An offshore mooring system stations a ship-shaped offshore installation in place while withstanding incoming loads from the marine environment with short-term and long-term uncertainties. This study aims to develop a novel framework for analysing the loads on floating systems, namely mooring line tension, mooring line fatigue damage, and hull bending moment, as a function of the mooring layout design variables and environmental random variables. The nonlinear influence of those variables is assessed by means of advanced techniques using response charts, response divergence charts, and Sobol's total-effect sensitivity indexes. The developed procedure includes a probabilistic selection of mooring scenarios, station-keeping numerical analyses, and metamodel selection to define input loads. An example of a hypothetical floating production storage and offloading (FPSO) unit with taut legs in the Gulf of Mexico illustrates the procedure. The details of the computations are documented, and the findings show that the mooring line top-tension has a high total-effect index for the wave-induced bending moment and the total mooring line tension, whereas the fatigue damage is mostly affected by the chain diameter. The results of this research offer useful insights to designers and propose the use of a surrogate model to be used in the reliability-based design of mooring systems.