This paper considers two stochastic models for a file recovery action with checkpoint generations when two kinds of failures; system failure and media failure, occur according to a homogeneous Poisson process and a renewal process, respectively. For the unknown media failure time distribution, we develop statistical non-parametric algorithms to estimate the optimal checkpoint intervals which maximize the system availabilities. The algorithms proposed are based on the corresponding total time on test (TTT) statistics to the media failure time distribution, and can provide strongly consistent estimates from its sample data.