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Development of a new chinese bra sizing system based on breast anthropometric measurements
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International Journal of Industrial Ergonomics 37 (2007) 697–705 www.elsevier.com/locate/ergon
Development of a new chinese bra sizing system based on breast anthropometric measurements Rong Zheng, Winnie Yu, Jintu Fan Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Received 19 October 2006; received in revised form 25 April 2007; accepted 11 May 2007 Available online 5 July 2007
Abstract Since 1935, the bra sizing system has been based on bust girth and underbust girth. Woman’s breast is however a very complex 3D geometry, the existing sizing system based on just two girth measurements may be inappropriate in the categorization of breast sizes for bras. Through analyzing the nude breast measurements from 456 subjects aged between 20 and 39, we hereby propose a new bra sizing system for Chinese women. The new sizing system uses underbust girth and the breast depth width ratio as the classifying parameters. They were identified through principal component factor analysis and K-means cluster analysis as the two most critical parameters out of 98 measurements obtained from 3D body scanning and 5 supplementary manual measurements as well as other relevant breast parameters including breast angles, distance, width, thickness, volume and curvature. Relevance to industry The existing bra sizing system is inadequate in classifying breast sizes for bras. This paper presents a method for classifying nude breast shape for establishing a new bra sizing system. The application of the new sizing system will be important to improve fitting comfort in intimate apparel. r 2007 Elsevier B.V. All rights reserved. Keywords: Bra sizing system; 3d breast anthropometric measurements; Principle component factor analysis; K-means cluster analysis
1. Introduction Sizing systems are used to fit different groups of the population based on demographic anthropometric data (Winks, 1997; Ashdown, 2003). In the apparel industry, many studies have been conducted aimed at establishing sizing standards for consumers’ body shapes (Armstrong, 1987). However, only very limited researches have been carried out in analyzing the breast shapes, which is yet essential for the design of intimate apparel. The first attempt of establishing bra sizing systems was carried out in 1926 (Morris et al., 2002), in which breast shapes were classified into analogous types. Later, Berlei Underwear Company in Australia carried out a size survey to study women’s figures between 1926 and 1928. It primarily used the circumference of the women’s chest, Corresponding author. Tel.: +852 2766 6525.
E-mail address: [email protected] (W. Yu). 0169-8141/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2007.05.008
bust and underbust to characterize the bra size. Subsequently in 1935, Warner in America incorporated the volume of breasts into the bra size specification. It first advertised the alphabet bras as A cup ¼ youthful, B cup ¼ average, C cup ¼ large and D cup ¼ heavy (Bressler et al., 1998) and such a system became the foundation of modern bra sizing standard. Since then, bra sizing systems have been based on only two measurements: bust girth and underbust girth. However, woman’s breast is a very complex 3D geometry. According to the breast curve side view, Martin (1957) classified the breast shape into four types, including flat, hemisphere, conic and goat shapes. Based on body measurements of 1115 female subjects, Wacoal found that the breast bottom shapes and the orientation of the breasts were two major factors of breasts’ balance (Wacoal Corp., 1995). A good bra sizing system divides the breast shapes scientifically and helps to improve the performance of bra
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fitting. However, many articles (Young, 1995; Lipton, 1996; Boyes, 1996) have reported that 70% of the UK female population, especially the large-breasted women, wore the wrong size bra. Pechter (1998) surveyed 100 women who were wearing the wrong-sized bra 77% of the time. There was a lack of reliable method to measure the breast size precisely (Schlomski, 2001). In order to improve the fitting of bra, medical researchers tried to develop new methods for determining cup size. Pechter (1998) commented that the traditional breast sizing system was frequently inaccurate and useless. As a plastic surgeon, he measured the boundary of the unclothed breast from the lateral breast crease to the anterior breast crease in the determination of cup size. He proposed that a mammary hemi-circumference of 700 corresponded to an ‘‘A’’ cup, 800 to a ‘‘B’’ cup, 900 to a ‘‘C’’ cup, with each 100 increment or decrease determining a cup size up or down. Kanhai and Hage (1999) however added that this formula was only valid for a 34 band size. The size and volume of a B cup on a small ribcage is different from that on a large chest. The same 8’’ mammary hemi-circumference corresponds not only to a 34B, but sometimes also to a 32C or 36A. Morris et al. (2002) proposed a method for calibrating 3D female breast sizes by modeling the breast in its ideal position and shape on the chest wall. They developed a range of 18 standard cup shapes based on 50 subjects’ breast root shapes and dimensions. The above studies on breast measurements, shape classification and sizing are still based on linear correlations rather than breast shape, angle and profile. Based on 3D body scanning data, we therefore aim at developing a new bra sizing system that clusters the Chinese women into different subgroups of breast shape, so as to improve the coverage rate and the fit performance of bra sizing system. 2. Review of the structure of sizing systems A good sizing system should be built based on appropriate anthropometric data to assign a suitable sized garment to an individual (Winks, 1997; Paal, 1997). To obtain accurate measurements for building a sizing system, it is important to control the human subject’s posture, clothing and body landmarks, as well as carefully selecting the measuring devices and relevant measurement items (Zheng et al., 2006). ISO 7250 (1996) specifies the procedures of measuring a naked subject who is wearing minimal clothing and no shoes. The subject stands fully erect with feet together, head in the Frankfurt plane1 and shoulders relaxed with arms hanging freely during measurements. 1 Standard horizontal plane at the level of the upper edge of the opening of the external auditory meatus (external ear opening) and the lower border of the orbital margin (lower edge of the eye socket), when the median plane of the head is held vertically (ISO 7250, 2.2.8).
