Simulation inferences for an availability system with general repair distribution and imperfect fault coverage

We study the statistical inferences of an availability system with imperfect coverage. The system consists of two active components and one warm standby. The time-to-failure and time-to-repair of the components are assumed to follow an exponential and a general distribution respectively. The coverage factors for an active-component failure and for a standby-component failure are assumed to be the same. We construct a consistent and asymptotically normal estimator of availability for such repairable system. Based on this estimator, interval estimation and testing hypothesis are performed. To implement the simulation inference for the system availability, we adopt two repair-time distributions, namely, lognormal and Weibull and three types of Weibull distributions characterized by their shape parameters are considered. Finally, all simulation results are displayed in appropriate tables and curves for highlighting the performance of the statistical inference procedures.