Reaching fault tolerance in technological systems requires to detect malfunctions. This paper presents a diagnostic method that is robust with respect to unknown-but-bounded uncertainties of the dynamical model and the measurements. By using models of the faultless and the faulty behaviours, a state-set observer computes polyhedral sets from which the consistency of the models with the interval measurements is determined. The diagnostic result is proven to be complete, i.e., the set of faults obtained by the diagnostic algorithm includes the actual fault. The algorithm is illustrated by an application example.