During and after the technological operation of pressing these factors significantly determine the residual stress states of tungsten carbide inserts, as well as in the areas near the holes of the cones’ crowns of the cone. The stressed state of the inserts and the magnitude of the stress concentration determine their fatigue strength of them and the durability of the inserted carbide rock-blasting equipment of the cones in the area where the inserts the cone. Dimensional analysis was done for the inserts and holes in the cones of bit and it was established that size errors of component links of dimensional chains are distributed according to laws that are similar to the normal law of distribution of random variables. The test was carried out according to the criteria of Pearson and Kolmogorov. The influence of various random and systematic factors results to the dispersion of dimensions on the dimensional processing of conjugated surfaces. The amount of tension is a function of the dimensions for mating surfaces during assembly operations. Dispersion of dimensions for the component links of the dimensional chain of a press connection causes the formation of a practical field of dispersion of the closing link. Accuracy control for the closing link in the dimensional chain is impossible if there are no direct measurements of the constituent links. A mathematical model of the process of assembling "cone-tungsten carbide insert" joints was created. For this, the methods of mathematical statistics were applied in the study. It was established that the tension values have a greater influence on the force of pressing inserts into the holes of drill steels 14 NiCrMo1, when its hardness value is HRC 59-60 compared to HRC 48-50. This dependence has a linear character within the limits of the studied tension values. The established relationships make it possible to reasonably and most accurately form selective groups of inserts and mark holes for them. This method significantly reduces losses in the production of drilling tools.