This study evaluates the mooring system of Floating Production Storage and Offloading Units (FPSOs) and Floating Liquefied Natural Gas (FLNGs) using the Gaidai reliability method. The focus is on predicting extreme mooring hawser tensions during operations, which are critical for design and safety. The study employs ANSYS-AQWA software to model vessel dynamics under hydrodynamic wave loads, validated with experimental data. A novel multi-dimensional reliability method based on Monte Carlo simulations is proposed to assess failure and damage risks efficiently. This method is particularly useful for optimizing vessel parameters and minimizing mooring hawser tensions. The study also discusses the importance of offloading operations, especially side-by-side (SBS) offloading in less deep waters, and the potential risks associated with mooring system failures. The research aims to benchmark the Gaidai reliability method and enhance the prediction of failure risks in complex offshore energy systems.This study evaluates the mooring system of Floating Production Storage and Offloading Units (FPSOs) and Floating Liquefied Natural Gas (FLNGs) using the Gaidai reliability method. The focus is on predicting extreme mooring hawser tensions during operations, which are critical for design and safety. The study employs ANSYS-AQWA software to model vessel dynamics under hydrodynamic wave loads, validated with experimental data. A novel multi-dimensional reliability method based on Monte Carlo simulations is proposed to assess failure and damage risks efficiently. This method is particularly useful for optimizing vessel parameters and minimizing mooring hawser tensions. The study also discusses the importance of offloading operations, especially side-by-side (SBS) offloading in less deep waters, and the potential risks associated with mooring system failures. The research aims to benchmark the Gaidai reliability method and enhance the prediction of failure risks in complex offshore energy systems.