We introduce a finite mixture of Poisson regression models with component distributions and mixing weights that depend on a set of covariates whose effect changes over time. The effect parameters are modeled in a semi-parametric way using piecewise constant functions. Inference is done in a Bayesian framework and the marginal particle filter algorithm is used to sample from the online posterior distribution. Generally, the performance of particle filter algorithms depends largely on the proposal distribution; we therefore design a proposal distribution tailored to the model using linear Bayes theory. We apply the model to a real dataset consisting of a history of faults reported on a series of a software upgrade releases. Preliminary results show that allowing the parameters to evolve over time greatly improves predictive performance. Further, we assess the performance of the model using different simulation scenarios.