This paper proposes a new Fault Detection algorithm based on Multiple Models approach for linear systems with bounded perturbations. The consistency of each model with the measurements is checked at each sample time based on set-membership state estimation. A Min-Max Model Predictive Control is developed in order to find the optimal control and the best model to use for the system in spite of the presence of component/actuator/sensor faults. An illustrative example is analyzed in order to show the effectiveness of the proposed approach. Index Terms— Fault Detection, Multiple Models, set-membership state estimation, Min-Max MPC, bounded noises and perturbations, linear systems, quadratic programming.