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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.1 pp.102-112
DOI : https://doi.org/10.7232/iems.2018.17.1.102

The Relationship between Dirt Levels of Inspection Surface and Defect Detection in Visual Inspection Utilizing Peripheral Vision

Ryosuke Nakajima*, Yuta Asano, Takuya Hida, Toshiyuki Matsumoto
Department of Systems Design Engineering, Seikei University, Tokyo, Japan
Department of Industrial Engineering & Systems Engineering, Aoyama Gakuin University, Kanagawa, Japan
Corresponding Author, nakajima@st.seikei.ac.jp
December 3, 2016 May 24, 2017 November 29, 2017

ABSTRACT


This study focuses on adhered dirt such as dust on a product in production process, and considers the relationship between dirt levels of inspection surface and defect detection in visual inspection utilizing peripheral vision. Specifically, images of an inspection surface in an actual factory are analyzed using image analysis for modeling dirt. Moreover, dirt levels of inspection surface, defect locations, and defect characteristics (luminance contrast, size, and bright-dark defects) are designed as experimental factors, and their effect on defect detection rate is evaluated. As a result, it is clarified that the defect detection rate suddenly reduces as the inspection surface becomes dirtier. Consequently, the defects that can be detected easily becomes harder to detect, as the inspection surface is dirtier in visual inspection utilizing peripheral vision.



초록


    1. INTRODUCTION

    In order to supply high-quality products to the market, manufacturing industries have given product inspection as much attention as processing and assembling. There are two types of inspections: functional inspection and appearance inspection. In functional inspection, the effectiveness of a product is inspected. In appearance inspection, visual defects such as scratches, surface dents, and unevenness of the coating color are inspected. Automation of functional inspection has advanced because it is easy to determine whether a product works or not (Aiyama, 2014; Aoki, 2014). However, it is not as simple to establish the standards to determine whether the appearance of a product is defective. First, there are many different types of defects. Second, categorization of a product as non-defective or defective is affected by the size and depth of the defect. Third, some products have recently become smaller and more detailed. Finally, production has shifted to high-mix and low-volume production. It is thus difficult to develop technologies that can discover small defects and to create algorithms that identify multiple types of defects with high precision. Therefore, appearance inspection still depends on visual inspection, which relies on human senses (Nayatani et al., 1982; Nickles et al., 2003; Yeow and Sen, 2004; Chang et al., 2009; Lee and Chan, 2009).

    Recently, a visual inspection method utilizing peripheral vision has been proposed (Sasaki, 2005, 2006), and its effectiveness has been reported by manufacturing factories (Sugawara et al., 2011). Human vision is divided into two ranges. Central vision is the 1-2° range of vision on either side of the center of the retina. The remaining range of vision is called peripheral vision. The spatial resolution of human vision decreases significantly as the angle from the center of the retina increases (Ikeda, 2004). Conventionally, an inspection method by scanning the entire product with only the central vision is performed, because of the instruction received by the inspectors from the managers to “just inspect carefully.” In this method, as the visual information to be processed by the inspector increases, degradation of the inspection accuracy and efficiency is induced. On the other hand, the visual inspection method utilizing peripheral vision is performed with both the peripheral vision and central vision. It involves two processes: first, a wide range is searched by the peripheral vision; then, the defect is decided by the high spatial resolution of the central vision. Thus, low-level processes such as sampling and characteristics clustering are processed by peripheral vision, next high-level processes such as discrimination is processes by the central vision to reduce the amount of information to be processed. From this, an efficient visual information processing is realized (Yoshida et al., 1992), the visual inspection method utilizing peripheral vision, which can be realized high accurate inspection in a short time has been expected.

    In order to prevent dust in the air and on clothing from adhering to a product, it is generally recommended that visual inspection for a high-quality product be performed in a clean room (Murata, 2010; Takase, 2012; Tazaki, 2013). However, in situations where the production process becomes more complex and more outsourcing in recent years, visual inspection is not often performed in a clean room. Further, there are many cases where visual inspection process is not a clean room because of constraints of existing equipment and economic problems. According to a questionnaire survey on the problems of actual manufacturing industries, which perform visual inspections, there are many opinions that “there is no margin in terms of financing” and “it is difficult to determine an appropriate inspection environment and/or method” (Hongou, 2016). Under such a scenario, although there are some variations of dirt levels of an inspection surface depending on manufacturing industries, a product must be visually inspected on a dirty inspection surface. That is, in a situation where both the dirt that can be cleaned and the defect that cannot be removed are mixed, inspectors are required to detect only the defect. This causes reduced defect detection accuracy.

