# A Method for Generation of a Sizing System and Representative Models for a Facial Mask Design
## 1 Introduction  
An efficient sizing system for a facial mask is important to properly accommodate various users having different face sizes. As the purpose of a sizing system is to divide a diverse population into homogeneous subgroups based on body sizes [1], the understanding of the anthropometric characteristics of the target population is essential. Previous studies emphasized that the selection of appropriate key anthropometric dimensions is important to develop a good sizing system [2; 3; 4; 5]. In addition to anthropometric dimensions, there are several more considerations for the development of an efficient sizing system, including (1) the number of sizing categories, (2) the accommodation range of each sizing category, (3) the overall accommodation percentage of the target population, and (4) economic efficiency for manufacturing and logistics [4; 6]. A sizing system for a facial mask requires to be properly designed based on facial anthropometric measurements to accommodate different facial sizes of a target population. For example, [PERSON] et al. [7] designed a sizing system consisting of five sizing categories (Small, Medium, Large, Long-Narrow, and Short-Wide categories) based on the principal component analysis (PCA) on 19 facial dimensions of 3997 US civilians (2543 males and 1454 females; age: 18 to 66) collected by [PERSON] and [PERSON] [8] for designing industrial masks (Figure 0(a)). [PERSON] et al. [9] used the same PCA-based sizing system design method of [PERSON], [PERSON] and [PERSON] [7] for the Chinese population and found the sizing criteria for the Chinese population need to be different from each other due to anthropometric differences between the US and Chinese populations (Figure 0(b)). MBU-20/P pilot oxygen masks (Gentex Corporation, Simpson, PA, USA), widely used by F-15, F-16, and F-22 pilots of US Air Force (USAF), were designed by [PERSON] et al. [10] and [PERSON] et al. [11] in five sizes (Extra Small Narrow, Small Narrow, Medium Narrow, Medium Wide, and LargeWide) based on face measurements of 2420 USAF pilots surveyed by [PERSON] et al. [12] (Figure 1c). After the sizing system of the MBU-20/P was developed by [PERSON], [PERSON], [PERSON] and [PERSON] [10], [PERSON], [PERSON], [PERSON] and [PERSON] [11] divided the Small Narrow size into Small Narrow and Extra Small Narrow to accommodate female pilots having small faces, who might not be sufficiently considered in [PERSON], [PERSON], [PERSON] and [PERSON] [10]'s study. A sizing system for a face mask is generally designed by considering a few key anthropometric facial dimensions. Previous studies in mask design [6; 10; 13; 14; 15; 16; 17] proposed some key facial anthropometric dimensions such as face length, lower-face length, lip width, and bigonial breadth for a mask sizing system. For example, [PERSON], [PERSON], [PERSON] and [PERSON] [10] used sellion-to-supramentale length (SSL; similar to face length) and lip width (LW) as key dimensions for the sizing system of MBU-20/P. As shown in Figure 1c, the sizing system of MBU-20/P consists of five sizing categories by combinations of extra small (SSL \(<\) 84 mm), small (84 mm \(\leq\) SSL \(<\) 87 mm), medium (87 mm \(\leq\) SSL \(<\) 100 mm) and large (SSL \(\geq\) 100 mm) in length and narrow (39 mm \(\leq\) LW \(<\) 54 mm) and wide (54 mm \(\leq\) LW \(<\) 69 mm) in width. As the pilot oxygen mask is an essential device for the safe and effective accomplishment of a flight mission, the pilot oxygen mask and its sizing system need to be designed based on the facial characteristics of the specific pilot population. For example, the pilot  
Figure 1: Sizing system for facial masks (illustrated). (a) Sizing system of industrial masks for US workforces generated based on the principal component analysis on facial anthropometric measurements [7]; (b) Inappropriateness of the sizing system for US workforces to Chinese workforces [9]; (c) Sizing system of MBU-20/P pilot oxygen mask.