This paper is about fault detection and identification of discrete event systems. The proposed approach is based on Petri nets (PNs) that are used to design reference and faulty models. The main contribution concerns the design and identification of these models according to the statistical analysis of the alarm sequences that are collected on the considered system. The model structure is described as a state graph, and the parameters of the probability density functions (pdfs) for transition firing periods are estimated. Normal and exponential pdfs are considered, and estimation is detailed in case of concurring behaviors. The reference models, described as timed PNs, are then used for fault detection and isolation issues. Finally, stochastic PNs with normal and exponential pdfs are considered to include a representation of the faulty behaviors.