Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility

We study a K-out-of-M + W + C: G mixed standby system with an unreliable repair facility, in which there are M primary operating components, W warm standby components and C cold standby components. The life times of primary components and warm components are assumed to be exponentially distributed random variables. The repair facility is performed preventive maintenance (PM) when it is idle, and it is subject to breakdowns when it repairs a failed component (called as active breakdowns). Upon arrival, a failed component is repaired immediately if the repair facility is found free, and the failed component enters a retrial orbit for seeking repair service after some time later if the repair facility is found busy, under PM, or under repair. By adopting a Markov process approach and solving equations of statistical equilibrium in matrix form, we obtain the system steady-state availability of the machine system, the steady-state availability and the expected busy cycle of the repair facility. Furthermore, we obtain the reliability function and the mean time to the failure (MTTF) of the system by using Laplace transform method. Numerical examples are presented to show the effects of system parameters on the reliability function, steady-state availability and MTTF and to analyze the optimization problem of the cost-effectiveness ratio.

Automated summary

This study investigates a mixed standby system with an unreliable repair facility, analyzing system parameters to understand system stability and reliability, while also optimizing the cost-effectiveness ratio.