    This study focuses on adhered dirt such as dust on a product in production process, in order to consider the relationship between the dirt levels of inspection surface and the defect detection accuracy. First, this study analyzes the images of inspection surfaces in an actual factory and then creates an inspection model for dirt density based on the pixel values of the images. Second, this study designs experiments using dirt levels of inspection surface, defect locations, and defect characteristics as experimental factors. Finally, the effects of these factors on the defect detection accuracy in visual inspection utilizing peripheral vision are examined.

    2. ANALYSIS AND MODELING OF DIRT

    2.1 Analysis of Dirt in an Actual Factory

    In order to analyze conditions of dirt on an inspection surface, a field survey at Company X, which performs visual inspections, is implemented. This company produces transparent parts for automobiles. Neither the production process nor the visual inspection process is conducted in a clean room. Therefore, the visual inspection is performed in location where the inspection surface is dirty.

    In the field survey, images of different inspection surface used for the visual inspection process were captured by a camera; these images were then sorted in the order of dirt levels. In order to evaluate the distribution of pixel values, the histograms of these images were analyzed as shown in Figure 1. As a result, it was obtained that both the dispersion of pixel values in the image and the shape of the histograms vary with the amount of dirt on the inspection surface.

    2.2 Modeling of Dirt

    2.2.1 Quantification of Dirt

    The analysis method described in Section 2.1 is applied to the inspection surface in the factory to quantify the dirt. That is, continuously distributed analog information such as luminance of inspection surface and adhered dirt is sampled as two-dimensional pixels by taken a digital camera. Next, the luminance of each pixels are quantized as pixel values (Murakami, 2004; Rafael and Richard, 2007). Then, the distribution of the pixel values is quantified as a histogram. Specifically, a known amount of dirt was intentionally scattered on the inspection surface, and the relationship between the applied dirt and the distribution of pixel values in the photographed image is considered.

    As for an inspection surface of a product, a product with a height of 100 mm and a width of 100 mm manufactured in the company was used. As for dirt, powders of diameters between 0.18 to 0.25 mm were used. The powders are scattered during the production processes to prevent the products from coming into contact with each other, and those are one of the typical dirt in the visual inspection process. In general, dust in the air is classified into ultrafine particles (less than 0.01×10-2 mm), submicron particles (between 0.01×10-2 mm to 0.01×10-1 mm), fine particles (between 0.01×10-1 to 0.02×10-1 mm), and coarse particles (0.02×10-1 to about 0.02mm) for each particle size (Japanese Industrial Standards, 1974). Among these particles, the coarse particles are only visible by human naked eyes, and the powders used in this study is assumed the coarse particles in the air. The amount of scattered powder varied from 0.0g to 1.0g, in 0.1g increments, and the histogram for each levels of powder is examined. The results for 0.0g, 0.3g, 0.6g, and 0.9g of dirt are shown in the bar graph in Figure 2. It was obtained that the dispersion of pixel values in the image varies with the amount of scattered powder.

    2.2.2 Formulation of Dirt

    Using the pixel values derived in Section 2.2.1, to formulation of the dirt is considered. Specifically, to determine the dispersion of pixel values for each amount of scattered powder, the kernel density estimation is applied (Schölkopf and Smola, 2002; Akaho, 2008; Hukumizu, 2010). The commonly used Gaussian kernel function k(x) is employed in this study (Bishop, 2006; Xavier, 2006). To capture a distribution of same data, histogram analysis is generally used. However, the result of histogram analysis greatly differs the distribution depending on how to set data classes. Therefore, in this study, the kernel density estimation is used as a method that does not require setting the data classes. From this, the influence of how to set the data classes becomes low, and a smooth distribution based on the measured pixel values is obtained. In this way, the distributions of pixel values for each amount of scattered powder in Section 2.2.1 are estimated using pixel values as population sample data. Then, it is possible to create a digital image described later in Section 2.2.3 according to the distribution estimated for each amount of scattered powder. It is calculated using Equation (1), where x is the frequencies of the pixel value. Bandwidth h is calculated in Equation (2) using the standard deviation, σ, of the frequencies of the pixel values. Then, the kernel dispersion f ^ k (x) is calculated in Equation (3) using the kernel function k(x) and the bandwidth h. The results for 0.0g, 0.3g, 0.6g, and 0.9g of scattered dirt are shown in the line graph in Figure 2. It was found that it is possible to estimate the probability density function of the distribution of pixel values with high accuracy.

