Songklanakarin Journal of Science and Technology SJST R2 LUMBA. Analyzing Motorcyclist s Accident Severity Using Bayesian Network

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1 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Analyzing Motorcyclist s Accident Severity Using Bayesian Network Journal: Songklanakarin Journal of Science and Technology Manuscript ID SJST-0-0.R Manuscript Type: Original Article Date Submitted by the Author: 0-Sep-0 Complete List of Authors: LUMBA, PADA; Universitas Gadjah Mada Fakultas Teknik, Civil and Environmental Engineering Priyanto, Sigit; Universitas Gadjah Mada, Civil and Environmental Engineering muthohar, imam; Universitas Gadjah Mada Fakultas Teknik, Civil and Environment Engineering Faculty Keyword: Accident Severity, Bayesian Network, Bekasi, Motorcycle

2 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 Original Article Analyzing Motorcyclist s Accident Severity Using Bayesian Network Pada Lumba, Sigit Priyanto, Imam Muthohar Student, Doctoral Program of Civil and Environmental Engineering, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta,, Indonesia Faculty Member, Civil and Environmental Engineering, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta,, Indonesia Faculty Member, Civil and Environmental Engineering, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta,, Indonesia * Corresponding author, address: pada.lumba@mail.ugm.ac.id, spriyanto00@yahoo.co.id, imam.muthohar@ugm.ac.id Abstract This paper focuses on the probability of crashes with severely and mildly injuries in motorcyclists. The probability of crashes took human, road and environment and vehicle factors into consideration. 0.% crashes that occured from July until December, 0 in Indonesia involved motorcycles. The research took place in Bekasi City, Indonesia. The samples consisted of respondents who had experienced crashes. The results indicated that the probability of severely injuries crashs was %, and mildly injuries was %. The Mean Absolute Deviation of model was 0.0%. Female drivers were more likely to severely injuries than male. Driving on roads which have road side variability and driving on curvy roads would be able to decrease the level of monotonous driving from % to %. Motorcycles which have engine capacity above cm were % more likely to experience crashes with severely injuries.

3 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Keywords: Accident Severity, Bayesian Network, Bekasi, Motorcycle. Introduction Age, sex, occupation, job status, vehicle type, licence status, fatigue, speed, and location of accident were independently correlated to the severity of the accident (Boufous & Williamson, 00). Elderly people more likely to suffer fatal crashes or severely rather than mildly injuries. The risk of crashes resulting in mildly injuries group is higher than fatal crashes or severely injuries group for the age under -yearsold (Vorko-Jovic, Kern, & Biloglav, 00). The increased severity rate was not only found when younger motorcyclists use higher-capacity vehicles, but also found in older motorcyclists who use lower-capacity vehicles (Yannis, Golias, & Papadimitriou, 00). Drivers of 0 years and below are almost times more likely to suffer fatal crashes, and decreases dramatically as the age of the driver increases, and then rises again after the drivers pass the age of (Clarke, Ward, Bartle, & Truman, 00). Wearing a helmet lowers the average probability of crashs for motorcyclists; and young motorcyclists on average are more likely to suffer from severely injuries or fatal crashs (Lapparent, 00). Male are. times more likely to die in a crash than female (Vorko-Jovic, Kern, & Biloglav, 00). In addition, males are less likely to ignore traffic rule than females (Susilo, Joewono, & Vandebona, 0). The characteristics of driver predicted to be the causes of serious and fatal injury were driving in the darkness, between Friday and Sunday, on the road with a

4 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 speed limit of mph, on single carriageways, overtaking, skidding, hitting an object off the carriageway, and passing by previous accident sites (Gray, Quddus, & Evans, 00). Monotonous situation experienced while driving are influenced by: road design monotony and roadside variability, which may reduce the vigilance level of the driver rapidly. The level of vigilance does not increase when the road is straight, but the vigilance increases on the turn (Laruea, Rakotonirainya, & Pettitt, 0). Monotonous roads, and long duration of driving, and lack of rest can due to fatigue in drivers (Ma, Wiliamson, & Friswell, 00). Monotonous road conditions and low-level traffic volume will likely due to fatigue earlier (Thiffault & Bergeron, 00a). Sportbikes were involved fatal accidents caused by excessive speed (Bjørnskau, Nævestad, & Akhtar, 0). The difference in motorcycle performance will affect the risk in driving behavior and the risk of fatal crashes (Teoh & Campbell, 0). Travelling to work by motorcycle is correlated with increased crash victims dead on the highway (Moeinaddini, Asadi-Shekari, Sultan, & Shah, 0). In 0, motorcycle accidents occurred in Bekasi. This number increased to in 0, and decreased to,, in the years of 0, 0, and 0 respectively. Moreover, the involvement in severely injuries were in 0. This was decreased to in 0, and increased to in 0. However, it was found that in 0 and 0 the serious injuries were found to be and respectively. In 0, there were motorcyclists were involved in fatal accidents and in the next following years of 0, 0, 0, and 0 the number decreased to,,, and respectively. In the periods of 0, 0, and 0 the number of motorcyclists

