The slip rate along major tectonic faults or subduction zones is assumed to be a random function. Thus, following a major earthquake, a range of slip rates is considered possible, where the mean and coefficient of variation of the slip rate are determined from geologic and geodetic information on the region. A semi-Markovian stochastic model is used to characterize such a sequence of earthquakes. The parameters of the model are estimated using Bayesian statistical methods. The model is applied to earthquakes occurring on the Mexican subduction zone. The results of this model are compared to results obtained from the constant slip rate model previously developed by the authors. With the constant slip rate model, the probability of occurrence of events of a given magnitude or larger than that magnitude reached 1 after a finite time, implying that events of a given size will occur with certainty in a finite period of time. The results from the random stress accumulation model appear to be more reasonable since the model is not forced to reach the maximum stress level as it is with the constant slip rate models. Thus, in the random slip rate model, the probabilities of occurrence of events of a given magnitude or larger approach one asymptotically in time. These probabilities are lower in value and in that respect may be considered to be less conservative than the probabilities obtained from the constant slip rate models. However, they are more realistic and representative of our knowledge (or lack of knowledge) of the event interarrival times and slip rates along major faults.