ISO 15535 (2003) defined the general requirements of establishing anthropometric databases, concerning data collection design, data-collection requirements, database format, database contents, anthropometric data sheets and statistical processing. ISO 20685 (2005) recommends three standing positions for various 3D body scanners to obtain body measurements defined in ISO 7250 that can be extracted from the 3D data. It was suggested that during 3D body scanning, the subject should quietly breathe with shoulders straight, be natural and relaxed. For the structure of sizing systems, a number of research studies have revealed that the systems resulting from either the percentile or the regression analysis methods, based on one or two dimensions, could not adequately represent the variability of complex body dimensions (McCulloch et al., 1998; Ashdown, 1998; Pechoux and Ghosh, 2002). They all commented that the existing sizing systems do not fully satisfy both consumers and manufacturers. The multivariate method is another technique used for establishing sizing systems, based on principal components analysis, which groups a large number of measurement variables into a small set depending on their significance of correlation or covariance. Some surveys utilized this method to cover 90% of the population using bivariate distribution (Salusso et al., 1985–1986; Pechoux and Ghosh, 2002). But the shortcoming is that the size range cannot cover the subjects outside the elliptical area that encompasses 90% of the observations. Paal (1997) and McCulloch et al. (1998) proposed an optimization approach to construct apparel sizing system based on a mathematical model. They revealed that the proposed method for establishing a sizing system could satisfy three aspects: (1) increase the accommodation of the population, (2) reduce the number of sizes in the system, (3) improve overall fit in the accommodated individuals. According to the previous studies, numerous consideration geared to the development of a sizing system: (1) to cover large percentage of the population, (2) to provide good fit for the accommodated (covered) individuals, (3) to use few sizes as far as possible (Gordon and Friedl, 1994; McCulloch et al., 1998) and (4) to show a clear structure containing simple formulas that are easy to understand (Hsu and Wang, 2004). Paal (1997) also mentioned that a sizing system was improved if the performance of any of these criteria is improved without degrading the performance of any other criteria. The current bra sizing system for Chinese women (FZ/T 73012-2004) is a metric sizing system, similar to that used in US, Europe and Japan. As shown in Table 1, the Chinese bra sizing system is structured by underbust girth and the difference between bust girth and underbust girth. In the sizing system, the bra size number directly indicates the underbust girth. For example, a bra size 75 corresponds to an underbust girth of 75 cm. The cup volume is presented by the centimeter difference between the full bust and the underbust measurement. A 12.5 cm difference
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Table 1 The bra sizing system for Chinese women (FZ/T 73012-2004) Cup classification Bust girth minus underbust girth
AA 7.5
A 10
B 12.5
C 15.0
D 17.5
E 20.0
F 22.5
G 25.0
Remark: The middle size of underbust girth is 75 cm and the intersize interval is 5 cm.
means a cup volume B, while cup C’s full bust girth is 15 cm larger than the underbust. However, the existing bra sizing systems have many shortcomings: (a) lack of scientific basis, (b) lack of accuracy, (c) various body proportions within the same size group (Pechter, 1998). 3. Acquisition of 3D breast anthropometric data A new bra sizing system should be developed based on large number of breast measurements. 3.1. Sampling and anthropometric methods The sample used in this study consisted of 456 Chinese female subjects aged between 20 and 39. The subjects were volunteers who were randomly chosen and stratified by area and age. According to ISO 15535 (2003), the age range of the current sample was divided into four age groups: 2024 (n ¼ 61), 2529 (n ¼ 237), 3034 (n ¼ 119) and 3539 (n ¼ 39). According to Chinese geographic segments used in Zhou et al. (1992), 78.3% of the current sample is from the Northeast and North of China, 11.2% from the Midwest of China and 10.5% from Middle and Lower reaches of the Changjiang River. In the sample, 51.1% were married, and about a third of them have children. Data were collected in a size survey carried out in Beijing from 2003 to 2004 using both the VOXELAN 3D laser body scanner and Martin’s anthropometer (Yu, 2004). The following procedures were adopted to ensure subjects stood erect during the processes of manual measurement and 3D body scanning. In the manual measuring process, each subject was asked to wear a close-fitting panty and no bra. She stood erect with bared heels together and opened feet at an angle of about 30 degrees, and looked straight ahead with arms hanging naturally. In order to obtain more reliable data from 3D scanning, the posture was changed with the heels separated by 100–150 mm and the upper arms held apart from the sides of the torso at an angle of 15–20 1. To normalize the orientation of the trunk, the subjects were asked to keep the heels matching the footprints marked on the measuring platform. Body landmarks based on the subcutaneous bone framework of the human body were labeled during the measuring processes (Miyoshi, 2001; Zheng, 2002). 3.2. Breast measurements To obtain more comprehensive measurement variables, 3D body scanning is generally regarded as more complete
and accurate than manual measurement (Jones and Rioux, 1997; Simmons and Istook, 2003; Loker et al., 2005). Therefore, the VOXELAN LPW-2000FW 3D laser body scanner was used in this study. Before the extraction of breast measurements, the 3D data cloud needed to be processed by eliminating redundant points, patching holes, and re-triangulating. The body parts of head, arms and legs were trimmed so that only the upper torso was retained for measuring. A total of 98 measurements were taken to describe the breast shape. Thirty-four items were defined according to ISO 8559 (1989) and ISO 7250 (1996) standards. They include the body circumference, height, width and thickness such as bust girth, underbust girth, body height, shoulder width and so on. Sixty-nine other measurements were newly defined and extracted from the breast cross-section, vertical-section, side profile, breast bottom curve and relevant torso part. They include the breast width, depth angle, distance, area, volume and curvature. To extract the above-mentioned body measurements, different software was used. 3D-rugle (Murakami et al., 1999; Sohmura et al., 2004) was applied to obtain simple measurements such as height, width, thickness and circumference. Rapidform (Lee et al., 2004; Rapidform, 2004) was used to measure detailed breast variables obtained from the cross-sections and the breast bottom curve. Shapeline-3D (Zheng et al., 2004) was useful to analyze the vertical profiles in measuring the angle and projected distance of upper torso. Fig. 1 shows some examples of anthropometric variables measured from the breast sections. Fig. 1(a) shows the perpendicular distance from lowermost point of the breast to the base width line of the breast. Fig. 1(b) illustrates the breast boundary defined for measuring volume. Fig. 1(c) shows two variables measured from the side view profile, T004 is the horizontal distance from front neck point to front waist center and T005 is the horizontal distance from front waist center to bust point. Since the 3D body scanner cannot capture the missing areas such as armhole, five manual measurements including chest girth, weight and fat thickness were added into the data set for investigation. 3.3. Comparison of sample distributions It would be ideal to measuring the entire population before defining the size range and body shape categorization of people. However, this is unrealistic in any sizing system development (Winks, 1997). Therefore, it is
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Fig. 1. Examples of 3D breast anthropometric measurements: (a) Variables measured from breast cross-section, (b) breast area and (c) view profile.