    k ( x ) = 1 2 π e 1 2 x 2
    (1)
    h = 0.9 σ 256 1 5
    (2)
    f ^ k ( x ) = 1 256 h i = 0 255 k ( x x i h )
    (3)

    2.2.3 Imaging of Dirt

    Using the probability density function shown in Section 2.2.2, the ability to create images of specific amounts of dirt is considered. In generally, to create a digital image, two steps of sampling and quantization are required (Murakami, 2004; Rafael and Richard, 2007). Sampling step is to determine pixel size of create image; quantization step is to determine density levels of each pixels and to color it according to these levels. In this study, as the sampling step, from minimum pixel size of a monitor (height 0.233mm × width 0.233mm) and size of creating image (height 300mm × width 300mm) which are described in Section 3.1, pixel size of creating images are determined to height 1,288 pixel × width 1,288 pixel. As the quantization step, the pixel values determined to create image based on the probability density function, then the pixels are colored according to the pixel values. The result images generated for 0.0g, 0.3g, 0.6g, and 0.9 g of scattered dirt are shown in image of Figure 3. It is inferred that it is possible to create images corresponding to a specific amount of scattered powder.

    3. EXPERIMENTAL DESIGN

    3.1 Experimental Task

    Experimental subjects are tasked with visual inspection of a model that is displayed on a monitor (CG276, EIZO Inc.). A model with a height of 300 mm, and a width of 300mm, and a black 10 mm diameter circle (used as a fixation point) on the center is used. This model is shown in Figure 4. In order to achieve inspection utilizing peripheral vision, the subjects are requested to detect the defect while fixing at the fixation point during the experiment. However, subjects are allowed to fix the defect by central vision only when detecting the defect by peripheral vision. The subjects are also requested to inspect the inspection model with 1.0 s as a guide. In the experimental tasks, the subjects detected the defect with peripheral vision and could not scan the inspection model with only the central vision. These experimental conditions were determined in reference to a preceding study on the relationship between the fixation time and defect detection accuracy in visual inspection (Nakajima et al., 2013). If no defect is detected, the subject presses the SPACE KEY on the key board, and the next inspection model will be displayed. If a defect is detected, the subject presses the ENTER KEY. The Experimental flow by a subject is shown in Figure 5.

    The experimental layout is shown in Figure 6. In order to ensure a uniform viewing distance between each subject and the inspection model, the chin holder was placed at 400 mm from the inspection model to fix the head of a subject.

    3.2 Experimental Factors

    3.2.1 Dirt Levels of Inspection Surface

    The dirt density for each inspection model is realized by using a background image that is created as described in Section 2.2.3. The four images (corresponding to 0.0g, 0.3g, 0.6g, and 0.9g of scattered dirt) shown in Figure 3 are employed in the experiment. The image for 0.9g of dirt was chosen as the upper limit, after the factory of Company X confirmed that the inspection surface was never dirtier than the image representing 0.9g of dirt. Hereafter, the four types of inspection models will be referred to as: Non dirty (0.0g), Slightly dirty (0.3g), Somewhat dirty (0.6g), and Very dirty (0.9g) respectively.

    3.2.2 Defect Locations

    This study focuses on the visual inspection method utilizing peripheral vision, change in accuracy of defect detection by position of defect in the field of view is verified for each dirt levels of the inspection surface. The inspection model is divided into 16 parts (4×4 horizontally and vertically), and the defect is located at the center of either one of these parts. As shown in Figure 7, the parts are divided into four areas, from area (1) to area (4) according to the distance from the fixation point. The horizontal distance, the vertical distance, and the straight-line distance from the fixation point and the defect are shown in Table 1. In generally, it is shown the spatial resolution of human vision decreases significantly as the angle from the center of the retina increases (Ikeda, 2004). Furthermore, it is shown that the decrease is more pronounced in the vertical direction than in the horizontal direction (Nakajima et al., 2015). That is, in the defect locations of this study, it is expected that the accuracy of defect detection becomes lower in the order of area (1) to area (4).

