A model-based approach for fault diagnosis is proposed, where the fault detection is based on checking the consistency of the Analytical Redundancy Relations (ARRs) using an interval tool. The tool takes into account the uncertainty in the parameters and the measurements using intervals. Faults are explicitly included in the model, which allows for the exploitation of additional information. This information is obtained from partial derivatives computed from the ARRs. The signs in the residuals are used to prune the candidate space when performing the fault diagnosis task. The method is illustrated using a two-tank example, in which these aspects are shown to have an impact on the diagnosis and fault discrimination, since the proposed method goes beyond the structural methods