important to identify a representative sample of the population (Ashdown, 2003). In this study, we compared the sample distribution of the key measurements between the current data set and the data set used in the existing Chinese bra sizing system which was established in 1998 and renewed in 2004. It was based on manual measurements of 5507 women collected in 1987, who were randomly sampled and stratified by area and age according to the Chinese population (Zhou et al., 1992). We compared four key measurements relevant to the building of bra sizing system. They included bust girth, underbust girth, weight and height. The sample distributions of the existing system and in the current survey are plotted together for easy comparison. The histograms in Fig. 2 show similar distributions of data in the current survey and the existing Chinese bra sizing system. The data of underbust girth in both surveys are almost normally distributed although there is a short tail on the right. The skewness of both surveys are 0.762 and 0.719, respectively. Similar case happens in the distribution of weight. Skewness of the two samples are, respectively, 0.713 and 0.913. This indicates that the sample used in this study is comparable with the sample used in the existing system. 4. The development of a new bra sizing system using multivariate statistic methods 4.1. Principal component factor analysis Factor analysis is based on a model in which the observed vector is divided into an unobserved systematic part and an unobserved error part. Sharma (1996) advised that factor analysis is aimed to identify the smallest number of common factors that could best explain or account for the correlations among the indicators. Johnson (1998) also mentioned that, five or six principal components might be required to account for more than 70–75% of the total variance for ‘‘people-type’’ data.
In this study, we identified 103 measurements which could be relevant to the breast shape. Principal component factor analysis was used with varimax rotation to determine the optimal groups of factors. The result of the scree plot of initial eigenvalues indicated that 7–14 factors might be optimal, which maintain the magnitude of the unobserved error parts from about 24% to 12%, respectively. The ideal result was determined based on the total quantity of factors, their descriptions and eigenvalues, as well as the cumulative proportion of total sample variance. Based on the observed results, eight factors were regarded as optimal (Table 2), which explain 78.9% of total sample variance and keep a reasonable number of factors. It can be seen that the first factor accounts for 23.5% of the total variance, while the second factor accounts for nearly 20% of the total variance. These two factors account for 43.3% of the total variance. This is much larger than the combined effect of the other six factors. Each factor could be defined according to the estimated factor loadings and communality results. For example, most of variables with relatively high loading in factor 1 were relevant to circumference variables such as underbust girth, chest girth; body build indices variables, e.g. BMI, VHI (Fan et al., 2004); depth and width variables including underbust depth, median chest depth and so on. Therefore, the first factor was labeled as overall body build. The definition of the other factors and the extreme two representative figures of each factor are presented in Fig. 3. 4.2. The breast shape classification based on K-means cluster analysis results In principal component factor analysis, factor loadings are indicators showing which variables are influential in forming new factors. The higher the loading is, the more important the variable is related to the factor score (Sharma, 1996; Johnson and Wichern, 2002). According to the factor loadings, underbust girth was most closely correlated with factor 1 (loading 0.940). With factor 2, both the angle B of right breast cross-section and the breast
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Fig. 2. The distribution histogram comparison of four key measurements for two samples: (a) bust girth; (b) underbust girth; (c) weight; (d) whole body height.
depth width ratio (DWR) had the highest correlations (0.947 and 0.9396, respectively). However, the angle B is difficult to obtain by manual measurement. On the other hand, the variable ‘‘bust girth minus underbust girth’’ presented a relative low correlation of
0.625. The right breast volume, which was normally considered an important indicator of breast shape also showed a lower correlation of 0.642. As mentioned, the first two factors together accounted for 43.26% of the total variance. Considering that a sizing
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Table 2 Summary of principal component factor analysis based on eight factors
Loaded measurements Initial eigenvalues Rotation sums of squared loadings % of variance explained Cumulative proportion of total sample variance explained (%)
Factor 1: overall body build (+) Fat (-) Thin
Factor 5: overall height proportion (+) Tall
(-) Short
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
Factor 7
Factor 8
33 36.98 24.22 23.51 23.51
29 12.58 20.34 19.75 43.26
12 10.66 9.77 9.48 52.74
10 6.17 7.63 7.41 60.15
8 5.09 6.37 6.18 66.33
3 4.09 4.64 4.51 70.84
3 3.14 4.40 4.27 75.11
5 2.59 3.94 3.82 78.93
Factor 2: volume of the breast (+) Large (-) Small
Factor 3: inner breast shape (+)Wide & firm (-) Narrow & low
Factor 6: orientation of the breast (+) Spreading
(-) Close
Factor 7: gradient of the upper breast (+) Slant
(-) Straight
Factor 4: outer breast shape (+) Wide & firm (-) Narrow & low
Factor 8: lower breast shape (+) Round
(-) Flat
Fig. 3. Extreme figures of eight factors.
system should possess a clear structure and should be easy to operate (Hsu and Wang, 2004), the two most important breast parameters in forming factor 1 and factor 2 should be used for classifying the breast shapes. As illustrated in Fig. 4, we have selected two main parameters for the new bra sizing system. They are underbust girth and the breast DWR. Since bras are generally stretched to a range of underbust, measurements to fit the wearer’s ribcage, the existing labelling for the bra’s underband size is reasonable. Therefore, the same 5 cm size interval of underbust girth is suggested remaining unchanged for the new bra sizing system. However, a layered clustering method based on underbust groups was carried out to classify the breast shape. First of all, 456 subjects were classified into different underbust groups from 65 to 100 cm with 5 cm interval according to their underbust girth (see the first column in Table 3). Secondly, a hierarchical clustering was conducted, and then layered K-means cluster analysis was carried out using the variable of breast DWR, referring to the preliminary hierarchical results. Five separate cluster analyses were run with 6, 7, 8, 9 and 10 clusters. Each K-means cluster result was evaluated with
Fig. 4. The two key control measurements for drawing up a new bra sizing system.
