## 2 Materials and Methods
### Validation of the Method  
Every research method is subject to measurement error. The source of error may be an operator, the measurement method itself, or inaccuracies resulting from the calibration of the sensors on the measuring device. The effectiveness of the measurement method was assessed to make sure that it is reliable and representative. The method (Section 2.4) involved preparing an original test stand including the preparation of samples. Provisions of ISO 5725-2 [44] were the basis for determining the accuracy and precision of the method. The stability of the measurement process was evaluated using the procedures of the R&R per AIAG [45] based on the analysis of variance (repeatability and reproducibility). To validate the measurement method effectively, the experiment needed careful planning. This involved breaking down the process into specific steps and identifying any factors that might cause variability in the Qd and RL measurements. Hence, the validation process had the following:  
* Two operators;
* Two reflectometers;
* Four randomly selected aggregate samples (light and dark). The results of the method validation are shown in Figure 5.  
Two hundred measurements were used in this study. Figure 5 shows the operator codes. Operator P represents measurements conducted at the Kielce University of Technology. Operator D was assigned to another research centre participating in the comparative study. The measurements were performed using a basic group of the following four aggregates: melanybre 2/5, quartzite 5/8, basalt 8/11, and dolomite 2/8, repeating each  
Figure 4: The measuring instrument and the luminance test stand: (**a**) LTL-X Mark II road retroreflectometer; (**b**) mould with test sample; (**c**) scheme of the test stand. measurement four times. As shown in Figure 5, the reproducibility is high, and the repeatability of the results is very similar. However, to definitively determine the process stability, a table summarising the characteristics of the research process is presented below (Table 3). Repeatability, reproducibility, and the contribution of R&R variability to overall process variability (stability) are crucial characteristics of the measurement method. Table 3 reveals excellent repeatability for both Qd (6.4 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\)) and RL (2.24 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\) i 0.6 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\)) characteristics. The reproducibility of Qd is 0.1 \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\). These values are quite low, considering the significant variation in aggregate petrography and grain size. The key metric is total R&R, reflecting overall measurement method stability. Qd and RL achieved total R&R values of 8.26% and 4.77%, respectively. According to AIAG procedures, a measurement process with a total R&R below 10% is considered stable. This signifies that the proposed method and its results are representative and highly reproducible by other trained operators using calibrated equipment. Low variability demonstrates the reliability of the measurement method and the resulting data. This stability is a crucial step for building reliable machine learning models. With this confirmation for individual aggregates, this study progressed to analysing mineral mixtures. Figure 5: Results of R&R procedure (validation). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Qd**} & \multicolumn{2}{c}{**RL**} \\ \cline{2-5}  & \multicolumn{1}{c}{**Value**} & \multicolumn{1}{c}{**Value**} & \multirow{2}{*}{**\% of R\&R**} & **Value** \\  & \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\) & & & \(\mathrm{mcd\cdot m^{-2}\cdot lx^{-1}}\) & \multicolumn{1}{c}{**\% of R\&R**} \\ \hline Repeatability & **6.41** & 8.26 & **2.24** & 4.45 \\ Reproducibility & **0.12** & 0.01 & **0.6** & 0.32 \\ Part & 21.37 & 91.74 & 10.35 & 95.23 \\ Total R\&R & 6.41 & **8.26** & 2.32 & **4.77** \\ Total & 22.31 & 100 & 10.61 & 100 \\ \hline \hline \end{tabular}
\end{table}