Estimating a precise data-driven failure rate of electrical components in the distribution networks is a prominent task in asset management of the network. To estimate the failure rates in the overhead distribution lines, there are two main challenges: data deficiency and population variability. In order to overcome difficulties, this paper proposes an applicable method based on hierarchical Bayesian Poisson regression (HBPR). The proposed method is applied to the real distribution system with 34 feeders. The deviance information criterion and model checking procedure are used to compare the goodness of fit between HBPR and exchangeable hierarchical Bayesian model (EHBM). Finally, to show the functionality of the HBPR model, the failure rates obtained from HPBR and EHBM are used to calculate reliability indices, and the results are compared with the actual value of indices.