practical considerations in minimizing the number of sizes, accommodating the maximum number of subjects and acknowledging probable garment tolerances (Laing et al., 1999). A good sizing system should provide high accommodation rate and use as few sizes as possible (Tryfos, 1986; McCulloch et al., 1998). Although 9 or 10 clusters can accommodate more people, it will increase 8–16 size combinations to the existing bra sizing system. Six or seven
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clusters will decrease 8–16 sizes and cannot provide regular size intervals from one group center to the next. Therefore, eight clusters (Table 3) appeared to be the best choice. It gave similar intervals among subgroups and had the same number of sizes as the existing bra sizing system. Size intervals were adjusted to be even, based on the mode or mean of the centers of the breast shape groups based on the K-means analysis. Table 4 shows the new bra sizing system based on the two key variables—underbust girth and the breast DWR. The cup sizes in the new bra sizing system are denoted by AA* to G*, corresponding to the existing system. 5. Accommodation rate of the two bra sizing systems Based on the existing bra sizing standard FZ/T 730122004, 456 subjects were divided into different bra size
703
groups according to two key measurements—underbust girth and ‘‘bust girth minus underbust girth’’. The results indicate that about 14 subjects (3%) were not covered in the existing system. Common bra sizes are 70A, 75A, 75B, 75C and 80A, each occupies at least 5% of the subjects. Table 5 shows the detailed percentile accommodation rate of the existing bra sizing system. In light of the fact that companies do not manufacture all categories of bra sizes, the partial coverage rates were calculated. In practice, manufacturers tend to ignore the bra size 65 and cups AA or G. The accommodation rate without size 65 declines to 93.7%, and it decreases even more sharply to about 80% when the size 65 and cups AA and G are all excluded. For the new bra sizing system, only five subjects (1%) were not covered. 70A*, 75A*, 75B*, 75C*, 75D*, 80A*,
Table 3 The center points of the breast shape categories and new sizing system center points based on eight clusters Underband size classification (cm)
65 70 75 80 85 90 95 100
The center points of the breast shape categories based on ‘‘the breast depth width ratio’’ Cluster 1
Cluster 2
Cluster 3
Cluster 4
Cluster 5
Cluster 6
0.26 0.25 0.27 0.25 0.25 0.29
0.30 0.30 0.31 0.29 0.31 0.31 0.32
0.33 0.35 0.34 0.33 0.34 0.34
0.37 0.39 0.38 0.38 0.37 0.38 0.38 0.38
0.41 0.42 0.42 0.41 0.41 0.43 0.41
0.46 0.44 0.46 0.45 0.44 0.46
0.38
0.42
0.46
Cluster 7
Cluster 8
0.48 0.50
0.55
0.50 0.51
New bra sizing system center points Adjusted center point
0.25
0.30
0.34
0.50
0.55
Table 4 The new bra sizing system for Chinese women Cup classification The breast ‘‘depth width ratio’’
AA* 0.25
A* 0.30
B* 0.34
C* 0.38
D* 0.42
E* 0.46
F* 0.50
G* 0.55
Remark: The middle size of underbust girth is 75 cm and the intersize interval is 5 cm.
Table 5 Accommodation rates of the existing bra sizing system Underband/cup
AA
A
B
C
65 70 75 80 85 90 95 100
0.88 3.51 5.26 3.29 0.88 0.44 0.22
1.32 5.26 11.4 8.33 4.39 0.88 0.66
0.44 3.51 10.75 4.82 2.85 1.1 0.66 0.22
0.44 3.95 7.46 4.17 1.32 1.1 0.22
Total (%) Without 65 cm underband (%) Without 65 cm underband, AA cup and G cup (%)
D
0.66 1.54 1.54 0.22 0.44 0.22 0.22
E
F
G
0.22 0.22 0.66 0.22 1.1
96.99 93.69 80.09
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Table 6 Accommodation rates of the new bra sizing system Underband/cup
AA*
A*
B*
C*
D*
E*
65 70 75 80 85 90 95 100
0.66 1.97 2.19 2.63 0.66
0.88 4.39 9.43 5.7 2.63 0.88 0.22
0.88 3.51 10.75 5.04 3.07 1.32 0.22
0.44 3.95 7.24 5.26 1.97 0.44 0.66 0.44
0.22 2.19 4.61 3.51 2.19 0.66 0.44
0.22 0.88 2.41 1.1 0.88 0.22
Total (%) Without 65 cm underband (%) Without 65 cm underband, AA* cup and G* cup (%)
80B* and 80C* are the most popular bra sizes. Each covers 5% or more subjects. The detailed percentile accommodation rate of the new bra sizing system is presented in Table 6. The r esults revealed that the partial coverage rate without size 65 showed a higher percentage of 95.4%. Particularly, the partial coverage rate without size 65, cups AA* and G* reaches a much higher coverage of around 87.5%. 6. Conclusion In this study, two multivariate statistical methods, including principal component factor analysis and K-means cluster analysis, were used to determine the sizing criteria and to establish a new bra sizing system for Chinese women based on 456 subjects and a set of 103 static anthropometric variables. Eight factors have been identified to describe the breast shape. A new bra sizing system has been developed based on two key variables— underbust girth and breast depth width ratio DWR. They had the highest factor loading on factor 1 and factor 2 in the principal component factor analysis. This is the first time that a bra sizing system protocol has been proposed based on 3D nude breast characteristics. Besides the intimate apparel industry, the new breast sizing system may be applied in the medical field to identify the breast size for plastic surgery or other apparel product development. Acknowledgments The authors would like to acknowledge the funding support from ITS/028/03 (Development of Innovative Apparel Products and Evaluation Technology) project of ITF (Innovation and Technology Fund). We also thank the 3D body scan data provided by AIMER HEC-BICT (Aimer Human Engineering Research Centre of the Beijing Institute of Clothing Technology).
