Computation and transient analysis of a k-out-of-n:G repairable system with general repair times

This paper considers a k-out-of-n:G repairable system, in which the working times and repair times of components are governed by exponential distributions and general distributions, respectively. Applying the semi-Markov process theory, the Cramer’s rule and the Laplace (Laplace–Stieltjes) transform, several important performance measures including the availability, the rate of occurrence of failures, the mean up time and the mean time between failures of the system are derived. Moreover, numerical inversion of Laplace transform is carried out to discuss the time-dependent behavior of system performance measures. In addition, a special case (n − 1)-out-of-n:G repairable system is presented to verify the correctness of the analytical results.