Checkpointing and rollback recovery is a commonly used technique to save the information on the main memory in file systems to a safe secondary medium. In this paper we develop fully Bayesian learning algorithms to place the checkpoint adaptively. Based on two kinds of prior distributions for the Weibull system failure time distribution, we give semi-parametric estimation methods of the optimal checkpoint interval minimizing the expected operating cost rate. Simulation experiments show how to determine the hyper-parameters as well as asymptotic properties of the resulting estimators.