## 4 Multi-Criteria Process Analysis  
### Defining Factors and Factor Combinations in Multi-Criteria Analysis  
Given that the experimental concept on which the model for optimizing the offset printing process was based relies on the ability to control influential factors in the studied process, the design of the research model itself was based on a stochastic approach, more specifically with technologically acceptable parameters. Therefore, all limiting factors in the problem were considered, as well as the optimality criteria defined by the objective function. This objective function is essentially a formalized (analytical) form of assessing the desired outcome in the process. The next step, in accordance with the defined critical product characteristics, Critical to Quality (CTQs) points, and process analysis, was to determine the maximum range for each characteristic, i.e., the factors of multi-criteria analysis and the variation in the process for each of the mentioned characteristics. Given that the process analysis revealed the most common deviations of \(\pm\)0.2 from the target value, the ranges in which the three controlled factors (independent variables) will extend, as well as their combinations, are shown in Table 5. The deviation of \(\pm\)0.2 from the target values refers to the most frequently observed differences between the actual and target values of the controlled factors under stable conditions of the initial process. This deviation is not defined as a tolerance but as the empirically observed range of variation within which the factors \(W_{1}\) (ink temperature), \(W_{2}\) (dampening solution temperature), and \(W_{3}\) (dampening solution acidity) have varied under normal conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \(\mathbf{W_{1}}\)**Ink** & \(\mathbf{W_{2}}\)**Dampening** & \(\mathbf{W_{3}}\)**Dampening** \\  & **Temperature** & **Solution Temperature** & **Solution Acidity** \\  & **Range (\({}^{\circ}\)C)** & **Range (\({}^{\circ}\)C)** & **Range (pH)** \\ \hline \multirow{3}{*}{Combination} & 26.8 = \(W_{1.1}\) & 10.0 = \(W_{2.1}\) & 5.4 = \(W_{3.1}\) \\  & 27.0 = \(W_{1.2}\) & 10.2 = \(W_{2.2}\) & 5.6 = \(W_{3.2}\) \\ \cline{1-1}  & 27.2 = \(W_{1.3}\) & 10.4 = \(W_{2.3}\) & 5.8 = \(W_{3.3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Combinations of Optimization Factor Triads. This range of \(\pm\)0.2 was defined as the basis for determining the modalities of the controlled factors in the experimental model in order to study their interactions on the output variable and determine the optimal settings for each one. The modalities of \(W_{1}\) (ink temperature) were defined as \(W_{1.1}\), \(W_{1.2}\), and \(W_{1.3}\), while the modalities of \(W_{2}\) (dampening solution temperature) and \(W_{3}\) (dampening solution acidity) were defined in the same way (\(W_{2.1}\), \(W_{2.2}\), \(W_{2.3}\), and \(W_{3.1}\), \(W_{3.2}\), \(W_{3.3}\)). An experimental model is based on these modalities, including all possible combinations (\(3^{3}=27\) combinations), to evaluate their impact on the sigma level of the process. The main objective of this approach is to identify the optimal combination of modalities that leads to the highest sigma level, thus minimizing process variability and ensuring consistent production quality. This approach enabled a systematic study of how the variability of controlled factors affects process stability, providing a basis for improving and optimizing production. Furthermore, the selection of these three controlled factors is based on a detailed analysis of recent literature in the field of the offset printing process. The studies show that \(W_{1}\), \(W_{2}\), and \(W_{3}\) are key parameters that have a direct impact on print quality and process stability, making them the most important input variables for the analysis.