Classification-based methods for fault detection and identification can be difficult to implement in industrial systems where process measurements are subject to noise and to variability from one fault occurrence to another. This paper uses statistical alarms generated from process measurements to improve the robustness of the fault detection and identification on an industrial process. Two levels of alarms are defined according to the position of the alarm threshold: level-1 alarms (low severity threshold) and level-2 alarms (high severity threshold). Relevant variables are selected using the minimal-Redundancy-Maximal-Relevance criterion of level-2 alarms to only retain variables with large variations relative to the level of noise. The classification-based fault detection and identification fuses the results of a discrete Bayesian classifier on level-1 alarms and of a continuous Bayesian classifier on process measurements. The discrete classifier offers a practical way to deal with noise during the development of the fault, and the continuous classifier ensures a correct classification during later stages of the fault. The method is demonstrated on a multiphase flow facility.