The optimal system for series systems with warm standby components and a repairable service station

This paper deals with the reliability and availability characteristics of three different series system configurations with warm standby components and a repairable service station. The failure time of the primary and warm standby are assumed to be exponentially distributed with parameters ${\lambda}$ and ${\alpha}$ respectively. The repair time distribution of each server is also exponentially distributed with parameter ${\mu}$. The breakdown time and the repair time of the service station are also assumed exponentially distributed with parameters ${\gamma}$ and ${\beta}$ respectively. We derive the reliability dependent on time, availability dependent on time, the mean time to failure, $MTTF_i$, and the steady-state availability $A_i$(${\infty}$) for three configurations and perform comparisons. Comparisons are made for specific values of distribution parameters and of the cost of the components. The three configurations are ranked based on: $MTTF_i$, $A_i$(${\infty}$), and $C_i/B_i$ where $B_i$ is either $MTTF_i$ or $A_i$(${\infty}$).