To ensure the high reliability of aircraft structures, the Refill Friction Stir Spot Welding (RFSSW) process must be characterized by a high load capacity of the welds and a small standard deviation of the load capacity spread. This allows us to obtain uniform functional properties in the connections, ensuring the high quality of the process. This work aims to select the most favorable technological parameters for the welding process of EN AW-7075-T6 Alclad aluminum alloy sheets, which are used for the production of aircraft structures. The best networks were calculated using the Statistica 13.3 program. The obtained results were compared with the results of previous investigations. It has been shown that a model using neural networks allows for the determination of connection parameters with much greater accuracy than the classical model. The maximum error in estimating the load capacity of the connection for the mathematical model was 6.13%, and the standard deviation was 14.51%. In the case of neural networks, the maximum error value did not exceed 1.55%, and the standard deviation was 3.74%. It was shown that, based on the neural model, it is possible to determine the process parameters that ensure the required quality capacity of the process, ensuring a probability of obtaining the required load capacity of the connections amounting to P = 0.999935 with a defect rate of 0.0065%. This possibility is not provided by the classical model due to its large error in estimating the process spread and the high sensitivity of the process input parameters to the output parameters.