The main objective of using the reliability analysis and assessment approaches in many industrial application is to avoid breakdown of their operation mode by extending their lifespan. In this context, some searchers have proposed a reliability model based on bath shaped rate failure function, it uses a graphical method which ensures the ease estimation of the parameters of the concerned model. However, it was found that in this proposed graphical model, a minor reading error will lead to poor estimation of the parameters of the reliability model. In this paper, an objective function based on root-mean-square error (RMSE) is proposed to achieve the best selection of the parameters of the previously proposed model. Indeed, the minimization of this objective function have been carried out using two algorithms such as the grey wolf optimizer (GWO) and particles swarm optimization (PSO). The obtained results for the both algorithms show that they can ensure better accuracy in parameters estimation compared the graphical method.