Electrical drives are more and more used in transportation applications and industrial process because of their effective cost and high efficiency. They have become critical components and therefore any fault or failure affecting them may seriously endanger the users and/or induce huge financial costs. As a consequence, early detection and isolation of these faults is recommended if not mandatory to enhance the safety, the availability, the reliability and improve the maintenance and the operational efficiency. Analytical Redundancy Relations (ARR) are used to compute to structured residuals on which the diagnosis is based. To smooth the residuals and enhance the fault detection capability, a sliding mode observer is developed to compute the derivatives. The analysis of the residuals reveals that they are Gaussian signals with a change in the mean. The comparison between the two-sigma and the two-sided CUSUM methods has shown that the latter is more efficient to compute the thresholds. Therefore with the two-sided CUSUM, the rotor resistance fault is detected with no false alarm. Moreover it is proved that the fault diagnosis is robust to the load torque variations. Beside, thanks to the residual, a load torque estimator is also developed. Extensive simulation results prove the validity of our approach.