A standby system with general repair and imperfect switching

We study the statistical inferences of an availability system with imperfect switching, with the system consisting of one active component and one warm standby. The time-to-failure and time-to-repair of components are assumed to follow an exponential and a general distribution, respectively. We construct a consistent and asymptotically normal estimator of the availability of such a repairable system. Based on this estimator, an interval estimation and a testing hypothesis are developed using logit transformation. To implement the simulation inference for the system availability, we adopt two repair-time distributions, namely, lognormal and Weibull. Three Weibull distributions characterized by distinct shape parameters are considered. Finally, all simulation results are displayed in appropriate tables and curves to highlight the performance of the statistical inference procedures.