Drones, or Unmanned Aerial Vehicles (UAVs), have revolutionized industries by providing a flexible and efficient solution for surveillance, mapping, and data collection. They are invaluable tools for environmental monitoring, agricultural surveying, and security applications. This study investigates the improvement of availability and reliability in UAV systems, focusing on small drone surveillance applications. Employing stochastic modeling with Petri Nets, we analyze the impact of integrating redundant components on UAV system availability. Our findings reveal that including spare batteries improves system dependability and uptime. Notably, an increase in system availability is observed with six or more spare batteries, reaching approximately 91.52%. Additionally, system reliability experiences a substantial rise from 33.78% to 54.66% when transitioning from four to five batteries during a 5-hour operation. Conversely, an incremental addition of batteries beyond ten yields a marginal increase in reliability, only 0.45%. The methodology encompasses sensitivity analyses and case studies, underscoring the effectiveness of battery redundancy configurations over the exclusive use of spare drones. This research contributes insights into optimizing the operational efficiency of UAV systems in drone surveillance applications.