In this paper, we analyze competing risks data using the two-parameters bathtub (TPBT) distribution. The hazard rate of the TPBT distribution can be either increasing or bathtub-shaped, which allows it to be a good fit for several data sets. In competing risks data, it is assumed that the objective (system) is under attack of many risks (causes of failure) that compete to destroy it. In this study, we assume that the objective will be destroyed by only one cause and all risks are independent. Two cases are considered: (1) the objective receives an attack from one of the risks and in this case, we observe the object lifetime and the cause of failure, (2) the objective has not received any attack during the study period and in this case, we observe the length of such period (censored time, there is no failure). We used the maximum likelihood and Bayes methods to estimate the parameters of all risks and some of the reliability measures of the system.