A fault detection method with parity equations is proposed in this paper. Due to its low cost implementation, the velocity of the motor is not measurable in electric parking brake (EPB) systems. Therefore, residuals are not reliable when estimating the motor velocity with a low-resolution encoder. In this paper, we propose a fault detection method with sensorless estimation using current ripples that estimates the position and velocity of the motor by detecting periodical oscillations of the armature current caused by rotor slots. In addition, this method can estimate the position and velocity of the motor with less computational effort than a state observer. Moreover, the method is less sensitive to motor parameters than model-based estimation methods. The effectiveness of this method is validated with experimental data, and the simulation results show that various faults have their own residual patterns. Therefore, we can detect the presence of faults by monitoring the residual signals.