The problem of robustness in fault detection and diagnosis has been treated using basically two kinds of approaches: actives and passives. Most of the literature in robust fault detection is focused on the problem of active approach based on decoupling the effects of the uncertainty from the effects of the faults on the residual. On the other hand, the passive approach is based of propagating the effect of the uncertainty on the residuals and then using adaptive thresholds. In this paper, the passive approach based on adaptive thresholds produced using a model with uncertain parameters bounded in intervals, also known as a “interval model”, will be presented in the context of parity equations and observers methodologies, deriving their corresponding interval versions. Algorithms for computing confidence intervals for the residuals are then introduced, and the proposed approaches are compared. Finally, a example based on a industrial actuator used as a FDI benchmark in the European project DAMADICS will be used for testing and comparing the proposed approaches.