In this paper we introduced a regression model considering the new Weibull extension distribution. This distribution can be used to model bathtub-shaped failure rate function assuming censored data, we considered a classic analysis and a Bayesian analysis assuming informative priors for the parameters of the model. A Bayesian approach is considered using Markov Chain Monte Carlo Methods, where Gibbs algorithms along with Metropolis steps are used to obtain the posterior summaries of interest. We illustrated methodology with two numeric examples.