Manufacturers need to evaluate the reliability of their products in order to increase the customer satisfaction. Proper analysis of reliability also requires an effective study of the failure process of a product, especially its failure time. So, the Failure Process Modeling (FPM) plays a key role in the reliability analysis of the system that has been less focused on. This paper introduces a framework defining an approach for the failure process modeling with censored data in Constant Stress Accelerated Life Tests (CSALTs). For the first time, various types of censoring schemes are considered in this study. Usually, in data analysis, it is impossible to get closed form of estimates of the unknown parameter due to complex and nonlinear likelihood equations. As a new approach, a mathematical programming problem is formed and the Maximum Likelihood Estimation (MLE) of parameters is obtained to maximize the likelihood function. A case study in red Light- Emitting Diode (LED) lamps is also presented. The MLE of parameters is obtained using genetic algorithm (GA). Furthermore, the Fisher information matrix is obtained for constructing the asymptotic variances and the approximate confidence intervals of estimates of the parameters.