## 1 Introduction  
A pilot oxygen mask worn over the face of a fighter pilot requires an ergonomic design that comfortably fits the face of the pilot. The pilot oxygen mask provides the pilot with oxygen while a mission is conducted at a high altitude where oxygen is lacking [1]. In addition, the pilot oxygen mask protects the pilot by supplying oxygen securely in a hazardous situation such as decompression, fire and fume in the cockpit, and windblast during ejection [2]. A pilot mask lacking the consideration of the facial characteristics of the user population can cause discomfort, pain, and/or leakage of air at some facial areas, especially around the nasal root [1, 3]. Although the facial characteristics of the user population need to be considered to design an ergonomic shape and size of a mask, the analysis of the fit of a mask to the user population has not been considered sufficiently. Existing studies [4, 5, 6, 7, 8, 9, 10] recommend face length, face width, lip width, nasal root breadth, and nose protrusion as key facial dimensions for mask design. However, measurements of the key facial dimensions are not sufficient in designing the ergonomic shape and size of a mask that properly accommodates the faces of the user population due to the high complexity and diversity of the face shape and size among the users [11, 12]. Several studies [13, 14, 15, 16] introduced mask design methodsusing the information of 3D facial shapes as well as facial sizes. [PERSON] et al. [15] reported an improved design of MBU-20/P (Gentex Corporation, Simpson, PA, USA) pilot oxygen mask using the profile curves of the 3D scanned faces of 30 male and 30 female pilots of the U.S. Air Force. [PERSON] et al. [14] designed an industrial respiratory mask of three sizes (small, medium, and large) for Korean industry workers using 3D representative head models identified by analyzing Korean faces. Lastly, [PERSON] et al. [13] used five 3D head forms representing U.S. workers in designing an industrial respiratory mask. However, the validation of a design with a large group of users is often limited due to time and cost [17; 18; 19]; therefore, a computerized method would be a practical solution for design validation with a large number of virtual individuals [20; 21]. A virtual fit analysis method that simulates the fit of a product design using the 3D face images of users and the CAD of the product still lacks its applicability to developing an ergonomic design of mask which is optimized for a large number of users. Virtual fit analysis methods have been introduced in designing wearable products such as clothing [22; 23; 24; 25], helmet [26; 27], and mask [15; 21; 28]. The previous studies focus on the analysis of fit between a product and the human body under a particular placement condition (e.g., the placement of a product to a predefined location of the human body) or the development of a custom design for a particular user. Studies including [PERSON] et al. [29] and [PERSON] et al. [30] applied the finite element analysis (FEA) using an FEA program such as ANSYS (ANSYS Inc., Canonsburg, PA, USA) to analyze the fit of a mask by estimating the contact pressure of a mask to the face. However, very few face models and mask designs were considered in the FEA studies due to the complex procedure and high demand of time to manipulate 3D face images and mask designs in an FEA program. Thus, the FEA approach shows limited applicability to virtual fit simulation for a large number of 3D faces (say, over 100 faces) in developing an ergonomic design of mask that is appropriate to a designated percentage (say, 90%) of the target population. Furthermore, an efficient method for virtual design validation and design optimization needs to be explored. The present study is intended to develop a virtual fit analysis method to develop an ergonomic design of a pilot oxygen mask for a particular user population.