Software rejuvenation is a preventive maintenance technique that has been extensively studied in the recent literature. In this paper, we consider a generalized problem to estimate the optimal software rejuvenation schedule. More precisely, the software rejuvenation model is formulated via the semi-Markov process, and the optimal software rejuvenation schedule which minimizes the expected total discounted cost over an infinite time horizon is derived analytically. Further, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, provided that the complete sample data of failure time is given. In numerical examples, we investigate how the discount factor affects the optimal policy and examine an asymptotic property for the statistical estimation algorithm.