This study is concerned with the performance modeling of a fault tolerant system consisting of operating units supported by a combination of warm and cold spares. The on-line as well as warm standby units are subject to failures and are send for the repair to a repair facility having single repairman which is prone to failure. If the failed unit is not detected, the system enters into an unsafe state from which it is cleared by the reboot and recovery action. The server is allowed to go for vacation if there is no failed unit present in the system. Markov model is developed to obtain the transient probabilities associated with the system states. Runge–Kutta method is used to evaluate the system state probabilities and queueing measures. To explore the sensitivity and cost associated with the system, numerical simulation is conducted.

In the present investigation, we deal with the reliability characteristics of a repairable system consisting of two independent operating units, by incorporating the coverage factor. The probability of the successful detection, location and recovery from a failure is known as the coverage probability. The reboot delay and common cause shock failure are also considered. The times to failure of the components, time to failure due to common cause, time to repair and time to reboot are assumed to follow exponential distributions. The Markov model of the system is developed and the system state transition probabilities are determined which are further used to evaluate some reliability indices such as availability and mean time to failure. We use fuzzy logic approach for analyzing the system performance by assuming the trapezoidal membership functions of the system descriptors viz. failure rates and repair rates. The fuzzy mean time to failure and fuzzy availability have been established. A numerical experiment has been performed to validate the analytical results.