Autonomous robotic fault detection is becoming increasingly important as robots are used in more inaccessible and hazardous environments. Detection algorithms, however, are adversely effected by the model simplification, parameter uncertainty, and computational inaccuracy inherent in robotic control, leading to an unacceptable number of false alarms and overzealous fault tolerance. The algorithms must use thresholds to mask out these errors. Typically, the thresholds are empirically determined from a specific robot trajectory. The effect of modeling inaccuracy, however, fluctuates dynamically as the robot moves and failures occur. The thresholds need to be dynamic and respond to the changes in the robot system so as to differentiate between real failures and misalignment due to modeling errors. This paper first summarizes the Reachable Measurement Intervals (RMI) method of computing dynamic thresholds and then, learning from the robot-oriented analysis of RMI, presents a more efficient threshold generation method using the manipulator dynamics property of linearity in parameters.