In this paper, a new combined approach for fault detection and diagnosis (FDD) of abrupt additive actuator and sensor faults, based on Kalman observer (KFO), on sliding mode observers (SMO), on singular values decomposition (SVD), and on principal component analysis (PCA), is proposed. The main contribution is the combined approach proposed for FDD based on ratios between singular values of the adaptive sliding-window SVD-PCA model and on an improved SMO observer that estimates the faults magnitude. In order to show the performance, simulation results with a DTS-200 benchmark linear model are presented.