F*
0.22 0.44
G*
0.44
0.44 0.22 98.72 95.42 87.53
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International Journal of Industrial Ergonomics 37 (2007) 697–705 www.elsevier.com/locate/ergon
Development of a new chinese bra sizing system based on breast anthropometric measurements Rong Zheng, Winnie Yu, Jintu Fan Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Received 19 October 2006; received in revised form 25 April 2007; accepted 11 May 2007 Available online 5 July 2007
Abstract Since 1935, the bra sizing system has been based on bust girth and underbust girth. Woman’s breast is however a very complex 3D geometry, the existing sizing system based on just two girth measurements may be inappropriate in the categorization of breast sizes for bras. Through analyzing the nude breast measurements from 456 subjects aged between 20 and 39, we hereby propose a new bra sizing system for Chinese women. The new sizing system uses underbust girth and the breast depth width ratio as the classifying parameters. They were identified through principal component factor analysis and K-means cluster analysis as the two most critical parameters out of 98 measurements obtained from 3D body scanning and 5 supplementary manual measurements as well as other relevant breast parameters including breast angles, distance, width, thickness, volume and curvature. Relevance to industry The existing bra sizing system is inadequate in classifying breast sizes for bras. This paper presents a method for classifying nude breast shape for establishing a new bra sizing system. The application of the new sizing system will be important to improve fitting comfort in intimate apparel. r 2007 Elsevier B.V. All rights reserved. Keywords: Bra sizing system; 3d breast anthropometric measurements; Principle component factor analysis; K-means cluster analysis
1. Introduction Sizing systems are used to fit different groups of the population based on demographic anthropometric data (Winks, 1997; Ashdown, 2003). In the apparel industry, many studies have been conducted aimed at establishing sizing standards for consumers’ body shapes (Armstrong, 1987). However, only very limited researches have been carried out in analyzing the breast shapes, which is yet essential for the design of intimate apparel. The first attempt of establishing bra sizing systems was carried out in 1926 (Morris et al., 2002), in which breast shapes were classified into analogous types. Later, Berlei Underwear Company in Australia carried out a size survey to study women’s figures between 1926 and 1928. It primarily used the circumference of the women’s chest, Corresponding author. Tel.: +852 2766 6525.
E-mail address: [email protected] (W. Yu). 0169-8141/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2007.05.008
bust and underbust to characterize the bra size. Subsequently in 1935, Warner in America incorporated the volume of breasts into the bra size specification. It first advertised the alphabet bras as A cup ¼ youthful, B cup ¼ average, C cup ¼ large and D cup ¼ heavy (Bressler et al., 1998) and such a system became the foundation of modern bra sizing standard. Since then, bra sizing systems have been based on only two measurements: bust girth and underbust girth. However, woman’s breast is a very complex 3D geometry. According to the breast curve side view, Martin (1957) classified the breast shape into four types, including flat, hemisphere, conic and goat shapes. Based on body measurements of 1115 female subjects, Wacoal found that the breast bottom shapes and the orientation of the breasts were two major factors of breasts’ balance (Wacoal Corp., 1995). A good bra sizing system divides the breast shapes scientifically and helps to improve the performance of bra
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fitting. However, many articles (Young, 1995; Lipton, 1996; Boyes, 1996) have reported that 70% of the UK female population, especially the large-breasted women, wore the wrong size bra. Pechter (1998) surveyed 100 women who were wearing the wrong-sized bra 77% of the time. There was a lack of reliable method to measure the breast size precisely (Schlomski, 2001). In order to improve the fitting of bra, medical researchers tried to develop new methods for determining cup size. Pechter (1998) commented that the traditional breast sizing system was frequently inaccurate and useless. As a plastic surgeon, he measured the boundary of the unclothed breast from the lateral breast crease to the anterior breast crease in the determination of cup size. He proposed that a mammary hemi-circumference of 700 corresponded to an ‘‘A’’ cup, 800 to a ‘‘B’’ cup, 900 to a ‘‘C’’ cup, with each 100 increment or decrease determining a cup size up or down. Kanhai and Hage (1999) however added that this formula was only valid for a 34 band size. The size and volume of a B cup on a small ribcage is different from that on a large chest. The same 8’’ mammary hemi-circumference corresponds not only to a 34B, but sometimes also to a 32C or 36A. Morris et al. (2002) proposed a method for calibrating 3D female breast sizes by modeling the breast in its ideal position and shape on the chest wall. They developed a range of 18 standard cup shapes based on 50 subjects’ breast root shapes and dimensions. The above studies on breast measurements, shape classification and sizing are still based on linear correlations rather than breast shape, angle and profile. Based on 3D body scanning data, we therefore aim at developing a new bra sizing system that clusters the Chinese women into different subgroups of breast shape, so as to improve the coverage rate and the fit performance of bra sizing system. 2. Review of the structure of sizing systems A good sizing system should be built based on appropriate anthropometric data to assign a suitable sized garment to an individual (Winks, 1997; Paal, 1997). To obtain accurate measurements for building a sizing system, it is important to control the human subject’s posture, clothing and body landmarks, as well as carefully selecting the measuring devices and relevant measurement items (Zheng et al., 2006). ISO 7250 (1996) specifies the procedures of measuring a naked subject who is wearing minimal clothing and no shoes. The subject stands fully erect with feet together, head in the Frankfurt plane1 and shoulders relaxed with arms hanging freely during measurements. 1 Standard horizontal plane at the level of the upper edge of the opening of the external auditory meatus (external ear opening) and the lower border of the orbital margin (lower edge of the eye socket), when the median plane of the head is held vertically (ISO 7250, 2.2.8).
