Fuzzy Reliability Evaluation of a Repairable System with Imperfect Coverage, Reboot and Common-cause Shock Failure

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.