# A Boundary Zone Method for the Generation of Multivariate Representative Humanoids
## 1 Introduction  
A small group of digital humanoids (manikins, human models, or cases) representing the target population is used in the ergonomics design and evaluation of products and workstations in a digital environment such as JACK(r) and RAMSIS(r). The use of a small group of representative humanoids (RHs) enables designers to efficiently apply the body size characteristics of the target population to product design and evaluation [1; 2]. Thus, RHs need to be carefully determined to develop an ergonomics design suitable for a designated accommodation percentage (\(\kappa\)) of the target population [3; 4]. The percentile RH generation method is commonly employed for its simplicity, although it is often criticized in terms of multivariate accommodation. [PERSON] et al. [5] evaluated an ergonomics design of a bus operator's workstation using 5 th, 50 th, and 95 th percentile humanoids specified by SAE J833 in a digital human simulation system. The percentile method determines the body sizes of RHs using designated percentile values of individual anthropometric dimensions (ADs) under consideration [2]. RHs created by the percentile method can accommodate a designated percentage of the target population for each individual AD, but not for multiple ADs [6; 7]. For example, in designing the height and width of a bus door for 95% of the U.S. population using 1988 U.S. Army anthropometric data ([PERSON] et al., 1988), the percentile method uses a 95 th percentile humanoid with a 95 th percentile stature (183.8 cm) and a 95 th percentile bideltoid breadth (41.8 cm). In this example, the height and width of the door would meet the designated \(\kappa\) if the stature and bideltoid breadth of the target population are considered independently, but become unsatisfactoryif both the ADs are considered simultaneously--only 91.8% of the target population are smaller both in stature and bideltoid breadth than the 95 th percentile humanoid. To overcome the multivariate accommodation limitation of the percentile method, multivariate RH generation methods such as the _rectangular_, _square_, and _circular_ methods (operationally termed in the present study) were developed using variable reduction techniques such as factor analysis (FA) and principal component analysis (PCA). The square method (SM; Figure 1a) generates RHs at the centroid and corners of a square boundary formed in the space of factors extracted by FA [8; 9]. Next, the rectangular method (RM; Figure 1b) follows the same technique used in the SM, except it uses a rectangular boundary formed to statistically enclose a designated percentage of the population, as proposed by [PERSON] and [PERSON] [10]. Lastly, the circular method (CM; Figure 1c) employs PCA for variable reduction [11; 12] and generates RHs at the centroid and points with a predefined angular interval (e.g., 45\({}^{\circ}\)) on the circular boundary formed in the space of components [13; 14; 15]. Limitations of the existing multivariate generation methods include loss of anthropometric variability, the estimation error of ADs, and lack of body size diversity, as illustrated in Figure 2. Data reduction techniques such as FA and PCA reduce an original set of ADs to a small set of factors or components, while the majority of the body size variability (e.g., 60-97%) of the target population is accounted for, as shown in Table 1. Although this information distillation greatly simplifies the generation process of RHs, a significant proportion (e.g., 3-40%) of the body size variability not explained by extracted factors is lost in the RH generation process. Next, the conversion process of the factor scores of RHs to values of ADs causes significant estimation errors if the extracted factors (or components) are not strongly correlated with the ADs. Lastly, missing zon  
Figure 1: Multivariate generation methods of representative humanoids (RHs). Small dots: Anthropometric cases of a target population; large dots: RHs; dashed lines: Accommodation boundaries.