Fault detection and fault tolerance are increasingly important for robots in space or hazardous environments due to the dangerous and often inaccessible nature of these environs. We have previously developed algorithms to enable robots to autonomously cope with failures or critical sensors and motors. Typically, the detection thresholds used in such algorithms to mask out model and sensor errors are empirically determined and are based on a specific robot trajectory. We have noted, however, that the effect of model and sensor inaccuracy fluctuates dynamically as the robot and as failures occur. The thresholds, therefore, need to be more dynamic and respond to the changes in the robot system so as to maintain an optimal bound for sensing real failures in the system versus misalignment due to modeling errors. In this paper, we analyze the Reachable Measurement Intervals method of computing dynamic thresholds and explore its applicability to robotic fault detection.