Reliability assessment of a series system with redundancy and repair facilities

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.