Aircraft maintenance is critical to an airline's operations to ensure the reliability, availability, and safety of their assets. Recently, the approach of using component prognostics in aircraft maintenance has received increasing attention in academic- and industrial research. Predictive maintenance has demonstrated promising results in using sensor-based prognostics for maintenance decisions. In this paper, we propose a novel predictive maintenance framework that is capable of mapping the individual component degradation levels to an optimal maintenance decision. The independent component degradation levels are computed by a supervised learning model, called "Long Short-Term Memory Networks". Subsequently, the computed degradation levels are utilized in a multi-component maintenance decision framework, by using a model-free reinforcement learning technique named "Deep Q-Learning". The predictive maintenance framework aims to minimize a cost objective based on the type and frequency of a maintenance action. In addition, we analyzed several key performance indicators, such as the number of components used, the component utilization level, as well as the wasted component lifetime. The predictive maintenance framework was evaluated using NASA's turbofan degradation dataset. Ultimately, the results of the numerical experiments showed that the proposed predictive maintenance framework resulted in lower costs than when using a time-based and corrective maintenance policy and competitive costs compared to an ideal maintenance policy. The proposed predictive maintenance framework opens new directions for multi-component sensor-based maintenance decisions. The results found form the basis for application suggestions and future research directions in practice.