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Analysis of factors that influence hazardous material transportation accidents based on Bayesian networks: A case study in China
Safety Science 50 (2012) 1049–1055
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Analysis of factors that influence hazardous material transportation accidents based on Bayesian networks: A case study in China Laijun Zhao a, Xulei Wang a,b,⇑, Ying Qian a a b
Shanghai University, School of Management, Shanghai 200444, PR China Qingdao Agriculture University, College of Economics and Management, Qingdao 266109, PR China
a r t i c l e
i n f o
Article history: Received 24 September 2010 Received in revised form 3 November 2011 Accepted 4 December 2011 Available online 27 December 2011 Keywords: Hazardous materials (Hazmat) Transportation Bayesian networks Dempster–Shafer evidence theory Expectation–maximization algorithm
a b s t r a c t In this study, we applied Bayesian networks to prioritize the factors that influence hazardous material (Hazmat) transportation accidents. The Bayesian network structure was built based on expert knowledge using Dempster–Shafer evidence theory, and the structure was modified based on a test for conditional independence. We collected and analyzed 94 cases of Chinese Hazmat transportation accidents to compute the posterior probability of each factor using the expectation–maximization learning algorithm. We found that the three most influential factors in Hazmat transportation accidents were human factors, the transport vehicle and facilities, and packing and loading of the Hazmat. These findings provide an empirically supported theoretical basis for Hazmat transportation corporations to take corrective and preventative measures to reduce the risk of accidents. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, many accidents caused by hazardous materials (Hazmat) transportation have resulted in catastrophic losses of human life and damage to the environment in China. Such accidents have attracted increasing attention from the general public and the government, and a growing amount of research about accident prevention has been conducted (Wang et al., 2005; Zhao et al., 2009; Yang et al., 2010). Analysis of the factors that influence Hazmat transportation accidents is an important issue in accident prevention because it can provide transportation corporations with actionable information on the causes of accidents. As a result, corrective and preventative measures can be implemented to exercise greater control over these factors. The most common methods that are used to analyze the factors that influence Hazmat transportation accidents, such as statistical methods and fault tree analysis, consider all factors to be independent rather than related (Wang et al., 2005; Oggero et al., 2006; Samuel et al., 2009; Trépanier et al., 2009; Zhao et al., 2009; Yang et al., 2010). In reality, multiple factors contribute to a Hazmat transportation accident, and these factors are often interrelated (Bird and Germain, 1990). Thus, it is necessary to consider the interplay of factors when analyzing such accidents. As a tool for ⇑ Corresponding author at: Shanghai University, School of Management, 99 Shangda Road, BaoShan District, Shanghai 200444, PR China. Tel.: +86 21 6613 7925; fax: +86 21 6613 4284. E-mail address: [email protected] (X. Wang). 0925-7535/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2011.12.003
studying uncertainty, Bayesian networks combine graph theory with probability theory, and can represent both the uncertainty and the interplay among the variables (Pearl, 1988, 2003). In this approach, probabilistic inference can be conducted to predict the values of some variables based on the observed values of other variables, and the predicted value is referred to as the ‘‘posterior probability’’. The posterior probability serves as a universally sufficient statistic for detection applications because it captures the relationships and interplay among the variables that describe a situation (Pearl, 2003). If we apply Bayesian networks to analyze Hazmat transportation accidents, we can assign the probability of the accident to be 1 (i.e., 100% probability because the accident has already occurred), and the posterior probability of each factor can then represent its influence on the accident. Based on this analysis, we can identify the most important factors that contributed to the accident and find relationships among these factors. The results of this analysis will help transportation corporations take the measures required to reduce the risk of an accident. A Bayesian network can be constructed manually, (semi-)automatically from the data, or by a combination of a manual and datadriven processes (Kjaerulff and Madsen, 2008). The last approach first develops the structure of the Bayesian network by taking advantage of the knowledge of domain experts, and then learns the parameters of the Bayesian network from a database using a learning algorithm such as the maximum-likelihood estimation algorithm or the expectation–maximization (EM) algorithm. This approach is sufficiently easy that it can be used in practice. Moreover, the network structure can be easily understood and the
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expert knowledge can be easily incorporated in the model. However, this method has two limitations: expert knowledge is subjective and limited, which results in poor reliability when building the network’s structure, and conditional independence among the variables is ignored when the experts confirm the causal relationship among variables. Overcoming these limitations is the key issue when constructing Bayesian networks using this approach. The remainder of this paper is organized as follows: Section 2 presents a literature review on the analysis of factors that influence Hazmat transportation accidents and Bayesian networks. Section 3 identifies key factors involved in Hazmat transportation accidents and builds a Bayesian network structure based on expert knowledge using Dempster–Shafer (D–S) evidence theory. Moreover, the structure of Bayesian network is modified according to the conditional independence test. Section 4 computes the posterior probability of the factors using the EM algorithm to find the influence of the different factors on transportation accidents. Section 5 analyzes the results and describes their implications for China’s Hazmat transportation corporations. Section 6 provides our conclusions.
