Propagation of faulty data in Delay Tolerant Networks can be a critical aspect to counteract due to the inherent feature of exhibiting frequent disconnections,. Indeed the rare meeting events require that nodes are effective and efficient in propagating correct information. Accordingly, mechanisms to rapidly identify possible faulty or misbehaving nodes should be searched. Distributed fault detection has been addressed in the literature in the context of sensor and vehicular networks, but already proposed solutions suffer from long delays in identifying and isolating misbehaving nodes. This paper proposes a fully distributed, easily implementable, and fast convergent approach to allow each DTN node to rapidly identify whether its sensors are producing outliers, i.e., fauty data. The behavior of the proposed algorithm is described by some continuous-time state equations, whose equilibrium is characterized. Detection and false alarm rates are estimated by comparing both theoretical and simulation results. Numerical results assess the effectiveness of the proposed solution and give guidelines in the design of the algorithm.