Peer-to-peer distributed storage systems aggregate the storage space of many peers spread over the Internet. Due to the dynamic and scalable nature of these systems, it is a challenging issue to access data in an available and reliable way through redundancy. Following the modeling methodology presented, we present the stochastic model to analyze redundancy evolution of these systems under churn. Different from the previous work based on the average peer availability, the stochastic model can be applied into the practice based on both conditional probabilities (alpha, theta) which can be obtained from network probing easily. First, we apply the model to characterize the redundancy evolution of a fragment system with temporary churn. Then, we use an empirical trace and a synthetic trace to validate the model. Second, based on the characteristics of different churn from the both probabilities, we propose the redundancy maintenance strategy assisted by network sampling. Our simulations evaluate the performance of the strategy driven by empirical and synthetic traces.