# A Method for Generation of a Sizing System and Representative Models for a Facial Mask Design
## 3 Comparative Selection of RFMs for a Pilot Oxygen Mask for KAF Pilots
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Face Dimension**} & \multirow{2}{*}{**Importance**} & \multirow{2}{*}{**Grand**} & \multicolumn{6}{c}{**Centroid of Mask Sizing Category**} \\ \cline{5-8}  & & & & **Small** & **Medium** & **Medium** & **Large** \\ \hline
1 & face length & H & 123.4 & 114.5 & 121.7 & 122.7 & 129.4 \\
2 & lower face length & M & 69.1 & 64.3 & 68.3 & 68.3 & 72.6 \\
3 & sellion-to-supramentale length \({}^{\ddagger}\) & M & 97.1 & 87.5 & 95.0 & 95.0 & 105.0 \\
4 & supramentale-to-menton length & L & 26.4 & 26.3 & 26.2 & 26.6 & 26.6 \\
5 & rhinion-to-menton length & M & 109.1 & 102.0 & 107.4 & 108.8 & 113.9 \\
6 & rhinion-to-promentale length & H & 95.8 & 88.0 & 94.1 & 95.8 & 100.3 \\
7 & promentale-to-menton length & L & 13.3 & 14.0 & 13.3 & 13.0 & 13.6 \\
8 & nose length & M & 54.3 & 50.1 & 53.5 & 54.4 & 56.8 \\
9 & nose protrusion & M & 18.4 & 17.8 & 17.9 & 18.5 & 19.0 \\
10 & face width & M & 154.8 & 148.6 & 153.5 & 157.2 & 156.5 \\
11 & chin width & L & 130.3 & 123.1 & 129.3 & 133.7 & 131.0 \\
12 & nasal root breadth & H & 20.0 & 17.7 & 19.6 & 20.9 & 20.6 \\
13 & maximum nasal bridge breadth & H & 30.5 & 27.4 & 30.0 & 31.4 & 31.4 \\
14 & nose width & H & 37.6 & 35.1 & 37.1 & 38.4 & 38.5 \\
15 & lip width \({}^{\ddagger}\) & H & 49.1 & 45.0 & 45.0 & 55.0 & 50.0 \\
16 & bitragion-menton arc & L & 313.7 & 295.3 & 310.1 & 318.5 & 319.5 \\
17 & bitragion-subnasale arc & L & 283.0 & 269.9 & 280.5 & 286.0 & 287.6 \\
18 & bizygomatic-menton arc & L & 304.8 & 288.9 & 301.5 & 308.4 & 311.5 \\ \hline \hline \end{tabular}  
* Two key dimensions of the sizing system were calculated as the median value of each sizing category, while the other 16 non-key dimensions were calculated as the average value of each sizing category.  
\end{table} 
Table 2: The medians (key dimensions) and averages of face measurements by mask sizing category (unit: mm). Representativeness of the identified RFMs derived through the four WSED calculation conditions was evaluated by the distance between the identified RFM in a sizing category and the average face of the same category. As different results of the calculated WSEDs under different conditions, normalized Euclidean distance (NED; Equation (2)) considering the weight of the facial dimensions was used to find the best RFMs. From the NED calculation results, the RFM selection condition using normalized values generated more representative RFMs than that using measured values in general (Table 4). The RFM selection method using measured values and unequal weights was applied in the present study because of its smaller mean and SD values in NEDs than those of other conditions. The four RFMs of KAF pilots and their locations in the proposed mask sizing system are presented in Table 5 and Figure 5, respectively. \[NED_{j}=\sqrt{\sum_{i=1}^{18}\left\{w_{i}\times\left(\frac{m_{ij}-\overline{m} _{ij}}{\sigma_{ij}}\right)^{2}\right\}}/sum\;of\;weights \tag{2}\]  
where  
\(w_{i}\) = the weight of facial dimension \(i\),  
\(m_{ij}\) = the measurements (measured value or normalized value) of facial dimension \(i\) of a representative face in sizing category \(j\),  
\(\overline{m}_{ij}\) = the averages (or medians) of the measurements (measured value or normalized value) of facial dimension \(i\) of all faces in sizing category \(j\), and  
\(\sigma_{ij}\) = the standard deviation of the measurements (measured value or normalized value) of facial dimension \(i\) of all faces in sizing category \(j\).