5 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 involved in mildly injuries accident increased by,, and respectively. However, the number decreased in 0 and 0 to 0 and respectively (Bekasi Police Department, 0). This research aims at analyzing some factors which affect the probability of accident severity rate in motorcyclists. Three factors reviewed in this research were human factor, road and environment, and condition of vehicle. The factors were analyzed simultaneously to obtain the probability of accident severity in motorcyclists. After obtaining several attributes that could affect the probability of accident severity using Bayesian Network Method, some scenarios could be developed to reduce the probability of accident severity on the motorcyclists. The scenarios could be developed by changing the percentage of attribute, which would also affect the probability of accident severity. Therefore, some of the best prevention can be developed as early as possible to minimize the risk of fatal injury due to an accident.. Materials and Methods The research took place in Bekasi City, Indonesia. Bekasi has the largest commuter trips in Jabodetabek, around. million compared to other cities in Jabodetabek..% of commuter trips in Jabodetabek use motorcycles..% of commuter trips in this city have a travel time above minutes. Therefore, the Bekasi City is appropriate to look for respondents for this study. To validate the model, data were also collected outside Bekasi City, such as: Bandung, Yogyakarta, Pekanbaru, Pasir Pengaraian City. Criteria for the respondents are motorcyclists who had experienced a traffic

6 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 crashes and respondents should be minimum age of years old. Some attributes calculated in this study were: gender, age, speed, fatigue, machine capacity, road side variability, road monotonous design, long duration of driving, road condition and visibility. The data were collected by interviews where every respondent took time approximately minutes. The number of respondents was determined based on Solvin technique approach with formula : Description : n = sample, N = population, e = margin of error. It was known that the number of accident victims ( N ) involving motorcycles in 0 in Bekasi was people (Bekasi Police Department, 0), and e value = %. The number of samples collected was respondents consisting of : respondents of motorcyclists who had an accident and did not take a break on the way before the accident, respondents of motorcyclists who had an accident and took a break on their way before the accident, while respondents did not have complete data. This research used respondents of motorcyclists who had an accident and did not take a break on the way before the accident. The data then, were analyzed using the Bayesian Network method. Bayesian Network was originated from Bayes theorem. Bayesian Network is more suitable to predict the severity of accident than the regression model (Zong, Xu, & Zhang, 0). There are fundamental differences between the

7 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Bayesian method and the classical method. In the classical method, the population parameter is regarded as an unknown quantity. The Bayesian method regards the population parameter as a variable that has a prior distribution. In addition, the regression model does not allow variables to have strong correlation, which does not apply in Bayesian network. The Bayesian Network analysis in this study used Software GeNIe.0. Variables and statistics based on data can be seen in Table. This theorem describes the relationship between the probability of the incident of event A and the previous incident of event B, which is formulated in the equation : P(B A) P(A) P(A B) = = () P(B A) P(A) + P(B -A) P(-A) Where P=Probability, P(A B) = posterior probability of structure A, P(A) = prior probability distribution of B, P(B) = probability distribution of data set B. Indicator to measure the accuracy of the model was the Mean Absolute Deviation (MAD), with the equation :. Results and Discussion The Structure of Bayesian Network can be seen in Figure. Attributes that affected the probability crash including : gender, age, speed, fatigue, engine capacity, road side variability, road monotonous design, long duration of driving and road condition. The results of the Structure of Bayesian Network analysis indicated that the probability of an crash resulting in severely injuries was %, and mildly injuries was

