Survival analysis is a fundamental statistical tool for studying the period leading up to a specific event, such as patient death or device failure. Interest in this analysis has grown due to its ability to provide accurate insights into survival rates and survival function estimation in various fields. This paper modifies the Log-logistic Distribution ( ) by adding a shape parameter to enhance its ability to predict more effectively.  After that, a new hybrid meta-heuristic algorithm (PSWGO), combining particle swarm optimization with the gray wolf algorithm, is proposed to estimate the survival function. To compare and investigate the performance of the proposed algorithm with three meta-heuristic algorithms (particle swarm optimization, the gray wolf algorithm, and genetic algorithm ), and different sample sizes (n = 25, 50, 75, and 100), a simulation study is conducted based on the mean square error (MSE). to obtain the numerical results, MATLAB version 2022a is used.  The results showed that the proposed method (PSWGO) provides an accurate and satisfactory estimate for the Survival function, as it has a less mean-square error than the other estimation methods in most cases. MATLAB version 2020a is used to obtain the numerical results