## 2 Description of the Issue  
An important challenge in the production process is the measurement of dimensional and shape-related characteristics of casing covers during finishing machining on a CNC machine and the generation of a measurement report to ensure that it is equivalent to a CMM measurement report. However, a number of factors stand in the way of such a task, which greatly complicate the mathematical and physical description of the relationship between the state of a body cover clamped on a CNC machining machine and a CMM. Among the many, there are at least three primary factors:  
1. According to the quality requirements, the ADT casing cover should be finally inspected after the finishing machining. On a CNC machine, however, measurements of the selected characteristics may be collected when surfaces and holes are finishing machined on one side of the cover only (on the side of bearing seats). However, on the opposite side of the body cover, there is still an allowance of 0.5-0.7 mm left after roughing operations. The allowance is removed in the next operation, while performing the sequence of operations in reverse order is impossible due to the nature of the body cover design. The existing conditions during the machining process result in not all characteristics being specified for a finished product--some are specified between individual machining operations. Figure 2: CAD model of an ADT casing cover: (**a**) exterior view; (**b**) interior view (from bearing seats). 2. The effect of stress released as a result of unclamping and machining of the other side of the casing covers leads to the fact that the shape of the casing during the measurement on a CNC machine differs from the condition during the final measurement on a CMM. 3. The body is measured on the CMM in the plant's measuring laboratory at a stable temperature of 20 \({}^{\circ}\)C and a relative humidity of 45%, after keeping the body in the laboratory room for about 5 h. Such measuring conditions are in practice impossible to achieve when measuring on a CNC machine In a machining station, the casing is set in a wet environment resulting from the use of coolants, and the ambient temperature is stable and repeatable but differs from the required 20 \({}^{\circ}\)C.  
For the above reasons, the development of a reliable measurement report based only on the data collected on a CNC machine is not possible. At the same time, CDT requires full automation of the production process, including quality control. That is why the results of measurements obtained on a CNC machine should be properly converted, according to specific principles, so that they are comparable with the results of measurements obtained in the measurement laboratory. Due to complex relationships, the above-mentioned principles may be specified using methods based on data analysis, and not on an analytical description of physical phenomena. Therefore it was decided to use ANFIS as the system to process input data from a CNC machine to output data as equivalent to measurements carried out on a CMM. ANFIS combines the properties of an artificial neural network (ANN) and a fuzzy system. The main advantages of the ANN include [20]: the ability to learn nonlinear mappings from a dataset, the properties of generalizing the information contained in the data, and robustness to errors and data noise. One of the main disadvantages of the ANN is that it is a so-called black box, which means that the relationships between input data and output data cannot be represented in the form of clear principles, and another disadvantage is that the ANN parameters are not interpreted in connection with the subject being solved. A feature of the fuzzy system [21] is a clear representation of knowledge in the form of inference rules and the possibility to operate on the basis of not only figures, but also linguistic data; thus, it is imprecise. It was shown in [22; 23; 24] that the fuzzy system may be converted into an ANN structure by creating an ANFIS combining the assets of both structures.