## 2 Materials and Methods
Studying the variability and assessing the repeatability of the two measurement systems are intended to answer which system is better in terms of accuracy, efficiency, and productivity. This is related to the optimization of processes, which in the perspective of Industry 4.0 seems to be a standard. The issue of optical measurements is often generalized because optical measurements are measurements with the use of a microscope, structured light, or laser triangulation, among others. The measuring systems available in these studies, including the Multisensory Measuring Machine Werth Scope Check, enable the use of an optical sensor that allows for image recording. The optical sensor can be used in the so-called static or dynamic measurement mode. These modes differ in that the dynamic measurement consists in scanning the entire detail using the Raster Scanning HD, which enables dynamic registration of contours, while the static mode is carried out by sequential runs from the characteristic measurement point to the next measuring point. A schematic example of a dynamic measurement is shown in Figure 4. Analyzing the results of various measurements, we can expect many variables that may cause differences that will raise doubts for the person deciding to accept the production process. Figure 3: The symmetry of the teeth on the left and right side defined as a phase shift of max. 0.05 mm (own study), A denotes symmetry line. Figure 2: Parameters of the blank showing the tooth height 5 \(\pm\) 0.08 mm and the tooth spacing 10 \(\pm\) 0.05 mm (own study). In this study, it has been established that the system analysis will start with checking the capability of the measuring equipment by determining the Cg/Cgk capability index for three types of equipment with the maximum permissible errors for the equipment specified according to [15]. This indicator evaluates only the measuring device (not the process and not the measuring system). It provides information about the extent the instrument is suitable for the assumed measurement task. * LH-600 Height gauge \(\rightarrow\) E\({}_{0\text{,MPE}}\) = 1.1 + 0.6 \(\times\) L/600 \(\upmu\)m, L in mm;
* DEA Global Coordinate Measuring Machine \(\rightarrow\) E\({}_{0\text{,MPE}}\) = 1.7 + L/333 \(\upmu\)m, L in mm;
* Werth Scope Check FB DZ Multisensory Measuring Machine \(\rightarrow\) E\({}_{0\text{,MPE}}\) = 2.9 + L/100 \(\upmu\)m, L in mm. As may be seen above, according to the MPE equations, the height gauge has the best MPE value. However, it should be remembered that this is the accuracy of the measuring device in one axis, namely, the Z axis. Coordinate machines have this accuracy specified in the XYZ space, so it cannot be compared 1:1. Before starting the experiment, measurements were carried out in an accredited laboratory and model values for the analyzed characteristics were obtained. Then, with the use of measurement systems available in the organization, the tested piece was measured 50 times and the results were obtained which are presented below using various graphs performed with the Minitab program. The measurement with the height gauge took place in the laboratory, where the temperature stability is controlled and was 21 \(\pm\) 0.3 \({}^{\circ}\)C during the measurement. The sample was attached to the prism, and the height gauge was placed on a granite plate in class \"0\". The measurement conditions are shown in Figure 5.  
Another series of fifty measurements of the same piece was carried out using the DEA Global Coordinate Measuring Machine with a contact head, and the sample was mounted on a tripod and locked with clamps, which ensured that the sample was firmly fixed during the measurement. The fixing and measurement are shown in Figure 6. When measuring with the Multisensory Measuring Machine Werth Scope Check, the detail was placed on the plate in such a way that the optical sensor used to measure the sample could scan the entire detail and obtain a scan view.