The Birnbaum-Saunders distribution has been widely used to model reliability and fatigue data. In this paper, we propose a regression of generalized linear models type based on a new bivariate Birnbaum-Saunders distribution. This is parameterized in terms of its means and allows data to be described in their original scale. We estimate the model parameters and carry out inference with the maximum likelihood method. A case study with realworld reliability data is conducted for motivating our investigation, illustrating the potential applications of the proposed results. We obtain a predictive model which can be a useful addition to the tool-kit of diverse practitioners, reliability engineers, applied statisticians, and data scientists.