## 2 Theoretical Background and Calculation
Possible adjustable variants of operating modes are shown in Figure 6.  
Figure 4: A more detailed description of the drilling rig parts: **1—**speed sensor of feed, **2—**ram slide, **3—**gear rod of speed sensor of feed, **4—**slide, **5—**prop of ram slide, **6—**double acting hydraulic cylinder, **7—**restraint of hydraulic cylinder, **8—**high-pressure tube, **9—** control system for the drive spindle, **10—**hose for supply drilling fluid. Figure 5: Drilling cores of disintegrated rocks. During the drilling process, several parameters that define this process are measured and recorded. However, they are not examined to determine statistical process control. A complete overview of the measured parameters and their values are shown in Table 1.  
Rock hardness is one of the longest-used properties for rock classification. Hardness is understood as the rock's mechanical property, expressed by the resistance to deformation of its surface, caused by the action of a foreign body. Rock hardness as a mechanical property is not a physical quantity because this value depends more than any other mechanical property on the rock's complex surface properties under test and on the test conditions under which the hardness is determined. During the hardness test, the test material's surface is mechanically loaded by the pressure of a foreign body, and the result of this action is quantified as the hardness value. It follows that the hardness of the rock is a technical-mechanical property that has a conventional character. This conventionality is determined by the defined test procedure and test conditions. Hardness and strength represent the properties of the rock characterizing their resistance to external forces' mechanical action. Simultaneously, the strength expresses the resistance of the whole body against the breaking of the whole volume by dividing the rock into parts. Hardness represents the body's resistance to the action of concentrated forces, not sufficient for complete disintegration, bu causing partial local failure or deformation. Andesite rock was selected to assess the stability of the drilling process. During its rotary disintegration, there was a significant instability of the process. Rotational disintegration of andesite was a motivating factor for this study. Figure 6: Operating mode variants. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Time (s)** & **Revolutions (tpm)** & **Pressure Force (N)** & **Torque (Nm)** & **Dilled Length (m)** & **Electric Current (A)** & **Electrical Voltage (V)** & **Acceleration (mms\({}^{-2}\))** \\ \hline
0.25 & 723 & 8137  
Tables 2-4 show the significant geomechanical properties that are observed during the rotary disintegration of the rocks. In the present issue, this is understood as uncontrollable process input parameters. Their fundamental influence is a separate subject of research and study. Direct research of the dependence between hardness and control parameters of rotational rock disintegration has not been carried out. This promising idea will be the subject of future research. For the drilling process analysis, control charts were selected by measurement and if the basic values are not determined. The statistical characteristics as the arithmetic mean, variation range, standard deviation, median, moving variation range, individual values, and moving arithmetic means were determined, and the corresponding control charts were constructed for them. The most commonly used pair of control charts by measurement is the control diagram \(\bar{x}-R\). Charts are used to monitor a continuous dynamic process with a relatively large amount of data. Its advantage is greater sensitivity to the existence of isolated outliers within a logical subgroup. In the first step, the range of the logical subgroup \(n\) was chosen. In this case, the range from 2 to 9 is most often chosen, with the recommended number being \(n=5\).