In survival analysis applications, when the failure rate function has an unimodal shape7 that is a common situation, the log normal or log-logistic distributions are used. In this paper, a regression model based in the Burr XII distribution is proposed for modeling data what has a unimodal failure rate function. The Burr XII distribution has a advantage over the log-normal that the Burr XII survival function is written in closed form and the leg-logistic distribution is a special case of the Burr XII distribution. Assuming censored data, we considered a classic analysis, a Bayesian analysis assuming no informative priors and jackknife estimator for the parameters of the model. The Bayesian approach is considered using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Besides, we used the sensitivity analysis to detect influential or outlying observations and residual analysis is used to cheek assumptions in the model such as departures from the error assumptions. The relevance of the approach is illustrated with a real data set.