Standby system with imperfect coverage and repairable service station

This paper analyzes the reliability characteristics of a system with imperfect coverage in which a repairable service station is considered. Failure times of primary and standby units are assumed to follow exponential distributions. With a coverage probability c, a failed unit is immediately detected and replaced by a standby if one is available. If the failed unit is not detected, the system enters an unsafe failure state and has to be refreshed by a reboot action. When the service station breaks down, it needs repair at a repair device. We present the expression for reliability function RY(t) and mean time to system failure MTTF. Several cases are analyzed to study the effects of various parameters on the system reliability RY(t) and MTTF. We also perform the sensitivity analysis of RY(t) and MTTF with respect to system parameters. Finally, we present an application example to demonstrate the applicability of investigated model.