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In this paper, a novel model-based fault diagnosis scheme is proposed for a class of uncertain nonlinear discrete-time systems which can be subjected to both additive and multiplicative faults. Faults are detected by using a novel (FD) observer consisting of two online approximators in discrete-time (OLAD) and a robust adaptive term. Upon detection, a fault diagnosis scheme is introduced to determine the fault type by monitoring the input residual generated via the first OLAD output. Then the appropriate OLAD is included in the observer while the other OLAD is switched off. Next, by using both the parameter update law of the active OLAD and user-selected failure thresholds, an online time-to-failure (TTF) scheme is introduced. Boundedness and asymptotic convergence of the residual and parameter estimation errors respectively are derived in the case of multiplicative and additive faults respectively. Finally a simulation example is used to demonstrate the proposed fault diagnosis scheme.