Model-based diagnosis of NOx sensor malfunction of a system for selective catalytic reduction

System that is useful for detecting a failure in a sensor that is disposed on board a motor vehicle, having a piston driven by the internal combustion engine with an air intake conduit and a conduit for escaping exhaust gas, comprising: a catalyst chamber comprising a part of the line for effluent gas, and includes a solid catalyst disposed therein, said catalyst chamber having an upstream side and a downstream side; a plurality of sensors which are arranged around the system, each of the sensors is useful with respect to the engine, for detecting an operating parameter, wherein the plurality of sensors a first nitrogen oxide sensor having a measured content of NOx at least one control module that is configured to receive a plurality of inputs to provide at least one output signal in response to at least one of the inputs, and that is further configured to to generate, based on the operating parameters of a virtual model nitrogen oxide sensor, the nitrogen oxide sensor virtual model during its working output an estimated NOx based on to determine the difference between the estimated output of nitrogen oxides and the measured content of nitrogen oxides at the upstream side of the catalyst chamber a residual value, to determine a first value for the conversion efficiency η a second value for the conversion efficiency η to detect