8 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 %. The calculation of probability crash severity for existing model and scenario of model use formula in equation, as shown in Table. The accuracy of Model in Table was measured by calculating the Mean Absolute Deviation (MAD). The Calculation the value of MAD, new data were used comprising of respondents as shown Table. For the validation of respondents, there were only probabilities to occur. Meanwhile, other probabilities did not occur. On the Bayesian network method, the probability that does not occur, such as this probability could be assumed that the value fatal injury was % and minor injury was %. The validation process in this research only used the real value obtained from the respondents, and did not use the assumption value in order to see the proximity between the actual value and the model value. The probability calculation of the severity of accidents in Table was directly affected by variables namely: gender, fatigue, speed, and age. Therefore, the probability of accident severity was possibilities consisting of possible severely injuries and possible mildly injuries. This was obtained from options of genfer response x options of response to fatigue x options of response to speed x options of age response x options of response to probability of accident severity. The result of the model accuracy indicated that the value of MAD was 0.0%, as shown in Table. The deviation between the condition actual and model quite varied. Such variation existed because the data used for validation were obtained from other cities outside Bekasi such as Bandung, Yogyakarta, Pekanbaru, and Pasir Pengaraian City. Meanwhile, the data used for analysis were from respondents in Bekasi. In addition, differences in motorcyclist characters and

9 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 behaviors in one region were highly likely to affect the probability of accident severity. Females were more likely to suffer severely injuries than males, as shown in Figure and. Based on data indicated that.% of female drivers violate traffic regulation before accident, meanwhile.% of male drivers violate traffic regulation before accident. Males are less likely to ignore traffic rule than females (Susilo, Joewono, & Vandebona, 0). This result is not in accordance with the studies conducted by (Vorko-Jovic, Kern, & Biloglav, 00). Drivers aged 0 years and above are more likely to suffer severely injuries than those aged 0 years and below, as shown in Figures. This study is in accordance with the studies conducted by (Vorko-Jovic, Kern, & Biloglav, 00; Yannis, Golias, & Papadimitriou, 00). This study is in not accordance with the studies conducted by (Clarke, Ward, Bartle, & Truman, 00; Lapparent, 00). In addition, based on data indicated that.% drivers aged 0 years and above had experienced fatigue before crash, and.% drivers aged 0 years and below had experienced fatigue before crash. The others research related to this studies conducted by (Clarke, Ward, Bartle, & Truman, 00; Dotzauer, Waard, Caljouw, Pöhler, & Brouwer, 0). -year-old drivers are less likely to perceive their risk of crash, and middle-aged drivers are likely to perceive their crashes between % -0%. Drivers aged - and above are more likely to contribute to crash and in general it is a right-turn crash on intersection (Clarke, Ward, Bartle, & Truman, 00). Young drivers have a maximum velocity which is significantly higher than older drivers (Dotzauer, Waard, Caljouw, Pöhler, & Brouwer, 0). In addition, based on data indicated that.% drivers aged 0 years and above had experienced fatigue before crash, and.% drivers aged 0 years and

10 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 below had experienced fatigue before crash. Motorcycles which have engine capacity above cm were % more likely to experience crashes with severely injuries and motorcycles with engine capacity cm and below were %. In the scenario of a motorcycle with an engine capacity > cm, the probability of drivers at a speed < km/h decreases from % to %, while the probability of drivers with a speed of -0 km/h increases from % to %, and so is for drivers at a speed > 0 km/j increasing from % to %, as shown in Figure and. This study is in accordance with the studies conducted by (Teoh & Campbell, 0; Yannis, Golias, & Papadimitriou, 00; Gray, Quddus, & Evans, 00; Bjørnskau, Nævestad, & Akhtar, 0). Driving on roads which have road side variability and driving on curvy roads would be able to decrease the level of monotonous driving from % to %, and decrease the probability of fatigue from % to % as shown in Figure. This study is in accordance with the studies conducted by (Laruea, Rakotonirainya, & Pettitt, 0; Thiffault & Bergeron, 00a).. Conclusions Attributes that affect the probability of severity crashes are caused by human, road and environment, vehicle factors including : gender, age, speed, fatigue, machine capacity, road side variability, road monotonous design, long duration of driving, road condition. The results of analysis indicated that the probability of an crash resulting in severely injuries was %, while mildly injuries was %. Driving on roads which have road side variability and driving on curvy roads would be able to decrease the level of