    3.2.3 Defect Characteristics

    The defect characteristics are defined by the luminance contrast between the inspection model and the defect, and the defect size. The shape of all defects is circular. The luminance contrast of each defect is one of the three different levels: 0.10, 0.15, and 0.20. There are also two types of defects in the factory: those that are darker than the inspection surface, such as scratches, and those that are brighter than the inspection surface, such as adhered inks. Therefore, the luminance contrast of each defect is also specified as either dark or bright.

    The size of the defect is specified by diameters of 1.0mm, 1.5mm, and 2.0mm. These defects are determined by assuming the standards for appearance inspection.

    All defects employed in the experiment are shown in Figure 8. The experiment is conducted for the four different locations (sixteen parts) of defect, three different luminance contrast levels, three different sizes, and two different types of defect (dark and bright). This is equal to 288 (location parts (16) × luminance contrast (3) × size (3) × dark and bright (2)) defective inspection models for each dirt levels of the inspection surface.

    3.3 Experimental Procedure

    Twelve subjects, aged between 21 to 26 years, are employed in this experiment. Only subjects with corrected eyesight score greater than 1.0 are employed. In order to familiarize the subjects with the experiment, an overview and the procedure of the experiment are explained, and a preliminary experiment are tasked. In the preliminary experiment, eye camera (NAC Image Technology Co., Ltd.: EMR-9) is attached to all subjects, and their eye movements are checked to realize visual inspection method utilizing peripheral vision. In the experiment, to inspect 576 (288 non-defective and 288 defective) inspection models is tasked for each dirt levels of inspection surface.

    The experimental room temperature was set between 18 to 24 °C, and the humidity was set between 40 to 60%. In the experiment, the luminance of the inspection model and the defects is realized using only the monitor light. Therefore, to prevent the influence of ambient light such as fluorescent lighting, the experiment was conducted in a dark room. The purpose and contents of the experiment were explained to the subjects in writing, and the informed consent of all the subjects was obtained.

    Using the results of the experiment that are obtained by the above procedures, the defect detection rate is calculated, which is the number of detected defects divided by the number of total defect. It is expressed in Equation (4) and used as the evaluation index.

    Defect detection rate [ % ] = Number of detected defects Number of total defects × 100
    (4)

    4. EXPERIMENTAL RESULTS

    4.1 Individual Characteristics of Subjects

    Using the relationship between the dirt levels of inspection surface and the defect detection is examined. However, it is possible that the individual subjects will also affect the results. Thus, before considering the abovementioned relationship, the uniformity of the results for various subjects is verified.

    The average value and standard deviation of the defect detection rate of the subjects are shown in Figure 9. One-way analysis of variance (ANOVA) is executed with the subjects (12) as for a factor. As a result, a significant difference of 1% is observed for the main effect [F(11, 3157) = 66.49]. It is found that the subjects in the experiment consist of subjects groups with some with variations in their ability to detect defects.

    Therefore, for each dirt levels of inspection surface, defect locations and defect characteristics, the defect detection rate of subject 8 (the subject detecting the highest number of defects), the defect detection rate of subject 7 (the subject detecting the lowest number of defects), and the average value of the defect detection rate of other subjects are shown in Figures 10-a, 10-b, and 10-c, respectively. As results, the following trends are common to all the subjects. As the dirt levels of the inspection surface increases and distance between the fixation point and the defects becomes longer, the defect detection rate decreases. Furthermore, as the amount of defect characteristics increases, the defect detection rate increases for all subjects. That is, it is confirmed that the reason why a significant difference occurs in the defect detection rate between subjects is not abnormal value under a specific condition. In addition, an outlier test (Smirnoff-Grubbs test, significance level 5%) of all subjects for each dirt levels of inspection surface are executed. As a result, there are no outlier values in the defect detection rates of any of the subjects.

    The above analyses, it is confirmed that the influence of the experimental factors on the defect detection rate is common for all subjects, and there were no outlier values in the defect detection rates of all the subjects. Therefore, the data of the 12 subjects are employed for further analysis and examination.

    4.2 Effect of Dirt Levels of Inspection Surface, Defect Locations, and Defect Characteristics

    In order to consider the effect of the dirt levels of inspection surface, defect locations, and defect characteristics, three-way ANOVA is executed with the dirt levels of inspection surface (4), defect locations (4), and defect characteristics (18) as for factors .

