This paper presents a new approach to residual-based fault detection in dynamic systems by introducing the "total measurable fault information residual", ToMFIR for short, which contains the essential fault information and remains unaffected by control actions in a closed-loop system. For linear time-invariant systems, this fault indicator is simple to calculate because it is an algebraic equation. A practical DC motor example, with a PID controller, is used to demonstrate the effectiveness of the ToMFIR-based fault detection. Comparison with standard observer-based technique is also provided.