Administrative processes in higher education institutions often encounter inefficiencies, duplication of efforts, and a lack of clarity, which undermine institutional sustainability and user satisfaction. This study introduces a hybrid optimization framework that integrates Failure Mode and Effects Analysis (FMEA) with machine learning (ML) to enhance the reliability and efficiency of processes in a renowned university in Ecuador. Due to the variability of the data, a tailored model was developed for each of the ten critical processes analyzed. Two models were employed for each process: one focused on predicting high RPN values (current state) and another on evaluating proposed improvements leading to low RPN values (optimized state). Significant reductions were observed in metrics such as the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). For instance, the RMSE decreased from a maximum of 9.07 in the high RPN model to 4.24 in the low RPN model, while the MAE improved from 2.86 to 3.25 across processes. Key improvements included addressing failure modes such as errors in requirements, unclear steps, and incomplete documentation. These findings underscore the effectiveness of combining FMEA with ML to optimize processes, align institutional practices with Sustainable Development Goals (SDGs), and establish a replicable framework for promoting resilience, transparency, and sustainability in administrative management.