Weights of Road Accident Causes using Analytic Hierarchy Process

VOL. 2, NO. 2, March 2012 ISSN 2225-7217 

ARPN Journal of Science and Technology 

©2011-2012. All rights reserved. 

http://www.ejournalofscience.org 

Weights of Road Accident Causes using Analytic Hierarchy Process 

Liana Najib, Lazim Abdullah, Ilyani Abdullah and Zabidin Salleh 

Department of Mathematics, Faculty of Science and Technology, University of Malaysia Terengganu, Kuala Terengganu, 

Terengganu, Malaysia 

E-Mail: liana_rufflix@yahoo.com lazim_m@umt.edu.my ilyani@umt.edu.my zabidin@umt.edu.my 

ABSTRACT 

The development of technologies, economics and industrial sectors in Malaysia leads to increasing of motorization sector. 

The increasing of demand in motorization leads to road accident problems. Road accident problem is one of the critical 

incidents and various preventive measures have been taken to reduce the rate of road accidents. Thus, it is important to 

know the actual causes contributing to the road accidents. This paper aims to propose weights and ranks of five selected 

causes associated with road accidents using decision making approach of Analytic Hierarchy Process (AHP). The linguistic 

judgement data were collected from three experts in road accident analysis. The experts rate the pair-wise comparison in 

measurement scale from one to nine. The comparison scales were averaged prior to computing the weights of road accident 

causes. The results show that ‘driving faster than limited speed’ is ranked as the highest cause with the weight 0.3242 and 

‘obstructions (i.e., animals or weather)’ is ranked as the lowest cause among the five road accident causes. Hence, the 

ranking gives rise to concerns about the contribution of the causes in reducing road accidents rate. 

Keywords: road accident, multi-criteria decision making, analytic hierarchy process, pair-wise comparison. 

1. INTRODUCTION 

Numbers of road accidents in Malaysia have been steadily 

increasing over time. Vehicles involve in road accident are 

increasing from year to year and the highest percentage of 

road accidents in Malaysia is Selangor [1]. In order to 

reduce the rate of road accident, many researchers 

investigate what actually the right decision and prevention 

which the public could take as the best method to solve 

this situation. As a saying goes, even one seconds the 

driver fall asleep then accident could happen [2]. Such in 

this situation, it can be specified as road user carelessness. 

So, to avoid this unfortunate incident from happen, the 

road users are advised to practise a good manner and good 

attitude in the road. 

It is compulsory to study about the relation of causes to 

road accident. In the term of definition, an accident is 

unpleasant and unpredictable incidents that are exposing 

people to several probabilities such as fatalities, bad 

injuries and damages of vehicle. Currently, road accident 

is rank as the eleventh leading to the death and predicted 

as the contributory to the global disease by 2020 

accompanied by HIV and tuberculosis by United Nations 

Economic and Social Council [3]. In Malaysia, road 

accident is considering as a very critical problem and 

always increases from times to times and it is about 9.7% 

per annum [4]. By the year of 2002, the number of 

fatalities reaches about 1.2 billion and 50 million are badly 

injured and incapable around the worldwide [5]. There 

were 414, 421 cases lead to 6, 872 fatalities in 2010. The 

values of road accident fatalities are consistently been 

above 6,000 cases since 2003, while for serious injuries 

and slight injuries are both 7, 781 and 13, 616 by Royal 

Police Malaysia [6]. The rising population of Malaysian 

people leads to high numbers of vehicle registered and rate 

of road accidents [7]. To decrease the road accident, the 

government ought to fully concern about the level of road 

safety and it is necessary to gather all of the information 

regarding road accident data to help researcher analyse the 

problems. Thus, the road safety programmes are 

introduced such as road safety research and evaluation, the 

national black-spot programme and the national accident 

database system [7] with the aim of lowering the accidents 

occur. 

