Summary: For estimating the lower confidence limit of system reliability, the virtual system method greatly improves the Lindstrom and Maddens method with such advantages as level consistency and asymptotic efficiency. In this paper, the generalized virtual system method is employed to estimate the parameter of any subsystem based on the data collected from the system. It is shown that the proposed estimator is asymptotically efficient and the constructed estimate for the lower confidence limit of the parameter is not only asymptotically efficient but also level consistent.