ISO 15535 (2003) defined the general requirements of establishing anthropometric databases, concerning data collection design, data-collection requirements, database format, database contents, anthropometric data sheets and statistical processing. ISO 20685 (2005) recommends three standing positions for various 3D body scanners to obtain body measurements defined in ISO 7250 that can be extracted from the 3D data. It was suggested that during 3D body scanning, the subject should quietly breathe with shoulders straight, be natural and relaxed. For the structure of sizing systems, a number of research studies have revealed that the systems resulting from either the percentile or the regression analysis methods, based on one or two dimensions, could not adequately represent the variability of complex body dimensions (McCulloch et al., 1998; Ashdown, 1998; Pechoux and Ghosh, 2002). They all commented that the existing sizing systems do not fully satisfy both consumers and manufacturers. The multivariate method is another technique used for establishing sizing systems, based on principal components analysis, which groups a large number of measurement variables into a small set depending on their significance of correlation or covariance. Some surveys utilized this method to cover 90% of the population using bivariate distribution (Salusso et al., 1985–1986; Pechoux and Ghosh, 2002). But the shortcoming is that the size range cannot cover the subjects outside the elliptical area that encompasses 90% of the observations. Paal (1997) and McCulloch et al. (1998) proposed an optimization approach to construct apparel sizing system based on a mathematical model. They revealed that the proposed method for establishing a sizing system could satisfy three aspects: (1) increase the accommodation of the population, (2) reduce the number of sizes in the system, (3) improve overall fit in the accommodated individuals. According to the previous studies, numerous consideration geared to the development of a sizing system: (1) to cover large percentage of the population, (2) to provide good fit for the accommodated (covered) individuals, (3) to use few sizes as far as possible (Gordon and Friedl, 1994; McCulloch et al., 1998) and (4) to show a clear structure containing simple formulas that are easy to understand (Hsu and Wang, 2004). Paal (1997) also mentioned that a sizing system was improved if the performance of any of these criteria is improved without degrading the performance of any other criteria. The current bra sizing system for Chinese women (FZ/T 73012-2004) is a metric sizing system, similar to that used in US, Europe and Japan. As shown in Table 1, the Chinese bra sizing system is structured by underbust girth and the difference between bust girth and underbust girth. In the sizing system, the bra size number directly indicates the underbust girth. For example, a bra size 75 corresponds to an underbust girth of 75 cm. The cup volume is presented by the centimeter difference between the full bust and the underbust measurement. A 12.5 cm difference
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Table 1 The bra sizing system for Chinese women (FZ/T 73012-2004) Cup classification Bust girth minus underbust girth
AA 7.5
A 10
B 12.5
C 15.0
D 17.5
E 20.0
F 22.5
G 25.0
Remark: The middle size of underbust girth is 75 cm and the intersize interval is 5 cm.
means a cup volume B, while cup C’s full bust girth is 15 cm larger than the underbust. However, the existing bra sizing systems have many shortcomings: (a) lack of scientific basis, (b) lack of accuracy, (c) various body proportions within the same size group (Pechter, 1998). 3. Acquisition of 3D breast anthropometric data A new bra sizing system should be developed based on large number of breast measurements. 3.1. Sampling and anthropometric methods The sample used in this study consisted of 456 Chinese female subjects aged between 20 and 39. The subjects were volunteers who were randomly chosen and stratified by area and age. According to ISO 15535 (2003), the age range of the current sample was divided into four age groups: 2024 (n ¼ 61), 2529 (n ¼ 237), 3034 (n ¼ 119) and 3539 (n ¼ 39). According to Chinese geographic segments used in Zhou et al. (1992), 78.3% of the current sample is from the Northeast and North of China, 11.2% from the Midwest of China and 10.5% from Middle and Lower reaches of the Changjiang River. In the sample, 51.1% were married, and about a third of them have children. Data were collected in a size survey carried out in Beijing from 2003 to 2004 using both the VOXELAN 3D laser body scanner and Martin’s anthropometer (Yu, 2004). The following procedures were adopted to ensure subjects stood erect during the processes of manual measurement and 3D body scanning. In the manual measuring process, each subject was asked to wear a close-fitting panty and no bra. She stood erect with bared heels together and opened feet at an angle of about 30 degrees, and looked straight ahead with arms hanging naturally. In order to obtain more reliable data from 3D scanning, the posture was changed with the heels separated by 100–150 mm and the upper arms held apart from the sides of the torso at an angle of 15–20 1. To normalize the orientation of the trunk, the subjects were asked to keep the heels matching the footprints marked on the measuring platform. Body landmarks based on the subcutaneous bone framework of the human body were labeled during the measuring processes (Miyoshi, 2001; Zheng, 2002). 3.2. Breast measurements To obtain more comprehensive measurement variables, 3D body scanning is generally regarded as more complete
and accurate than manual measurement (Jones and Rioux, 1997; Simmons and Istook, 2003; Loker et al., 2005). Therefore, the VOXELAN LPW-2000FW 3D laser body scanner was used in this study. Before the extraction of breast measurements, the 3D data cloud needed to be processed by eliminating redundant points, patching holes, and re-triangulating. The body parts of head, arms and legs were trimmed so that only the upper torso was retained for measuring. A total of 98 measurements were taken to describe the breast shape. Thirty-four items were defined according to ISO 8559 (1989) and ISO 7250 (1996) standards. They include the body circumference, height, width and thickness such as bust girth, underbust girth, body height, shoulder width and so on. Sixty-nine other measurements were newly defined and extracted from the breast cross-section, vertical-section, side profile, breast bottom curve and relevant torso part. They include the breast width, depth angle, distance, area, volume and curvature. To extract the above-mentioned body measurements, different software was used. 3D-rugle (Murakami et al., 1999; Sohmura et al., 2004) was applied to obtain simple measurements such as height, width, thickness and circumference. Rapidform (Lee et al., 2004; Rapidform, 2004) was used to measure detailed breast variables obtained from the cross-sections and the breast bottom curve. Shapeline-3D (Zheng et al., 2004) was useful to analyze the vertical profiles in measuring the angle and projected distance of upper torso. Fig. 1 shows some examples of anthropometric variables measured from the breast sections. Fig. 1(a) shows the perpendicular distance from lowermost point of the breast to the base width line of the breast. Fig. 1(b) illustrates the breast boundary defined for measuring volume. Fig. 1(c) shows two variables measured from the side view profile, T004 is the horizontal distance from front neck point to front waist center and T005 is the horizontal distance from front waist center to bust point. Since the 3D body scanner cannot capture the missing areas such as armhole, five manual measurements including chest girth, weight and fat thickness were added into the data set for investigation. 3.3. Comparison of sample distributions It would be ideal to measuring the entire population before defining the size range and body shape categorization of people. However, this is unrealistic in any sizing system development (Winks, 1997). Therefore, it is
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Fig. 1. Examples of 3D breast anthropometric measurements: (a) Variables measured from breast cross-section, (b) breast area and (c) view profile.
