Electronic noses or artificial olfaction systems based on chemical gas sensors present lack of robustness, a problem that is mainly technological and requires more research to improve fabrication processes and develop new technologies. However, statistical signal processing can help to mathematically reduce those unwanted effects on the sensors responses before the prediction step. In this chapter, the authors explore the concept of robustness in electronic nose instruments and the use of several multivariate signal processing techniques to deal with two specific problems related to such lack of robustness: time instability (drift) and the detection of a possible faulty sensor in the array. In particular, three different techniques that deal with drift problems are reviewed. These techniques address drift by correction of unwanted variance, by taking advantage of the characteristics of a three-way data arrangement, or by using a blind strategy to extract information with chemical meaning. Finally, a method based on principal component analysis is presented for fault detection, faulty sensor identification, and correction of a fault in a sensor array.