Comparative analysis of standby systems with unreliable server and switching failure

• We construct three spare systems with switching failure and an unreliable server.
• We use the supplementary variable method to obtain the steady-state availability.
• We compare the cost/benefit ratio and availability among three systems.
• The analysis helps the manager to find the optimal availability.

The purpose of this paper is to study the steady-state availability of a repairable system with standby switching failure. The repairable system configuration includes the primary and standby components, where an unreliable server is responsible to repair or monitor the failed ones. The time-to-failure and time-to-repair of the components follow exponential and general distribution, respectively. The server subjects to active breakdown when it is repairing. The time-to-breakdown of the server is also assumed to be exponentially distributed. When the primary components fail, the standby components replace the primary components successfully with probability 1−q. The repair time of the failed components and the repair time of the breakdown server are generally distributed. Further, we frame a practical model with three different repairable system configurations. We use supplementary variable method and integro-differential equations to obtain the steady-state availability of these three different repairable system configurations. Finally, we compare the cost/benefit ratio among the three configurations given the distribution parameters, and to the cost of the primary and standby components.