Regarding the past research, the total numbers of 

motorcycles per 1, 000, 000 Km involve in road accident 

increasing from 45% in 1990 to 82% in 1998 with the 

82.2% increasing rate [8] and report from MIROS [9] 

shows that accident fatalities involving motorcycle road 

user always increasing since 1994 to 2010 and almost 6.2 

million active registered motorcycles on the road, but 

almost 113,962 involve in road accident. Road accidents 

fatality causes by bus and lorry not as much as motorcycle 

since both of its only involve about 77 and 202 

respectively for last year by Bernama [10]. According to 

Harmeet et al., [11] almost half of road accidents 

percentage fatalities injured the driver aged from 18 years 

to 39 years old and the ratio of fatally-injured by males are 

higher than female drivers. The tendency of young males 

drivers (aged at 15-25 years old) are higher compared to 

older males drivers (aged at 35-50 years old) due to lack 

of experiences compared to older drivers [12]. 

There are lots of contributing causes which leading to road 

accidents problem in the worldwide. A comprehensive 

research from Treat et al., [13] recommended that almost 

93% of road accidents problem occurring causes from 

human factor themselves which included improper 

lookout, improper distance avoid, excessive speed and 

careless. Besides, from the view of environmental and 

vehicle causes, both of the causes contribute about 34% 

and 13% of the road accident problems [13]. The 

environment causes probably view as obstructions such as 

road design problems while vehicle causes include brakes, 

tyres and steering control. In addition, the weather also can 

be one of the causes contributing to the road accident 

especially when rainy day. Rainy day usually would result 

the road become wet and slippery. The condition of rainy 

weather usually can limit the road user vision and the 

slippery of wet road can be hazard to the user which can 

occur at least one fatality case [14]. James and Scott [15] 

stated that among young drivers involve in road accident 

definitely because of the behaviour causes such as 

adjusting speed which includes high speed, traffic 

39




conditions and other (20.8%), attention in the road (23%) 

and emergencies such as tyres and brakes failure (1.4%). 

The tyres and brakes defect usually because of lack of 

maintenance and services. As mentioned above, 

drowsiness also leads to road accident with the percentage 

of 3.9% [2]. Generally the drowsy drivers could contribute 

themselves to the statistic of the road accident injured and 

that is why the drowsy can be one of the hazard factors 

contributing to the road accident. 

In order to overcome the road accidents problem, there are 

lots of researches on investigating the causal of road 

accident, but generally lack of study about the decision on 

the most important causes contributing to the road 

accidents. Fuzzy approach can be one of method to 

recognize the causes associated with road accident since 

road accident problems are one of the uncertainty cases to 

happen. Recently, Lazim Abdullah and Nurnadiah Zamri 

[16] used correlation analysis and Fuzzy TOPSIS to rank 

the factors of road accidents. Correlation analysis uses 

statistical data to measures the variables and Fuzzy 

TOPSIS uses the linguistic data collected from the expert 

and as part of multi-criteria decision making (MCDM). 

Hence, the decision making using Fuzzy approach can be 

use to decide the main factors of the road accidents 

problem. One of the most well-known methods in 

determining the weight for priority factors of the problem 

is Analytic Hierarchy Process (AHP). The AHP is 

practically used in many fields such as health issues, 

management and business, banking, sciences and 

engineering courses. For example, Lazim and Fateen [17] 

discuss the weight determination of factors related to 

obesity by using AHP procedures. By AHP procedures, 

the weight of each the factors associated with obesity is 

defined by comparison of pair-wise measurement for each 

of the factors. Recently, Liberatore [18] applied the 

application of AHP in medical and health care decision 

making. In business and economics, the AHP method can 

be used to define the optimum ranking of stocks for the 

portfolio [19]. Esra et al., [20] has been use AHP 

procedures to improve employee performance in 

organization. In addition, Hambali et al., [21] also uses 

AHP to select the best design concept and emphasizes the 

importance of making accurate decision in manufacturing 

and designing industrial. Newly, Sambasivan et al., [22] 

used the AHP to find the relative weights factors and 

benefits in the electrical and electronic sectors in 

Malaysia. Since AHP had been used widely in the many 

areas, thus the main purposes of this paper is to determine 

the weight and rank of the factors related to road accident 

problems. The finding from this research would help the 

public to understand the causal of the road accident. 

2. ANALYTIC HIERARCHY PROCESS 

The analytic hierarchy process (AHP) is a mathematical 

device in multi-criteria decision making which designing 

the decision factors in a hierarchic problem structure [23]. 

