This paper presents an approach for survival analysis under censored data conditions. It is based on discretizing the time axis and employing gradient boosting (XGBoost). A parametric survival model based on the Weibull distribution is introduced, which provides theoretical coherence through its shared probability structure across time intervals. This approach offers an efficient parameter estimation via the gradient-based optimization, a smooth survival curve estimation, and a natural handling of censored data within a probabilistic framework. Numerical experiments on both synthetic and real-world datasets are conducted to evaluate model performance. Key findings demonstrate that our methods achieve competitive accuracy while addressing fundamental limitations of existing survival analysis techniques. The parametric model shows particular strength in scenarios with well-defined failure time distributions. This work advances the field of survival analysis by combining the interpretability of classical statistical methods with the predictive power of modern machine learning techniques. A code implementing the proposed models is publicly available.