The concept of genetic algorithm (GA) is used to model the cost of maintenance and repair of a liquefied natural gas (LNG) containment system and its transfer arm, after assessing the total risk of the systems using the probabilistic risk assessment technique. The failure frequency data of the basic events of the fault tree developed to model the LNG containment system and transfer arm, which is implemented and evaluated to estimate the failure frequencies of the systems, are derived from a careful literature search. A total risk formula is developed, which is dependent on hazard severity weight, failure frequencies, and the time and cost of maintenance and repair of the LNG carrier systems. The formula serves as the objective function, while new total cost allocated for the maintenance and repair of the LNG carrier systems as a whole is the constraint with the boundaries of presenting initial/unit cost of maintenance and repair of each containment system and transfer arm. Optimization is carried out on the objective function and its constraint for the identification of new cost of maintaining and repairing the containment system and transfer arm independently with the powerful tool of GA using Matlab version 7.7 software for improvement of the system's safety level.