In this paper we tackle the sensor location problem for fault detection and isolation based on structural analysis for linear systems with faults. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. With such structured systems one can associate a graph. A dedicated residual set is designed using a bank of observers for solving the FDI problem. A major tool in this analysis is the notion of input separator in the associated graph, these separators form a lattice structure. The main contribution of this paper is the formulation of necessary and sufficient solvability conditions for the FDI problem in terms of number of additional sensors measuring variables between faults and input separators in the associated graph. (C) 2008 Elsevier Ltd. All rights reserved.