# Efficient and Sustainable Cleaning: A Comparative Analysis of Cryogenic Technology
## 2 Materials and Methods
### Comparative Analysis of Cryo-Cleaning Equipment (Quantitative Methodology)
#### 2.2.1 Scoring Methodology  
The pre-existing scores come from data sheets and information provided by the manufacturers. The numerical data were normalised with respect to the maximum (\(\beta\)) and minimum (\(\alpha\)) values. This normalisation allows for fair and relative comparisons between devices, regardless of absolute differences in their technical specifications.  
The derived scores were calculated by applying conditional formulae to the technical characteristics of the equipment and the criteria evaluated. These rules were designed to reflect operational efficiency and sustainability, with the highest scores given to features that promote efficiency and reduce environmental impact. In this sense, some criteria with higher values could be unfavourable. For example, higher CO\({}_{2}\) consumption results in higher environmental impact and lower efficiency. Conversely, efficiency and cleaning capacity increase with a higher air pressure range. Therefore, the derived scores were calculated accordingly. The value of \(I\) (iota) in the formulae presented is crucial to normalise and compare different operating parameters of the cryo-cleaning equipment. This value is calculated from the minimum (\(\alpha\)) and maximum (\(\beta\)) values recorded for each criterion evaluated by applying the formula below:  
\[I=\frac{(\beta-\alpha)}{5}\]  
This formula allows the total range of possible values for a specific criterion to be divided into five equal intervals. The purpose is to assign comparative scores based on these ranges, thus facilitating a fair evaluation between different machines.  
The minimum (\(\alpha\)) and maximum (\(\beta\)) values used to calculate \(I\) come from the data sheets and information provided by the manufacturers about the assessed equipment. These sources include detailed data on the technical and operational characteristics of the equipment, such as dimensions, air pressure, volumetric flow rate, sound pressure level, tank capacity, pellet size, CO\({}_{2}\) consumption, and weight without accessories. The information was collected from manufacturers such as Cryosnow(r) and Polartech(r), among others.  
To illustrate the calculation of \(I\), let us consider the air pressure criterion. If the minimum and maximum values recorded are 6 and 50 bar, respectively, the \(I\) value would be calculated as follows:  
\[I=\frac{(50-6)}{5}=8.8\;\text{bar}\]  
These ranges are applied in conditional formulas to assign scores that reflect the operational efficiency and sustainability of the equipment.  
The scoring methodology uses these ranges to rank machines on a scale of 1-5. Depending on the criterion assessed, two assumptions are applied:  
Assumption A: When the most favourable condition (5) is close to the minimum value (\(\alpha\)):  
IF value \(<(\alpha+\text{I});\;5\); IF value \(<[\alpha+(\text{I}\times 2)];4\); IF value \(<[\alpha+(\text{I}\times 3)];3\);  
IF value \(<[\alpha+(\text{I}\times 4)];2\); IF value \(<[\alpha+(\text{I}\times 5)];1\).  
Assumption B: When the most favourable condition (5) is close to the maximum value (\(\beta\)):  
IF value \(<(\alpha+\text{I});1\); IF value \(<[\alpha+(\text{I}\times 2)];2\); IF value \(<[\alpha+(\text{I}\times 3)];3\);  
IF value \(<[\alpha+(\text{I}\times 4)];4\); IF value \(<[\alpha+(\text{I}\times 5)];5\)  
This methodology ensures a fair and uniform assessment, enabling equal comparisons between the different equipment assessed.  
Missing values were addressed by excluding cells with incomplete data on key characteristics, thus ensuring that only units with complete data were included in the final assessment. This approach maintains the integrity and reliability of the analysis.