## 2 Modelling Background
### Materials and Equipment  
The research was conducted under strictly defined and controlled microenvironment conditions to minimize any potential external impact of temperature and humidity on the printing process. Therefore, the temperature in the production facility was maintained at 22 \({}^{\circ}\)C, with a relative air humidity of 45%. Printing was performed on a six-colour KBA Rapida 105 press, B1 format. All prints were made on identical printing substrates, Brigl & Bergmeister BioMatt 130 g/m\({}^{2}\). Quality control of the offset printing process was carried out both densitometrically and spectrophotometrically using control strips on the printed sheets. For this purpose, measurement strips for grey balance, relative print contrast, tonal errors, and ink efficiency were used, along with signal strips that indicate geometric deformation of halftone elements (i.e., for detecting slurring, doubling, and smudging), as well as signal strips for detecting print register and alignment errors (Figures 3 and 4). For measurements, a thermometer and hygrometer for paper (the so-called'sword') Dostmann P300W (Dostmann electronic GmbH, Wertheim am Main, Germany), a densitometer TECHKON SpectroDens D-61462 A603013 Advanced (TECHKON GmbH, Konigstein im Taunus, Germany), and a photometer Hanna Instruments HI96735 (Hanna Instruments, Woonsocket, RI, USA) were used, along with the KBA Rapida 105 LogoTronic and ErgoTronic professional software (for regulation and control of all machine conditions) and KBA Rapida 105 DensiTronic (for regulation and control of ink application) (Koenig & Bauer Gruppe GmbH, Wurzburg, Germany). The key process parameters, i.e., main input variables, in the future model are:  
* \(W_{1}\) (ink temperature): the ink temperature is defined as a key process parameter and is automatically set and controlled by the ErgoTronic system integrated into the press. Figure 4: Signal Strip and Grey Balance Strip Ugra. Figure 3: Control Strip KBA K C215. The ink temperature set point is maintained within a precise range of \(\pm\)0.1 \({}^{\circ}\)C to ensure stable ink viscosity and consistent application to the offset plate. Continuous monitoring and regulation of the temperature prevents possible variations in ink viscosity, which are essential for consistent printing at all halftone values. * \(W_{2}\) (dampening solution temperature): the dampening solution temperature is defined as a key process parameter and is automatically set and controlled by the ErgoTronic system. The temperature is maintained within the specified range with a regulation precision of \(\pm\)0.1 \({}^{\circ}\)C. Controlling the dampening solution temperature ensures optimal stability in solution transfer to the offset plate, minimizing the transfer of dampening solution to the paper and ensuring the dimensional stability of the paper and the print quality. * \(W_{3}\) (acidity of the dampening solution): the acidity of the dampening solution is defined as a key process parameter and is precisely set and controlled by the ErgoTronic system with a regulation accuracy of \(\pm\)0.1. Proper pH control ensures the chemical stability of the dampening solution throughout the printing process and prevents unwanted reactions between the dampening solution and the ink. The pH value is defined according to industry standards. The output variables (CTQs) associated with Critical Product Characteristics (CPCs) and required for the calculation of the sigma level are controlled and maintained within the defined values through the integration of the DensiTronic and ErgoTronic systems. DensiTronic analyses and measures colour parameters, including dot gain at different halftone values, ink density, and grey balance. The system uses spectral and densitometric measurements to detect deviations from the specified values, with the results displayed on the ErgoTronic console. It also detects geometric deformations of halftone elements (slurring, doubling, and smudging).