## 2 Modelling Background
### Defining Critical to Quality and Critical Product Characteristics  
Considering the principles of the Six Sigma methodology, it was necessary to define potential variability limits in the process by determining the functional requirements of the product and the methods for controlling them. Critical Product Characteristics (CPCs) were also defined, analysed, and grouped according to cause categories. The functional requirements of the product are most often defined by its design and can be categorized as [27; 28] product usability, ergonomic adaptability, technical reliability, and aesthetic sensitivity. Based on the functional requirements, the current sigma level (\(k\sigma\)) of the process was calculated. To identify Critical to Quality (CTQs) points through process analysis, Critical Product Characteristics (CPCs) were defined as dependent variables, which include:  
* Dot gain at 40% halftone value for cyan, magenta, yellow and black inks
* Dot gain at 80% halftone value for cyan, magenta, yellow and black inks
* Ink density at 100% halftone value for cyan, magenta, yellow and black inks
* Grey balance
* Print register (alignment)
* Geometric deformations of halftone elements (slurring, doubling, smudging)
* Paper folding register
* Paper cutting register
* Print rub register  
Figure 1: General Framework of Research. Critical Product Characteristics (CPCs) are the points on the product that are closely associated to the Critical to Quality (CTQs) points. * \(W_{1}\): ink temperature (\({}^{\circ}\)C)--crucial for maintaining ink viscosity stability and uniform ink transfer
* \(W_{2}\): dampening solution temperature (\({}^{\circ}\)C)--ensures stable transfer of the dampening solution to the rollers and process balance
* \(W_{3}\): dampening solution acidity (pH)--controls chemical stability during printing
* \(X_{1}\): paper temperature (\({}^{\circ}\)C)--ensures the dimensional stability of the paper during the printing process
* \(X_{2}\): paper humidity (\(\%\))--is related to the hygroscopic nature of the paper and its stability during the printing process
* \(Z_{1}\): ink viscosity (mPa-s)--ensures consistent ink application and print quality
* \(Z_{2}\): dampening solution conductivity (\(\mu\)S/cm)--enabled proper interaction between the dampening solution and the paper surface
* \(Z_{3}\): dampening solution hardness (dH)--helps to maintain the stability of the solution during the printing process
* \(Z_{4}\): alcohol content in the dampening solution (\(\%\) vol.) --crucial for stable solution transfer and preventing excessive evaporation. From the analysis of the relevant literature and processes, it was concluded that the most critical and characteristic points for quality in the offset printing process are the ink temperature, the dampening solution temperature, and the pH of the dampening solution [29; 30; 31; 32; 33; 34; 35]. These independent variables in the model, identified through preliminary process analysis and research, directly influence the chemical and physical interactions within the printing process. Their control is crucial for maintaining consistency, stability, and high-quality print outcomes. In particular, ink temperature (\(W_{1}\)) affects drying speed, dot gain, and colour balance; dampening solution temperature (\(W_{2}\)) is essential for maintaining process stability and the balance between ink and water; and the dampening solution acidity (\(W_{3}\)) directly affects the chemical stability of the solution and ensures proper ink distribution. The impact of these variables on the Critical to Quality (CTQs) characteristics was analysed using statistical tools such as correlation analysis and descriptive statistics. The selection of these parameters was based on their strong association with quality metrics such as process stability and print accuracy. The specification limits for these parameters, listed in Table 1, include the lower specification limit (LSL), the upper specification limit (USL), and the target value (TV).