Fault detection has become increasingly important for improving the reliability and safety of process systems. This paper presents a model-based fault detection methodology for nonlinear process systems. The objective of this work is to detect faults by estimating the model parameters using multiparametric programming. The parameter estimates are obtained as an explicit function of the measurements by using multiparametric programming. The diagnosis of fault is carried out by monitoring the changes in the residual of model parameters. Case studies of fault detection for a single stage evaporator system and quadruple tank system are presented. A number of faulty and fault-free scenarios are considered to show the effectiveness of the presented approach. The proposed approach successfully estimates the model parameters and detects the faults through a simple function evaluation of explicit functions.