The problem of detecting and identifying sensor faults is critical for efficient, safe, regulatory-compliant and sustainable operations of modern systems. Their increasing complexity brings new challenges for the Sensor Fault Detection and Isolation (SFD-SFI) tasks. One of the key enablers for any SFD-SFI methods employed in modern complex sensor systems, is the so-called analytical redundancy, which is nothing but building an analytical model of the sensors observations (either derived from first principles or identified from historical data in a data-driven fashion). In a nutshell, SFD amounts to generate and to monitor residuals by comparing the sensor measurements with the model predictions with the idea that the faulty sensors will result in large residuals (i.e. the defective sensors generate measurement that are inconsistent with their expected behavior represented by the model). In this paper we introduce a disentangled Recurrent Neural Network (RNN) with the objective to cope with the \textit{smearing-out} effect, i.e. the propagation of a sensor fault to the non-faulty sensors resulting in large misleading residuals. Moreover, the introduction of a probabilistic model for the residual generation allows us to develop a novel procedure for the identification of the faulty sensors. The computational complexity of the proposed algorithm is linear in the number of sensors as opposed to the combinatorial nature of the SFI problem. Finally, we empirically verify the performances of the proposed SFD-SFI architecture using a real data set collected at a petrochemical plant.