important to identify a representative sample of the population (Ashdown, 2003). In this study, we compared the sample distribution of the key measurements between the current data set and the data set used in the existing Chinese bra sizing system which was established in 1998 and renewed in 2004. It was based on manual measurements of 5507 women collected in 1987, who were randomly sampled and stratified by area and age according to the Chinese population (Zhou et al., 1992). We compared four key measurements relevant to the building of bra sizing system. They included bust girth, underbust girth, weight and height. The sample distributions of the existing system and in the current survey are plotted together for easy comparison. The histograms in Fig. 2 show similar distributions of data in the current survey and the existing Chinese bra sizing system. The data of underbust girth in both surveys are almost normally distributed although there is a short tail on the right. The skewness of both surveys are 0.762 and 0.719, respectively. Similar case happens in the distribution of weight. Skewness of the two samples are, respectively, 0.713 and 0.913. This indicates that the sample used in this study is comparable with the sample used in the existing system. 4. The development of a new bra sizing system using multivariate statistic methods 4.1. Principal component factor analysis Factor analysis is based on a model in which the observed vector is divided into an unobserved systematic part and an unobserved error part. Sharma (1996) advised that factor analysis is aimed to identify the smallest number of common factors that could best explain or account for the correlations among the indicators. Johnson (1998) also mentioned that, five or six principal components might be required to account for more than 70–75% of the total variance for ‘‘people-type’’ data.
In this study, we identified 103 measurements which could be relevant to the breast shape. Principal component factor analysis was used with varimax rotation to determine the optimal groups of factors. The result of the scree plot of initial eigenvalues indicated that 7–14 factors might be optimal, which maintain the magnitude of the unobserved error parts from about 24% to 12%, respectively. The ideal result was determined based on the total quantity of factors, their descriptions and eigenvalues, as well as the cumulative proportion of total sample variance. Based on the observed results, eight factors were regarded as optimal (Table 2), which explain 78.9% of total sample variance and keep a reasonable number of factors. It can be seen that the first factor accounts for 23.5% of the total variance, while the second factor accounts for nearly 20% of the total variance. These two factors account for 43.3% of the total variance. This is much larger than the combined effect of the other six factors. Each factor could be defined according to the estimated factor loadings and communality results. For example, most of variables with relatively high loading in factor 1 were relevant to circumference variables such as underbust girth, chest girth; body build indices variables, e.g. BMI, VHI (Fan et al., 2004); depth and width variables including underbust depth, median chest depth and so on. Therefore, the first factor was labeled as overall body build. The definition of the other factors and the extreme two representative figures of each factor are presented in Fig. 3. 4.2. The breast shape classification based on K-means cluster analysis results In principal component factor analysis, factor loadings are indicators showing which variables are influential in forming new factors. The higher the loading is, the more important the variable is related to the factor score (Sharma, 1996; Johnson and Wichern, 2002). According to the factor loadings, underbust girth was most closely correlated with factor 1 (loading 0.940). With factor 2, both the angle B of right breast cross-section and the breast
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Fig. 2. The distribution histogram comparison of four key measurements for two samples: (a) bust girth; (b) underbust girth; (c) weight; (d) whole body height.
depth width ratio (DWR) had the highest correlations (0.947 and 0.9396, respectively). However, the angle B is difficult to obtain by manual measurement. On the other hand, the variable ‘‘bust girth minus underbust girth’’ presented a relative low correlation of
0.625. The right breast volume, which was normally considered an important indicator of breast shape also showed a lower correlation of 0.642. As mentioned, the first two factors together accounted for 43.26% of the total variance. Considering that a sizing
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Table 2 Summary of principal component factor analysis based on eight factors
Loaded measurements Initial eigenvalues Rotation sums of squared loadings % of variance explained Cumulative proportion of total sample variance explained (%)
Factor 1: overall body build (+) Fat (-) Thin
Factor 5: overall height proportion (+) Tall
(-) Short
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
Factor 7
Factor 8
33 36.98 24.22 23.51 23.51
29 12.58 20.34 19.75 43.26
12 10.66 9.77 9.48 52.74
10 6.17 7.63 7.41 60.15
8 5.09 6.37 6.18 66.33
3 4.09 4.64 4.51 70.84
3 3.14 4.40 4.27 75.11
5 2.59 3.94 3.82 78.93
Factor 2: volume of the breast (+) Large (-) Small
Factor 3: inner breast shape (+)Wide & firm (-) Narrow & low
Factor 6: orientation of the breast (+) Spreading
(-) Close
Factor 7: gradient of the upper breast (+) Slant
(-) Straight
Factor 4: outer breast shape (+) Wide & firm (-) Narrow & low
Factor 8: lower breast shape (+) Round
(-) Flat
Fig. 3. Extreme figures of eight factors.
system should possess a clear structure and should be easy to operate (Hsu and Wang, 2004), the two most important breast parameters in forming factor 1 and factor 2 should be used for classifying the breast shapes. As illustrated in Fig. 4, we have selected two main parameters for the new bra sizing system. They are underbust girth and the breast DWR. Since bras are generally stretched to a range of underbust, measurements to fit the wearer’s ribcage, the existing labelling for the bra’s underband size is reasonable. Therefore, the same 5 cm size interval of underbust girth is suggested remaining unchanged for the new bra sizing system. However, a layered clustering method based on underbust groups was carried out to classify the breast shape. First of all, 456 subjects were classified into different underbust groups from 65 to 100 cm with 5 cm interval according to their underbust girth (see the first column in Table 3). Secondly, a hierarchical clustering was conducted, and then layered K-means cluster analysis was carried out using the variable of breast DWR, referring to the preliminary hierarchical results. Five separate cluster analyses were run with 6, 7, 8, 9 and 10 clusters. Each K-means cluster result was evaluated with
Fig. 4. The two key control measurements for drawing up a new bra sizing system.
