## 1 Introduction  
Over the years, the production of tubes has had a tremendous importance for industry. A clear example of this is the automotive sector, which is the fuel for many European economies such as the Slovak economy. Usually, tubes are either produced by cold or hot approaches, and depending on the production process or the intended final use of the tubes, there are either loose or increased demands for the accuracy of the tubes' dimensions. In the case of precision steel tubes, these have a narrower tolerance field of diameters as well as wall thicknesses, and thus, in this specific case, there is an increased demand for precise production environments where the correct selection of process parameters and the very construction of the drawing tool play a major role. This cold forming process achieves a higher surface quality and higher dimensional accuracy of tube production compared to hot forming. The principle of cold tube drawing is analyzed in detail in [1; 2; 3; 4]. Cold tube drawing, as a production process, focuses on the reduction in tube dimensions as well as the tube outer and inner diameters, while the process of plastic change of shape, i.e., reduction in tube cross-sections, is carried out by the drawing tool (also known as a die). The shape and dimensions of the die are the key factors in meeting the requirements for the geometric accuracy of the final tube and the roughness of its surface. In the state of the art and the practice, there are several scientific publications which have been aimed at optimizing the shape of the die and monitoring the influence of the die geometry on the final quality of precision tube production using finite element analysis [5; 6; 7; 8]. Similarly, in this particular field, numerical simulation is also known for being an important tool for monitoring the plastic flow of the material in the drawing tool during cold tube drawing. Moreover, it also allows for optimizing process and technological parameters and predicting their possible effects on the accuracy of the tube production process, as stated in [9; 10; 11; 12; 13; 14; 15; 16]. Another important parameter that influences the accuracy of drawn tube dimensions is the plastic strain degree (also known as reduction), i.e., a relative change in cross-sections. In cold tube drawing, it is also necessary to compare the actually achieved strain values with the limit values, because exceeding the limit degree of strain leads to the failure of the tube or the occurrence of defects on its surface. Additionally, the flawlessness of tube drawing is also affected by the plasticity and formability of the drawn material, as these affect the limit of plastic deformation and thus the number of drawing operations required to produce tubes of the required dimensions. The limit of formability in conventional tube drawing has been published in, for example [17]. This research clearly investigated the potential for optimizing the cold drawing process of steel tubes by reducing the number of drawing operations while minimizing residual tensile stresses, which is particularly important and closely related to some of the goals of this paper. On the other hand, even though, at present, the application of statistical methods continues to prove its great potential for a fast and reliable evaluation of dimensional and shape deviations of drawn tubes, this potential is not yet sufficiently used in production processes and metrology activities, which is detrimental because of its great importance for the production sphere, especially in terms of reducing the failure of production, increasing the certainty of measurement experiments, and reducing production costs.