The space shuttle main engine (SSME) is part of the Main Propnlsion System (MPS) which is an extremely complex system containing several sub-systems and components, each of which must work precisely in order to achieve a successful mission. A critical component under study is the flow control valve (FCV) which controls the pressure of the gaseous hydrogen between the SSME and the external fuel tank. The FCV has received added attention since a Space Shuttle Mission in November 2008, where it was discovered during the mission that an anomaly had occurred in one of the three FCV's. Subsequent inspection revealed that one FCV cracked during ascent. This type of fault is of high criticality because it can lead to potentially catastrophic gaseous hydrogen leakage. A supervised learning method known as Virtual Sensors (VS), and an unsupervised learning method known as the Inductive Monitoring System (IMS) were used to detect anomalies related to the FCV in the MPS. Both algorithms identify the time of the anomaly in a multi-dimensional time series of temperatures, pressures, and control signals related to the FCV. This discovery corroborates the results of the inspection and also reveals the time at which the anomaly likely occurred. The methods were applied to data obtained from the March 2009 launch of Space Shuttle Discovery to determine whether an anomaly occurred in the same sub-system. According to our models, the FCV SUb-system showed nominal behavior during ascent.