The aim of this paper is to discuss the methodology of Fault Detection and Diagnosis (FDD) in dynamic systems. Fault diagnosis is characterized as a control system that controls the ability to adapt system component faults automatically. Fault detection is an implementation of using the error signals, where when error signal is zero or approximately zero. A coupled water tank system was used as a study case model for implementing and testing the proposed methodology. The developed system should generate a set of signals to notify the process operator about the faults that are occurring, enabling changes in control strategy or control parameters. Due to the damage risks involved with sensors, actuators and structural faults of the real plant, the data set of the faults are computationally generated and the results will be collected from numerical simulations of the process model. A Recurrent Neural Networks (RNN) is employed in this paper for modeling the used system. This paper shows how to determine the structure and how to estimate the results using the gradient-based algorithm which it is allowed to obtain a Neural Network with relatively small modeling uncertainly. It describes how to increase the stability of dynamic systems using FDD based on RNN. Faults in the study case are faults in the sensors, faults in the actuators and the structural faults. The faults which are presented in the controlled system are reduced to 98% from the default value.