Bridge structural health monitoring (SHM) systems rely on a network of sensors, such as accelerometers, to assess the condition of infrastructure designed to last for decades. Over time, bridges can experience degradation-related damage, while the monitoring systems themselves can age and degrade, becoming less reliable. This aging of SHM systems can result in sensor faults that produce plausible but incorrect data, leading to misinterpretations of structural integrity and potentially catastrophic failures. Therefore, distinguishing between sensor faults and structural damage is critical to ensuring the reliability of SHM throughout the structure's lifetime. In this study, we present a probabilistic sensor fault detection approach to address this issue. The sensor correlation within the sensor network is analyzed, and sensor faults are detected using Mahalanobis distance. The method is validated on the Nibelungen Bridge, a prestressed concrete bridge in Worms, Germany. It demonstrates its ability to accurately detect sensor faults, including bias, drift, and gain. Increasing the robustness of SHM systems will significantly improve the reliability of data-based assessments of bridges, a task that is becoming increasingly important due to recent structural failures.