## 1 Introduction  
The trend of lightweight construction in applications such as aerospace, railway, and automotive [1] has included new joining technologies (Friction stir welding [1, 2], Laser beam welding [3], Refill friction stir welding [4], Pinless friction stir spot welding [5], adhesive joints [6]) and new materials (high strength steels, aluminum, magnesium and titanium alloys). The Friction Stir Welding (FSW) technology is used, among others, on non-weldable aluminum alloys, as the process does not involve melting and, therefore, cannot solidify [7]. Other benefits associated with this process are higher weld quality compared to traditional arc welding techniques [8], repeatability of welding parameters, low environmental impact in terms of gas generation, simple equipment requiring relatively low levels of operator training, refurbishment of damaged components previously considered uneconomical [9]. Joints obtained by this method reduce costs by up to 30% and weight reduction by 10% compared to the mechanical joining technique [10]. In joints made by the FSW method, as well as in other conventional welding processes, the weakest point in terms of fatigue strength is the welded joint [11].This is related to the introduction of tensile residual stresses at the weld zone. Burnishing is one of the methods that has a beneficial effect on the strengthening of the surface layer [12, 13]. It includes methods such as slide diamond burnishing (SDB) [14],ball burnishing (BB) [15, 16], roller burnishing (RB) [17], or shot peening (SP) [18]. In the case of slide burnishing, tooltips are usually made of small-sized diamond composites. The small contact surface of the tool with the workpiece necessary for plastic deformation is smaller than in other burnishing methods. This, in turn, enables the strengthening of thin-walled elements such as FSW welded joints [19]. By using slide burnishing, we can obtain good surface smoothness, improve hardness and introduce compressive stresses in the top layer [20]. These features have a positive effect on fatigue strength [12, 14], corrosion resistance [21], or tribological wear [22, 23]. [PERSON] et al. [12] applied slide burnishing to improve the fatigue strength of shoulder fillets of the shaft made of X19 NiCrMo4 steel. The slide burnishing process improved the fatigue strength by 28.5%, reduced the surface roughness Ra in the range from 64.1% to 85.8%, and strengthened the surface layer by 32% down to a depth of 0.018 mm compared to the hardness of the core. [PERSON] et al. [14] studied the effect of SDB on the fatigue strength of chromium-coated elements made of 42 CrMo4 alloy steel. They indicate that after burnishing, the fatigue strength of shafts can be improved by up to 40%. In work [21], authors analyzed the influence of drawing, polishing, and slide diamond burnishing on the corrosion resistance of 1.4571 stainless steel. Based on microscopic observations, they found that the best corrosion resistance was found after burnishing. [PERSON] and [PERSON] [24] examined the SDB of aluminum matrix composites. The results demonstrate that this treatment significantly reduces the value of surface roughness and imperfections such as voids. They also indicated that the burnishing feed has the greatest influence on surface roughness. In the literature, only a few articles were found on the application of the burnishing process in elements welded using the FSW method. In works [25, 26],the authors investigated the influence of the ball-burnishing process on the mechanical properties of 2050 Al alloy using different burnishing configurations. They found that the ball-burnishing treatment of FSW joints increased the hardness in the range of 10-40% and generated compressive residual stresses from \(-\)315 MPa to \(-\)700 Mpa. Statistical methods Design of Experiments (DoE) allows one to conduct an experiment and obtain results often impossible to obtain in any other way or require much higher costs [27].