## 3 Preliminary Process Analysis
### Descriptive Analysis of Variables in the Model  
In the first step, a descriptive analysis of the obtained data was conducted to assess their consistency and stability. This analysis provides insight into the statistical characteristics of the variables, allowing for the identification of deviations from the target values and an evaluation of compliance with the specification limits (LSL and USL). Descriptive analysis also enabled the identification of potential issues in the data, such as outliers, skewness, or high coefficients of variation, which may indicate the presence of variability within the process [57]. Table 2 presents a descriptive analysis of the key variables in this study, which provides a detailed insight into the behaviour of the offset printing process. The following statistical characteristics were quantified:  
Minimum and Maximum: define the extreme values of the data for each variable and illustrate the range within which the variables are distributed. Mean: Represents the arithmetic mean of the values for each variable and provides information about its central tendency. Median: Indicates the middle value of the data and divides the dataset into two equal halves, regardless of the extreme values. Mode: indicates the most frequently recorded value, which is useful for identifying dominant patterns in the data. Variance: quantifies the overall variability of the data and indicates how far the values deviate from the mean. Standard deviation: represents the average deviation of the data from the mean, which is a key indicator of process stability. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Var** & **N** & **Min** & **Max** & **Mean** & **Median** & **Mode** & **Var** & **Std. Dev. ** & **Co. Var. ** & **Skew. ** & **Kurt. ** \\ \hline \(W_{1}\) & 100 & 26.9 & 27.2 & 27.024 & 27.0 & 1.0 & 0.0039 & 0.0622 & 0.2230 & 0.3042 & 0.3345 \\ \hline \(W_{2}\) & 100 & 9.2 & 10.5 &  
* Coefficient of variation: expresses the relative variability as a percentage and enabled the comparison of variables with different measures. * Skewness: indicates an imbalance in the data distribution. Positive values indicate a higher frequency of low values, while negative values indicate the opposite trend. * Kurtosis: describes the shape of the data distribution. A high positive value indicates a peaked distribution, while a negative value indicates a flat and broad distribution. These statistics provide a basic insight into the stability, distribution, and variability of a process and enable model validation and the identification of optimization opportunities. The analysis showed that all variables are within the specified tolerance limits and the deviations from the target values are negligible. All measured values in Table 2 remained within the specification limits, with the exception of variable \(W_{1}\) (ink temperature), whose mean value was above the upper limit defined in Table 1 (USL: 24.0 \({}^{\circ}\)C). This deviation is the result of the specific operating conditions in the pre-analysis phase, in which the actual operating settings were adapted to industrial practice and not to the experimental conditions. For the purpose of the experiment, the controlled parameters were adjusted within the limits defined by the specifications, ensuring complete process stability and precision of the results. This indicates process stability and high-quality control in the production process. In addition, the symmetrical distribution of most variables and the low coefficient of variation indicate a high level of measurement consistency, which is critical for maintaining the robustness and predictability of the process in accordance with Six Sigma standards. These results indicate that key production parameters are well defined and controlled, thereby minimizing variability and ensuring process quality and stability.