For industrial and military applications, a sequence of missions would be performed with a limited break between two adjacent missions. To improve the system reliability, selective maintenance may be performed on components during the break. Most studies on selective maintenance generally use minimal repair and replacement as maintenance actions while break duration is assumed to be deterministic. However, in practical engineering, many maintenance actions are imperfect maintenance, and the break duration is stochastic due to environmental and other factors. Therefore, a selective maintenance optimization model is proposed with imperfect maintenance for stochastic break duration. The model is aimed to maximize the reliability of system successfully completing the next mission. The reinforcement learning(RL) method is applied to optimally select maintenance actions for selected components. The proposed model and the advantages of the RL are verified by three case studies verify.