The main target of the AHP is to decide and help decision 

makers in making resolution for the complex problem by 

structuring the criterion hierarchy of multi-criteria 

decision making (MCDM). The AHP is known as the most 

powerful tools for decision making. As the first part of 


AHP procedures, the determination of focus or aim of the 

problem must identify. It is consider as the first level for 

the AHP hierarchy, next would be multiple criterion that 

define alternatives and the last level is the contributing 

alternatives (causes/factors) for the focus. The standard 

scale with absolute numbers would use as a measurement 

in order to manage the weight of each alternatives. The 

weight can be used as comparing and ranking the 

alternatives of the problem and lead the decision maker in 

making choice. The AHP method has the following 

general steps: 

a) Construct a hierarchy structure for an MADM 

problem. 

Figure-1. Hierarchy of Alternatives Selection. 

b) Scaling the relative of data and constructing the pairwise 

comparison matrixes. For this step, construct the 

comparison matrixes of each attributes (criteria). 

Thus, the matrixes would be: 

C 1 C 2 � n C A ij 

C 1 1 1 / w2 

w � w 1 / wn 

1 w 

C 2 w 2 / w1 

1 � w 2 / wn 

2 w 

� � � � � = � 

C n wn / w1 

/ w2 

wn � 1 w n 

The scale should be measurement from 1 to 9 in a 

fundamental scale of measurement provided by Saaty 

(1980). The measurement scale is shown in Table-2.1. 

Table-2.1. Pair-wise Comparison Scale for 

AHP Preference. 

Preference on pair wise 

Preference 

comparison 

number 

Equally important 1 

Moderately more important 3 

Strongly more important 5 

Very strong more important 7 

Extremely more important 9 

Intermediate value 2, 4, 6, 8 

c) Calculating of matrix eigenvector, Aij and consistency 

index test (CI) of the criterion. For matrix eigenvector, 

A multiply the n elements in each row, take the nth 

ij 

40




root, and prepare a new column for the resulting 

values. Then divide each number by the sum of 

resulting values of the new column [21]. 

ij 

Eigenvector, A = 

⎡ n 

⎢ 

⎢⎣ 

i= 

⎡ 

∑ 

1 

∑ ⎢∑ 

⎢⎣ 

( w / w × w / w × ... × w / w ) 

n 

i= 

1 

1 

1/ 

n 

n 

( w / w × w / w × ... × w / w ) 

1 

1 

1 

1 

1 

2 

2 

1 

1 

1 

n 


⎤ 

⎥ 

⎥⎦ 

⎤ / n 

⎥ 

⎥⎦ 

(1) 

Eigenvalue, λ i = 

Consistency test, CI = 

⎛ 

n n 

⎜ A ⎟ ∑⎜∑ ij ⎟ 

j i=1 

⎝ 

A 

ij 

⎞ 

w 

⎠ 

λmax 

− n 

n −1 

Table-2.2. Random indices of sizes of matrices (Saaty, 1980). 

n 1-2 3 4 5 6 7 8 9 

RI 0.0 .58 .90 1.12 1.24 1.32 1.41 1.45 

Consistency ratio (CR) is acceptable if it is does not 

exceed 0.10 [21]. If the CR of CI is greater than 0.10, the 

judgment matrix should be considered as inconsistent. 

Thus, the comparison should be repeated. 

d) Constructing the pair-wise comparisons of alternatives 

with respect to factors (criteria) in a matrix. Find the 

eigenvector, A ij and CR. 

e) Computing the relative weight and ranking the 

alternatives. 

w 

∑ 

i = Ai 

K ij 

Where: 

w i = Overall relative rating for factors i 

A i = Average normalized weight for factors i 

K ij = Average normalized rating for alternatives j with 

respect to factors i. 

f) Ranks the alternatives 

These six general steps are practically used to decide the 

most preferred factors contributing to road accidents. 

3. CASE STUDY 

The AHP questionnaire was designed to compare the 

causes associated with road accidents. The questionnaire 

was used as a guideline in personal interview with the road 

accidents experts. Three road accident experts were sought 

to provide linguistic judgement data based on the AHP 

questionnaire. Three of the experts were traffic police 

inspector, road transport department officer and fire 

brigade department officer. The experts need to judge the 

relative measurement between the criterion and the 

alternatives using pair-wise comparison proposed by Saaty 

[24]. The scale and the relative importance are presented 

in Table-2.1. 