    As a result, as shown in Table 2, a significant difference of 1% is observed for the main effect and the mutual interaction of all factors. In addition, as a sub-effect test of the main effect of the dirt levels of inspection surface, an analysis of multiple comparisons (Tukey method) is executed. As a result, a significant difference of 1% is observed between Non dirty and the other levels, and between Slightly dirty and Very dirty. A significant difference of 5% is also observed between Slightly dirty and Somewhat dirty. It is clarified that the defect detection rate is lower according to the inspection surface is dirtier. Table 3

    Firstly, the relationship between the dirt levels of inspection surface and the defect locations is shown in Figure 11-a. From the overall trend, it is confirmed that the defect detection rate decreases as the inspection surface becomes dirtier and the distance from the fixation point and defect becomes longer. However, it is also confirmed that the defect detection rate becomes sharply decreases as the distance from the fixation point and defect increases. That is, it is found that the influence of the dirt levels of inspection surface on the defect detection varies depending on the defect locations. These experimental results suggest that the defect that can be detected easily even in peripheral vision becomes harder to detect even with central vision according as the inspection surface is dirtier. In other words, it is clarified that the dirt levels of inspection surface significantly affects defect detection in with visual inspection utilizing peripheral vision.

    Second, the relationship between the dirt levels of inspection surface and the defect characteristics is shown in Figure 11-b. As an overall trend, it is confirmed that the defect detection rate decreases as the dirt levels of inspection surface increases, and the defect detection rate increases as quantity of the defect characteristics. However, it is also confirmed that the influence of the dirt levels of inspection surface on the defect detection varies depending on the defect characteristics. The characteristics of defect to be detected in an actual inspection set as an acceptable limit of defect, these experimental results suggest that the defect that can be detected easily becomes harder to detect according as the inspection surface is dirtier in visual inspection utilizing peripheral vision regardless of the defect characteristics. In other words, it is clarified that the dirt levels of inspection surface significantly affects defect detection in visual inspection utilizing peripheral vision.

    Third, the relationship between the defect locations and the defect characteristics is shown in Figure 11-c. As an overall trend, it is confirmed that the defect detection rate decreases as the distance from the fixation point and defect becomes longer, and the defect detection rate increases as quantity of the defect characteristics. That is, it is found that the influence of the defect char-acteristics on the defect detection varies depending on the defect locations. The experimental results ratify the preceding study focusing on the relationship between the defect characteristics and defect detection (Shida et al., 2012), the same result is obtained under the experi-mental conditions of this study.

    5. DISCUSSION

    From the experimental results in Section 4, it is shown that the defect detection rate is suddenly reduced as the inspection surface becomes dirtier, and the influ-ence of the dirt levels of inspection surface on the de-fect detection depends on the defect locations and de-fect characteristics.

    Therefore, in order to consider the influence of these experimental factors on the defect detection rate comprehensively, the multiple regression analysis is exe-cuted. The objective variable is set at the defect detec-tion rate. The explanatory variables are set at 1) the dirt levels of inspection surface, 2) the horizontal distance from the fixation point and the defects, 3) the vertical distance from the fixation point and the defects, 4) the luminance contrast between the inspection model and the defect, 5) the size of the defect, and 6) the dark-bright defects (dummy variable, dark: 0, bright: 1). In this analysis, the variable selection method uses the stepwise method, and Pin (the variable introduction reference value) and Pout (the variable removal refer-ence value) are set to 0.05. As a result, as shown in Ta-ble 3, the highest standard deviation regression coeffi-cient of each explanatory variable is the size of the de-fect, then the dirt levels of inspection surface, the lumi-nance contrast between the inspection model and de-fect, the dark-bright of defect, the vertical distance from the fixation point and the defects, the horizontal dis-tance from the fixation point and the defects. In addi-tion, the regression equation from the multiple regres-sion analysis is shown in Equation (5); the adjusted R-square is 0.77, which affirms that the regression equa-tion explains the defect detection rate with high accuracy.

    That is, it is clarified that the size of the defect is the most influence on the defect detection rate in visual inspection utilizing peripheral vision, and then the dirt levels of inspection surface, the luminance contrast be-tween the inspection model and defect, the dark-bright of defect, the vertical distance from the fixation point and the defects, the horizontal distance from the fixa-tion point and the defects.

