This article proposes a robust set-membership fault detection method based on the use of polytopes to bound the parameter uncertainty set. The proposed polytope-based fault detection algorithm is able to handle systems with bounded parameter variation between samples. It is shown that consistency checks indicating faults can be performed in a natural manner with a polytope description of the feasible parameter set.. Finally, an application example is given, which demonstrates how the algorithm works on a simulated process(a four-tank system). A comparison with a zonotope-based faultdetection approach recently proposed in the literature is included.