To find the contributing causes related to road accident, 

the criteria and alternatives are defined. The alternatives of 

road accident are ‘driving faster than limited speed’ (A1), 

‘driving carelessly (i.e., failed to look, misjudged distance 

and decision)’ (A2), ‘adverse road and traffic conditions’ 

(A3), ‘tyre and brake defects’ (A4), and ‘obstructions’ (i.e., 

CI 

Consistency Ratio, CR = (4) 

RI 

animals or weather) (A5). The selected criteria are Cars 

(C1), Motorcycles (C2), Buses (C3) and Lorries (C4). The 

hierarchical structure of focus, criteria and alternatives are 

shown in Figure-2. 

Figure-2. Hierarchical Structures of Road 

Accident Factors. 

The experts were asked to specify rating the alternatives 

with the linguistic expression (for example driving faster 

than limited speed vs. driving carelessly) and to indicate 

whether they felt that one factor was ‘strongly more 

important’ or ‘extremely more important’ to another factor 

on a nine-point degree of association scale. The judgement 

must strongly aim to all of the focus; criterion and 

alternatives for getting consistently result. 

4. COMPUTATIONAL PROCEDURES AND 

RESULTS 

The relationships among the alternatives and criteria 

related to road accident are computed using AHP 

procedures. The computations are executed using the 

proposed six steps of AHP. 

Step 1 : Construct hierarchy structure for the problems. 

The hierarchical structure of road accidents problem is 

given in Figure-2.1 

Step 2 : Construct the matrix of criteria and scale the 

matrix based on relative scale measurement. 

The scale of relative measurement of the criteria in pairwise 

comparison is presented in Table-4.1 

j 

41 

(2) 

(3)





Table-4.1. Criteria Pair-wise comparison AHP. 

Cn C1 C2 C3 C4 

C1 1 3 1/3 1/7 

C2 1/3 1 1/7 1/9 

C3 3 7 1 1/3 

C4 7 9 3 1 

Step 3: Find Eigenvector and Eigen-value of the criterion. 

Eigenvector and eigenvalue are obtained using equation (1) and (2). 

For example the calculation of weights criteria is: 

Eigenvector, A ij = 

( 1× 

3× 

1/ 

3× 

1/ 

7) 

Table-4.2. Eigenvector and Eigen-value of criterion. 

Cn C1 C2 C3 C4 ( ) n 1/ 

1 × ...× c A n 

ij 

i 

C1 1 3 1/3 1/7 3/5 0.0989 4.0596 

C2 1/3 1 1/7 1/9 1/4 0.0434 4.1489 

C3 3 7 1 1/3 1 5/8 0.2616 4.0534 

C4 7 9 3 1 3 5/7 0.5962 4.1314 

Total 6 2/9 1 16.3943 

1/ 

4 

= 

0. 

09889 

2 

6 

9 

The eigenvector of each criterion is computed as the 

example given. 

To obtain the consistency ratio (CR), the calculation of 

Eigen-value is needed as follows: 

λ 

Eigen value, i 

( 1× 

0. 

098856 + 3× 

0. 

043368 + 1/ 

3× 

0. 

261556 + 1/ 

7 × 0. 

596217) 

= 

0. 

098859 

= 4. 

05956 

Next, calculate the consistency index (CI) using equation 

(3). 

⎛16. 

3948 ⎞ 

⎜ − 4⎟ 

Consistency test, CI = ⎝ 4 ⎠ 

= 0. 

03285 

3 

The calculation of Consistency Ratio (CR) is 0.0365 by 

equation (4). Thus, the judgment is acceptable since CR is 

less than 0.1. 

Step 4 : Compute the eigenvector and Eigen-value of 

alternatives pair-wise measurement and CR. The 

alternatives Table are illustrated as Table-4.3 

The calculations of the eigenvector, Eigen-value and 

consistency ratio are computed as same as example and 

formula from above. 

c 

λ 

Table-4.3. Alternatives pair-wise comparison with 

respect to criteria of Car, C1. 