practical considerations in minimizing the number of sizes, accommodating the maximum number of subjects and acknowledging probable garment tolerances (Laing et al., 1999). A good sizing system should provide high accommodation rate and use as few sizes as possible (Tryfos, 1986; McCulloch et al., 1998). Although 9 or 10 clusters can accommodate more people, it will increase 8–16 size combinations to the existing bra sizing system. Six or seven
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clusters will decrease 8–16 sizes and cannot provide regular size intervals from one group center to the next. Therefore, eight clusters (Table 3) appeared to be the best choice. It gave similar intervals among subgroups and had the same number of sizes as the existing bra sizing system. Size intervals were adjusted to be even, based on the mode or mean of the centers of the breast shape groups based on the K-means analysis. Table 4 shows the new bra sizing system based on the two key variables—underbust girth and the breast DWR. The cup sizes in the new bra sizing system are denoted by AA* to G*, corresponding to the existing system. 5. Accommodation rate of the two bra sizing systems Based on the existing bra sizing standard FZ/T 730122004, 456 subjects were divided into different bra size
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groups according to two key measurements—underbust girth and ‘‘bust girth minus underbust girth’’. The results indicate that about 14 subjects (3%) were not covered in the existing system. Common bra sizes are 70A, 75A, 75B, 75C and 80A, each occupies at least 5% of the subjects. Table 5 shows the detailed percentile accommodation rate of the existing bra sizing system. In light of the fact that companies do not manufacture all categories of bra sizes, the partial coverage rates were calculated. In practice, manufacturers tend to ignore the bra size 65 and cups AA or G. The accommodation rate without size 65 declines to 93.7%, and it decreases even more sharply to about 80% when the size 65 and cups AA and G are all excluded. For the new bra sizing system, only five subjects (1%) were not covered. 70A*, 75A*, 75B*, 75C*, 75D*, 80A*,
Table 3 The center points of the breast shape categories and new sizing system center points based on eight clusters Underband size classification (cm)
65 70 75 80 85 90 95 100
The center points of the breast shape categories based on ‘‘the breast depth width ratio’’ Cluster 1
Cluster 2
Cluster 3
Cluster 4
Cluster 5
Cluster 6
0.26 0.25 0.27 0.25 0.25 0.29
0.30 0.30 0.31 0.29 0.31 0.31 0.32
0.33 0.35 0.34 0.33 0.34 0.34
0.37 0.39 0.38 0.38 0.37 0.38 0.38 0.38
0.41 0.42 0.42 0.41 0.41 0.43 0.41
0.46 0.44 0.46 0.45 0.44 0.46
0.38
0.42
0.46
Cluster 7
Cluster 8
0.48 0.50
0.55
0.50 0.51
New bra sizing system center points Adjusted center point
0.25
0.30
0.34
0.50
0.55
Table 4 The new bra sizing system for Chinese women Cup classification The breast ‘‘depth width ratio’’
AA* 0.25
A* 0.30
B* 0.34
C* 0.38
D* 0.42
E* 0.46
F* 0.50
G* 0.55
Remark: The middle size of underbust girth is 75 cm and the intersize interval is 5 cm.
Table 5 Accommodation rates of the existing bra sizing system Underband/cup
AA
A
B
C
65 70 75 80 85 90 95 100
0.88 3.51 5.26 3.29 0.88 0.44 0.22
1.32 5.26 11.4 8.33 4.39 0.88 0.66
0.44 3.51 10.75 4.82 2.85 1.1 0.66 0.22
0.44 3.95 7.46 4.17 1.32 1.1 0.22
Total (%) Without 65 cm underband (%) Without 65 cm underband, AA cup and G cup (%)
D
0.66 1.54 1.54 0.22 0.44 0.22 0.22
E
F
G
0.22 0.22 0.66 0.22 1.1
96.99 93.69 80.09
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Table 6 Accommodation rates of the new bra sizing system Underband/cup
AA*
A*
B*
C*
D*
E*
65 70 75 80 85 90 95 100
0.66 1.97 2.19 2.63 0.66
0.88 4.39 9.43 5.7 2.63 0.88 0.22
0.88 3.51 10.75 5.04 3.07 1.32 0.22
0.44 3.95 7.24 5.26 1.97 0.44 0.66 0.44
0.22 2.19 4.61 3.51 2.19 0.66 0.44
0.22 0.88 2.41 1.1 0.88 0.22
Total (%) Without 65 cm underband (%) Without 65 cm underband, AA* cup and G* cup (%)
80B* and 80C* are the most popular bra sizes. Each covers 5% or more subjects. The detailed percentile accommodation rate of the new bra sizing system is presented in Table 6. The r esults revealed that the partial coverage rate without size 65 showed a higher percentage of 95.4%. Particularly, the partial coverage rate without size 65, cups AA* and G* reaches a much higher coverage of around 87.5%. 6. Conclusion In this study, two multivariate statistical methods, including principal component factor analysis and K-means cluster analysis, were used to determine the sizing criteria and to establish a new bra sizing system for Chinese women based on 456 subjects and a set of 103 static anthropometric variables. Eight factors have been identified to describe the breast shape. A new bra sizing system has been developed based on two key variables— underbust girth and breast depth width ratio DWR. They had the highest factor loading on factor 1 and factor 2 in the principal component factor analysis. This is the first time that a bra sizing system protocol has been proposed based on 3D nude breast characteristics. Besides the intimate apparel industry, the new breast sizing system may be applied in the medical field to identify the breast size for plastic surgery or other apparel product development. Acknowledgments The authors would like to acknowledge the funding support from ITS/028/03 (Development of Innovative Apparel Products and Evaluation Technology) project of ITF (Innovation and Technology Fund). We also thank the 3D body scan data provided by AIMER HEC-BICT (Aimer Human Engineering Research Centre of the Beijing Institute of Clothing Technology).
F*
0.22 0.44
G*
0.44
0.44 0.22 98.72 95.42 87.53
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