Abstract: This paper considers how to schedule rechargeable sensors to maximize the overall quality of monitoring (QoM) for event capture when stochastic events follow arbitrary probabilistic distribution. The problem is first formulated as an NP-complete problem, and then we prove that the objective function of the optimization problem is monotone sub modular. Next, an approximation algorithm is designed by expressing the problem as a maximization of a sub-modular function subject to a matroid constraint, which provably achieves a factor of 1/2 of the optimum. Extensive simulation is conducted to verify our theoretical findings.