11 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 monotonous driving from % to %. Motorcycles with engine capacity above cm are more likely to suffer severely injuries than motorcycles with engine capacity cm and below. Aproximately.0% of crashes take place due to fatigue and.% of crashes involving motorcyclists aged 0 years and below. In addition, speeding is more likely to increase the probability crash severity. Acknowledgments The author would like to express our sincere gratitude to The Ministry of Research, Technology and Higher Education, who provide funding for The Doctoral Research Universitas Gadjah Mada. Moreover, thanks are also extended to Departement of Civil Engineering and environmental for it s encouragement to publish this research result. References BayesFusion Downloads for Academia. Retrieved from Bekasi Police Department. (0). Accident that occured from 0 to 0 in Bekasi City involved motorcycles. Bjørnskau, T., Nævestad, T. O., & Akhtar, J. (0). Traffic safety among motorcyclists in Norway: A study of subgroups and risk factors. Accident Analysis and Prevention, (0),. Boufous, S., & Williamson, A. (00). Factors affecting the severity of work related traffic crashes in drivers receiving a worker s compensation claim. Accident Analysis and Prevention, (00),.

12 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 Clarke, D. D., Ward, P., Bartle, C., & Truman, W. (00). Older drivers road traffic crashes in the UK. Accident Analysis and Prevention, (0),. Dotzauer, M., Waard, D. D., Caljouw, S. R., Pöhler, G., & Brouwer, W. H. (0). Behavioral adaptation of young and older drivers to an intersection crossing advisory system. Accident Analysis and Prevention, (0),. Gray, R. C., Quddus, M. A., & Evans, A. (00). Injury severity analysis of accidents involving young male drivers in Great Britain. Journal of Safety Research, (00),. Lapparent, M. D. (00). Individual cyclists probability distributions of severe/fatal crashes in large french urban areas. Accident Analysis and Prevention, (00), Laruea, G. S., Rakotonirainya, A., & Pettitt, A. N. (0). Driving performance impairments due to hypovigilance on monotonous roads. Accident. Analysis and Prevention, (0), 0 0. Ma, T., Wiliamson, A., & Friswell, R. (00). A Pilot Study of Fatigue on Motorcycle Day Trips. Sydney, Australia: NSW Injury Risk Management Research Centre. Moeinaddini, M., Asadi-Shekari, Z., Sultan, Z., & Shah, M. Z. (0). Analyzing the relationships between the number of deaths in road accidents and the work travel mode choice at the city level. Safety Science, (0),. Susilo, Y. O., Joewono, T. B., & Vandebona, U. (0), Reasons underlying behaviour of motorcyclists disregarding traffic regulations in urban areas of Indonesia. Accident Analysis and Prevention, (0),.

13 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Teoh, E. R., & Campbell, M. (0). Role of motorcycle type in fatal motorcycle crashes. Journal of Safety Research, (0),. Thiffault, P., & Bergeron, J. (00a). Monotony of Road Environment and Driver Fatigue: A Simulator Study. Accident Analysis and Prevention, (), -. Vorko-Jovic, A., Kern, J., & Biloglav, Z. (00). Risk factors in urban road traffic accidents. Journal of Safety Research, (00),. Yannis, G., Golias, J., & Papadimitriou, E. (00). Driver age and vehicle engine size effects on fault and severity in young motorcyclists accidents. Accident Analysis and Prevention, (00),. Zong, F., Xu, H., & Zhang, H. (0). Prediction for Traffic Accident Severity: Comparing the Bayesian Network and Regression Models. Hindawi Publishing Corporation Mathematical Problems in Engineering, Volume 0, Article ID, pages

14 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 G C C = % C = % G = % G = % S RS RS = % RS = % S = % S = % S = % RC RC = % RC = % F F = % F = % AS AS = % AS = % RMD RMD = % RMD = % Where: RS=Road side variability, RS=Variability, RS=Unvariability, RMD=Road monotonous design, RMD=Flat and Straight, RMD=Hill and Bend, C=Engine capacity, C = cm, C = > cm, RC=Road condition, RC=Monotonous, RC=Unmonotonous, A=Age, A = 0 years, A = > 0 years, L=Long duration of driving, L=Time min, L=Time min, L=Time min, G=Gender, G=Female, G=Male, F=Fatigue, F=Not Fatigue, F=Fatigue, S=Speed, S = km/h, S=- 0 km/h, S = >0 km/h, AS=Accident Severity, AS=Severly injured, AS=Mildly Injured Figure Structure of Bayesian Network L L = % L = % L = % A A = % A = %

