## 3 Preliminary Process Analysis
### Calculation of the Current Sigma Level of the Process  
Before implementing the Six Sigma methodology or a model based on it, it was necessary to calculate the current sigma level of the process, which should be at least within the range of average global companies, i.e., (\(3\div 4\)) \(\cdot\)\(\sigma\)[58]. The calculation of the current sigma level for processes (\(k\sigma\)), based on Allen [3], is determined by the number of products or outputs from the process, the number of requirements that define the conformity of the process outputs, and the number of errors in the processes. The mathematical expression is as follows:  
\[\delta=\frac{\varepsilon_{1}+\varepsilon_{2}+\ldots\varepsilon_{n}}{G\times z} \tag{1}\]  
where: \(\delta\) is errors per unit, \(\varepsilon\) is the number of errors for a defined requirement, \(G\) is the total number of products (process outputs), and \(z\) is the number of requirements. Since sigma is evaluated per million units, the result (errors per unit) is multiplied by one million to obtain the number of errors per million products or process outputs (\(N\)). \[N=\delta\cdot 10^{6} \tag{2}\]  
Table 3 showed the current, initial sigma level of the process to verify whether the process has a sigma level above 3, which represents a critical threshold for assessing process stability and quality and for determining the need to introduce the Six Sigma model for further optimization and reduction in variability. These 20 requirements are related to the Critical Product Characteristics (CPCs), key characteristics defined according to quality standards. They cover specific aspects of the product that have a direct impact on its functionality and aesthetic value. Table 3 showed the current sigma level of the process (\(k\sigma=3.625\)), calculated based on the total number of products (\(G=100\)), the number of requirements (\(z=20\)), and the total number of defects (\(\Sigma\varepsilon=33\)). The Errors per unit (\(\varepsilon/u=0.0165\)) are defined as the ratio between the total number of defects and the total number of products and requirements. The parameter \(\varepsilon/u\) (errors per unit) represents the number of defects per unit and is defined as the ratio of the total number of defects to the total number of products and requirements, as expressed in Equation (1). This metric serves as a key measure of process performance, providing a direct assessment of defect rates within the production process. This value is used to calculate the number of defects per million products (\(N=16\),\(500\)) and the sigma level (\(k\sigma\)). It is important to emphasize that \(\delta\) is not the standard deviation of the population but a key indicator that enabled the evaluation of process stability and quality within the Six Sigma methodology. Unlike standard deviation, which measures dispersion within a dataset, \(\delta\) is derived directly from defect rates and reflects process performance rather than statistical variance. The sigma level of \(k\sigma=3.625\) includes a standard sigma shift of 1.5, which is common in the Six Sigma methodology for processes that are not perfectly stable. The sigma shift of 1.5 takes into account potential long-term fluctuations in the process