Based on the derived formulas for MTTF and MTBF, as well as for the stationary availability coefficient, graphical dependencies on the input parameters are constructed and analyzed.

Keywords
Markov birth–death models, reliability analysis, repairable systems with redundancy, series systems, parallel systems

Cite this paper
Yurii Zhernovyi, Kostiantyn Zhernovyi, Markov Birth–Death Models for Reliability Analysis of Repairable Systems , SCIREA Journal of Mathematics. Volume 10, Issue 4, August 2025 | PP. 69-89. 10.54647/mathematics110549

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