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International audienceThis paper addresses the sensor classification problem for fault detection and isolation (FDI) with observability requirement in a structural way. The system under consideration is a linear system subject to additive faults and affected by unknown input disturbances. This system is equipped with a sensor network subject to sensor failures. We represent the dynamics of the system by a linear parameterized state space model called linear structured model. The underlying prior knowledge on the system is reduced to the existence or non-existence of relations between variables in the model. A dedicated residual set using a bank of observers is designed in order to detect and isolate the faults. The failure of some sensors may affect the observability of the system which is a natural requirement in order to build stable observers and also may affect the FDI solvability. The main contribution of this paper is to classify the sensors with respect to their importance in case of failure relatively to the considered FDI problem. More precisely, we characterize the sensors that are essential i.e. whose failure leads to FDI solvability loss and those which are useless for such property. We also quantify the relative importance of the sensors which are not useless. The proposed graph approach is visual, easy to handle and close to the physical structure of the system. It is well adapted to large-scale systems and essentially leads to polynomial algorithms here