Problems related to the design of observer-based parametric fault detection (PFD) systems are studied. The core of our study is to first describe the faults occurring in system actuators, sensors and components in the form of additive parameter deviations, then to transform the PFD problems into a similar additive fault setup, based on which an optimal observer-based optimization fault detection approach is proposed. A constructive solution optimal in the sense of minimizing a certain performance index is developed. The main results consist of defining parametric fault detectability, formulating a PFD optimization problem and its solution. A numerical example to demonstrate the effectiveness of the proposed approach is provided. Problems related to the design of observer-based parametric fault detection (PFD) systems are studied. The core of our study is to first describe the faults occurring in system actuators, sensors and components in the form of additive parameter deviations, then to transform the PFD problems into a similar additive fault setup, based on which an optimal observer-based optimization fault detection approach is proposed. A constructive solution optimal in the sense of minimizing a certain performance index is developed. The main results consist of defining parametric fault detectionability, formulating a PFD optimization problem and its solution. A numerical example to demonstrate the effectiveness of the proposed approach is provided.