This paper presents a new model-based fault detection and failure prediction framework for a class of multi-input and multi-output (MIMO) nonlinear distributed parameter systems (DPS) described by partial differential equations (PDE) with actuator and sensor faults. The fault functions cover both abrupt and incipient faults. A Luenberger type observer is used to monitor the health of the DPS as a detection observer on the basis of the nonlinear PDE representation of the system and by utilizing only the measured output vector. By taking the difference between measured and estimated outputs, a residual signal is generated for fault detection. If the detection residual exceeds a predefined threshold, a fault is claimed to be active. Once an actuator or a sensor fault is detected, an appropriate fault parameter update law is developed to learn the fault dynamics online with the help of an additional measurement. Later, an explicit formula is introduced to estimate the time-to-failure in the presence of an actuator/sensor fault by utilizing the limiting values of the output vector along with the estimated fault parameter vector. Eventually, the effectiveness of the proposed detection and prediction framework is demonstrated on a nonlinear process.