In a wastewater treatment plant reliable fault detection is an integral component of process supervision and ensuring safe operation of the process. Detecting and isolating process faults requires that sensors in the process can be used to uniquely identify such faults. However, sensors in the wastewater treatment process operate in hostile environments and often require expensive equipment and maintenance. This work addresses this problem by identifying a minimal set of sensors which can detect and isolate these faults in the Benchmark Simulation Model No. 1.Residual-based fault signatures are used to determine this sensor set using a graph-based approach; these fault signatures can be used in future work developing fault detection methods. It is recommended that further work investigate what sizes of faults are critical to detect based on their potential effects on the process, as well as ways to select an optimal sensor set from multiple valid configurations.