C1 A1 A2 A3 A4 A5 

A1 1 5 7 3 3 

A2 1/5 1 1/5 1/5 1/3 

A3 1/7 5 1 1/3 3 

A4 1/3 5 3 1 1 

A5 1/3 3 1/3 1 1 

Table-4.4. Eigenvector and Eigen-value of alternatives 

with respect to criteria, C1. 

1 / n 

C1 ( ) 

× An 

ij A i 

A1 

... × 

A1 3 1/6 0.4800 5.6268 

A2 1/3 0.0464 5.4579 

A3 1 0.1420 6.1851 

A4 1 3/8 0.2096 5.4856 

A5 4/5 0.1219 5.5612 

Column 

sum 

6 4/7 1 28.3168 

The CR of the matrix above is 0.1480. Thus, the judgment 

is acceptable since CR is less than 0.1. 

In addition, the weights priorities for the hierarchy of 

alternatives with respect to each criterion are also 

computed as the same way. Table-4.5 is shown from the 

result of weights calculation for each alternative to the 

criterion. 

Step 5 : Compute the composite priority (Overall 

weights in the entire hierarchy). 

λ 

42





Table-4.5. Weight factors associated with road accident. 

C1 C2 C3 C4 Aij Weight 

A1 0.4800 0.1019 0.1111 0.4081 0.0989 0.3242 

A2 0.0464 0.2626 0.2113 0.2813 0.0434 0.2389 

A3 0.1420 0.1582 0.1908 0.1530 0.2616 0.1620 

A4 0.2096 0.4216 0.1908 0.0409 0.5962 0.1133 

A5 0.1219 0.0554 0.2961 0.1168 0.1615 

Step 6: Ranks the alternatives 

Based on weight, the final rank for alternatives is 

established in Table-4.6. 

Table-4.6. Ranking of weights alternatives using AHP. 

Alternatives Weights Rank 

A1 0.3242 1 

A2 0.2389 2 

A3 0.1620 3 

A4 0.1133 5 

A5 0.1615 4 

Table-4.6 shows the weights and ranks for all of the 

factors contributing to road accident in Malaysia. As a 

conclusion, the best factors which often lead to accident 

are ‘driving faster than limited speed’ and followed by 

‘driving carelessly’. Both of these factors are contributed 

from human behaviour themselves. The third ranking is 

‘adverse road and followed by obstructions with consider 

as the environment factors. Last ranking is contributed by 

vehicle factor itself. The poor maintenance of tyres and 

brakes also lead to road accident. Based on the fives 

causes, driving faster than limited speed contributed as 

much as 32.42% to road accident. 

5. CONCLUSIONS 

The purpose of this paper is to identify the perfect causes 

contributed to the road accident in Malaysia using the pairwise 

comparison method of AHP. This six-step of AHP 

method has successfully identified that ‘driving faster than 

limited speed’ has the highest weights among all of the 

causes which leading to road accident. Regarding the past 

research, it is identically prove that human behaviour 

themselves [13] which contribute almost 17% of human 

indirect causal of road accident is excessive speed. The 

second highest factor is driving carelessly which including 

failed to look and improper misjudge distance contributed 

about 23.89%. Next causes are adverse road and traffic 

condition and obstructions (i.e., animals) both contributed 

by 16.20% and 16.15% which also known as factors for 

environment consequences. Last but not least, the factors 

for vehicle condition, which is tyres, are brakes defect 

contributed of 11.33% to road accident. In conclusion, this 

study is hoped to help people by acknowledge the causes 

may lead to road accidents and the importance of taking 

road safety prevention. Thus, from this research it is better 

to extend by considering more causal and other types of 

accident to recognize and validate the sensitivity and 

accuracy of AHP procedure. Besides, further research can 

be used to weights the factors using fuzzy approach such 

as fuzzy set and numbers and intuitionistic fuzzy sets. 

ACKNOWLEGMENT 

The present work is part of the Fundamental Research 

Grant Scheme, project number 59173. We acknowledge 

financial support from the Malaysian Ministry of Higher 

Education and University of Malaysia Terengganu. 

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