15 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Variability = % Unvariability = % Engine Capacity cm = % > cm = % Gender Speed Female = 0% Male = 0% Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Engine Capacity cm = % > cm = % Gender Female = 0% Male = 0% Road Side Variability Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Road Side Variability Variability = % Unvariability = % Speed Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Figure Scenario Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Flat and Straight = % Hill and Bend = % Figure Scenario Road Monotonous Design Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = % > 0 years = % Road Monotonous Design Flat and Straight = % Hill and Bend = % Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = % > 0 years = %

16 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 Gender Female = % Male = % Variability = % Unvariability = % Engine Capacity cm = % > cm = % Speed Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Engine Capacity cm = 0% > cm = 0% Gender Female = % Male = % Road Side Variability Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Road Side Variability Variability = % Unvariability = % Speed Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Figure Scenario Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Figure Scenario Road Monotonous Design Flat and Straight = % Hill and Bend = % Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = 0% > 0 years = 0% Road Monotonous Design Flat and Straight = % Hill and Bend = % Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = % > 0 years = %

17 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Gender Female = % Male = % Variability = % Unvariability = % Engine Capacity cm = 0% > cm = 0% Speed Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Engine Capacity cm = % > cm = % Gender Female = % Male = % Road Side Variability Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Road Side Variability Variability = 0% Unvariability = 0% Speed Speed of km/h = % Speed of -0 km/h = % Speed of > 0 km/h = % Figure Scenario Road Condition Monotonous = % Unmonotonous = % Fatigue No = % Yes = % Probability of Accident Severity Severely Injured = % Mildly Injured = % Figure Scenario Road Monotonous Design Flat and Straight = % Hill and Bend = % Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = % > 0 years = % Road Monotonous Design Flat and Straight = 0% Hill and Bend = 0% Long Duration of Driving Time min = % Time min = % Time min = % Age 0 years = % > 0 years = %

18 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 Number Variables Value Percentage Gender Male. Female. Age 0 years old. > 0 years old. Speed < km/h. -0 km/h.0 > 0 km/h. Fatigue before to accident Yes.0 No.0 Engine capacity cm. > cm. Road side variability Variability. Unvariability. Road monotonous design Flat and straight. Hill and bend.

19 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Long duration of driving minute. minute. minute. Road condition Monotonous. Table Variables and statistics Unmonotonous.0

20 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page 0 of 0 P P(G) P(F) P(A) P(S) P(AS) G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) G F A S G F A S G F A S G F A S G F A S G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD)

21 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) G F A S G F A S G F A S G F A S G F A S 0 G F A S P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) P(S C) P(F RC,L) P(RC RS,RMD) P(AS)0 = P(AS G,F,A,S,C,RC,L,RS,RMD)

22 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) P(AS) = P(AS G,F,A,S,C,RC,L,RS,RMD) G F A S P(S C) P(F RC,L) P(RC RS,RMD) Ʃ P(AS) Where: P=Probability, AS=Accident Severity, G=Gender, G=Female, G=Male, F=Fatigue, F=Not Fatigue, F=Fatigue, A=Age, A = 0 years, A= > 0 years, S=Speed, S= km/h, S=-0 km/h, S = >0 km/h, C=Engine capacity, RC=Road condition, L=Long duration of driving, RS=Road side variability, RMD=Road monotonous design Table The equation of probability accident severity

23 Page of Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA 0 Probability of Number of respondents severely injured Proba Speed Deviati Gender Fatigue Age severely mildlly bility (Km/h) on % Actual Model injured injured % % (respondent) (respondent) F No < F No < > F No F No -0 > F Yes < > F Yes F Yes -0 > M No < M No < > M No M No -0 > M Yes <

24 Songklanakarin Journal of Science and Technology SJST-0-0.R LUMBA Page of 0 0 M Yes < > M Yes M Yes -0 > M Yes > M Yes > 0 > Number of Respondent + = Mean Absolute Deviation (MAD) 0.0 Where : M=Male, F=Female Table The Calculation of the mean absolute deviation (MAD) value