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Markov reliability models of series systems with redundancy and repair facilities

Zhernovyi Yuriy, Kopytko Bohdan

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 3

89--96

In this paper, we use Markov models for studying the reliability of series systems with redundancy and repair facilities. We suppose that the units’ time to failure and recovery times are exponentially distributed. We consider the cases when 1≤ c ≤ m and m + 1 ≤ c ≤ m + n, for the system of n operating units, m unloaded redundant units and c repair facilities. Using the exponential distributions properties, we obtain stationary reliability indices of the series systems: steady-state probabilities, a stationary availability coefficient, mean time to failure, mean time between failures and mean downtime.

Reliability assessment of a series system with redundancy and repair facilities

Zhernovyi Yuriy, Kopytko Bohdan

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

123--131

In this paper, we propose a method for studying the reliability of series systems with redundancy and repair facilities. We consider arbitrary distributions of the units’ time to failure and exponentially distributed recovery times. The approach based on the use of fictitious phases and hyperexponential approximations of arbitrary distributions by the method of moments. We consider cases of fictitious hyperexponential distributions with paradoxical and complex parameters. We define conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best and same accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.