Abstract: Problems related to observer-based fault detection of uncertain dynamical systems are studied. The aim of this study is to develop a general procedure for designing optimal fault detectors which consist of a residual generator and a residual evaluator. The study is motivated by the observation that residual generator and evaluator designs are often carried out independently, which may, as shown in this contribution, affect the performance of the fault detector. The basic idea of the developed procedure for designing optimal fault detectors is to maximize the set of detectable faults. Relationships between detectable faults and residual generator, evaluation function as well as threshold are derived, based on which the designing procedure is developed.