Standby System with Imperfect Coverage and Repairable Service Station

[[abstract]]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 MT T F. Several cases are analyzed to study the effects of various parameters on the system reliability RY (t) and MT T F. We also perform the sensitivity analysis of RY (t) and MT T F with respect to system parameters. Finally, we present an application example to demonstrate the applicability of investigated model