In this paper we consider the problem of Distributed Fault Detection and Isolation (D-FDI) in large networked systems with imprecise models. Taking a previously proposed D-FDI scheme for a given initial network model, we analyze its performance under small changes in the network graph, namely the addition or removal of edges. Under some assumptions, it is shown that for this kind of perturbations there exist suitable thresholds for which fault detection and isolation is achieved. As our second contribution, we propose solutions to accomplish D-FDI with considerably lower computational burden, while handling imprecise network models. Numerical experiments demonstrating the effectiveness of the proposed solution are presented, taking the IEEE 118 bus power network as an example.