    Moreover, compering the standard regression coef-ficients of the horizontal and vertical distance from the fixation point and the defects, the ratio of the influence of the horizontal direction to vertical direction on the defect detection rate is -0.16: -0.17. It is confirmed that the defect detection rate is lower in the vertical direction than in the horizontal direction. This result ratifies the preceding study focusing on the anisotropy of the hu-man vision (Chaikin et al., 1962; Kumada et al., 1996; Yamanaka et al., 2006), the study considered the fact that the detection accuracy in the horizontal direction is higher than that in the vertical direction. In other words, it is inferred that the conspicuity field in a situation where the inspection surface is dirty, as in this experi-ment, has a horizontal oval shape, similar to the conspicuity field in the preceding study (Nakajima et al., 2015).

    Defect detection rate [%] = 47.51 × Dirt level of inspection surface  [ g ] 0.08 × Horizontal distance between fixation point and defect [mm] 0.08 × Vertical distance between fixation point and defect [mm] + 307.29 × Luminace contrast of defect [mm] +19.59 × Size of defect [mm] +19.7047.51 × Dark ( 0 ) and bright ( 1 ) of defect -14.78
    (5)

    In the actual visual inspection process, the luminance contrast, the size, and the dark-bright of the defect to be detected are determined according to the quality required by the customer. That is, in order to improve the defect detection rate in a visual inspection process, there are two policies: a policy to decrease the dirt of the inspection surface, and a policy to increase the fixation point. Based on the results of this experiment that decreasing the dirt of inspection surface is effectiveness to improve the defect detection rate, it is necessary to inspect in a state where no dirt adheres as first policy. In other words, it is urgent to follow strategies such as conducting the production process into a clean room and cleaning the inspection surface before the visual inspection process.

    6. CONCLUSIONS

    This study focused on adhered dirt such as dust on a product in production process, in order to consider the relationship between the dirt levels of inspection surface and the defect detection accuracy in visual inspection utilizing peripheral vision, images of the inspection surface in the actual factory were analyzed, and the dirt of inspection surface was modeled. Then, the dirt levels of inspection surface, defect locations, and defect characteristics were designed as experimental factors, and the experiment was conducted with 12 subjects. As the result, it is clarified that the defect detection rate significantly decreased as the inspection surface becomes dirtier.

    As mentioned in INTRODUCTION of Chapter 1, in actual visual inspection processes, some visual inspections are performed even though an inspection surface is dirty. On the other hand, in this study, it is shown that the dirty inspection surface affects the inspection accuracy. To comprehensively summarize the above, it is shown that the importance of a clean inspection surface for a highly accurate visual inspection process, it is urgent to take policies such as making the production process in a clean room and cleaning an inspection surface before the visual inspection process.

    Future tasks are application of the methodology for different types (material, color etc.) of products and dirt and application of the findings in the manufacturing industry and examination of the results.

    ACKNOWLEDGEMENT

    This study was supported by Grant-in-Aid for JSPS Fellows (14J09642), JSPS Grant-in-Aid for Research Activity Start-up (16H07202), Special Research of Faculty of Science and Technology in Seikei University.

    Figure

    IEMS-17-102_F1.gif

    Distribution of pixel value in each photographed image.

    IEMS-17-102_F2.gif

    Distribution and probability of pixel value in the photographed images for each amount of scattered dirt.

    IEMS-17-102_F3.gif

    Created images for each application amount of scattered dirt.

    IEMS-17-102_F4.gif

    Inspection model.

    IEMS-17-102_F5.gif

    Variable selection: overlapped-period method.

    IEMS-17-102_F6.gif

    Experimental flow by a subject.

    IEMS-17-102_F7.gif

    Defect locations.

    IEMS-17-102_F8.gif

    Defects employed in the experiment.

    IEMS-17-102_F9.gif

    Mean and standard deviation of defect detection rate.

    IEMS-17-102_F10.gif

    Range of defect detection rate.

    IEMS-17-102_F11.gif

    Interaction between experimental factors.

    Table

    Distances between the fixation point and the defect

    Three-way analysis of variation (ANOVA) for defect detection rate p < 0.01: **

    Multiple regression analysis for defect detection rate

    R-square: 0.78 Adjusted R-square: 0.77.

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