2. Previous related work Most previous studies that analyzed the factors responsible for Hazmat transportation accidents used a statistical method. The researchers largely confined themselves to the collection, analysis, and interpretation of data derived from accident reports or an accident database. For example, Oggero et al. (2006) studied 1932 accidents that occurred during the transport of Hazmat by road and rail from the beginning of the 20th century to July 2004, and concluded that the following major factors were responsible for the accidents: external factors such as the weather, human factors such as operator error, and mechanical failures. Wang et al. (2005) studied Hazmat transportation accidents in China and concluded that six groups of factors were responsible for these accidents: human, vehicle, packing, transportation facilities, road conditions, and environmental conditions. Zhao et al. (2009) studied 650 Hazmat transportation accidents from 2005 to 2008 to analyze the influencing factors and found results similar to those of Wang et al. (2005). Although statistical methods can analyze the relationships between an accident and the factors that influence it, they cannot account for the interplay among different factors and fail to reflect the fact that an accident is usually the result of more than one factor (Bird and Germain, 1990). To avoid this problem, tree-based methods such as fault-tree analysis, event-tree analysis, and cause-consequence analysis are often used to identify the influencing factors (Roland and Moriarty, 1990; Hamada et al., 2004). However, tree-based methods are based on three assumptions: (1) accidents are binary events, (2) events are statistically independent, and (3) the relationship among events can be represented by means of ‘‘logical gates’’ (Singer, 1990; Andrews and Moss, 2002; Rao et al., 2009). These assumptions restrict the use of these methods to static, logic-based modeling. The tree-based methods are therefore not suitable to describe influencing factors with more than two potential states and make it difficult to represent the relationships among factors. For Hazmat transportation accidents, some factors may have more than two states; for example, weather conditions and road conditions have a wide range of possible states. In addition, the relationships among the factors responsible for an accident cannot be easily represented by means of logical gates. Thus, tree-based methods are not suitable for analyzing the factors that influence Hazmat transportation accidents. A more promising approach involves the use of Bayesian networks, which have previously been applied in accident analysis.
For example, Trucco et al. (2008) developed a Bayesian belief network to model the maritime transport system. Their model represented various factors and their mutual influences by means of a set of dependent variables. Marsh and Bearfield (2004) described a method of modeling the organizational causes of accidents using Bayesian networks, and demonstrated how such a model can be used for risk assessment based on examples from a model of the causes of Signals Passed at Danger (SPAD) incidents in the UK railway system. Maglogiannis et al. (2006) developed a Bayesian network model to concisely represent all the interactions among undesirable events in a risk analysis for health information systems, and the Bayesian network model identified and prioritized the most critical events. The structures of the abovementioned Bayesian networks were often developed based on the causal relationships determined by domain experts. However, due to the subjectivity of the opinions of domain experts, the Bayesian network’s structure may be inconsistent with the actual situation. Moreover, the domain experts in these studies did not consider the possibility of conditional independence relationships between nodes, which can lead to an incorrect description of the relationships between nodes in the network structure. 3. A Bayesian network structure for Hazmat transportation accidents For detailed information about Bayesian networks, refer to the work of Pearl (1988, 2003). Here, we present only a basic mathematical description. Given a directed acyclic graph, f = (V, E), where V denotes a set of nodes and E denotes a set of directed edges, we can describe a joint probability distribution, P, over the set of variables X = {X1, X2, . . ., Xn}, which can be factorized as follows:
PfX 1 ; X 2 ; . . . X n g ¼ Pi PðX i jp½X i Þ
ð1Þ
where p[Xi] denotes the set of parent variables of variable Xi for each node m 2 V. The nodes in V are in one-to-one correspondence with the variables Xi. For a node without any parent nodes, the conditional probability is the same as the prior probability. 3.1. Define the variables and their structures Based on a review of the literature (Oggero et al., 2006; Samuel et al., 2009; Trépanier et al., 2009; Zhao et al., 2009) and a survey of transportation corporations, we identified 11 direct and indirect factors related to Hazmat transportation accidents (Tables 1 and 2). According to the theory of accident causation (Bird and Germain, 1990), the root causes of accidents can be grouped as ‘‘immediate’’ or ‘‘contributing’’. The immediate causes are unsafe acts by a worker and unsafe working conditions. The contributing causes include management-related factors, environmental conditions, and the physical or mental condition of the worker. Here, we have defined human factors (H), Hazmat packing and loading (C), and transport vehicles and facilities (T) as direct factors responsible for accidents. Human factors include skill level (H1), health (H2), and safety awareness (H3). Hazmat packing and loading includes packing (C1), and loading and unloading (C2). Transport vehicles and facilities (T) include transport vehicles (T1), protective equipment (T2), and maintenance and monitoring (T3). H, C, and T are parent direct factors, and H1, H2, H3, C1, C2, T1, T2, and T3 are child direct factors. The indirect factors are road conditions (R), weather conditions (W), and management (M). Road conditions and weather might increase the probability of accidents through their impact on humans, transport vehicles, and the hazardous material itself. Both humans and materials are subject to management impacts. Therefore, road conditions, weather, and management (which have
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L. Zhao et al. / Safety Science 50 (2012) 1049–1055 Table 1 Direct factors involved in Hazmat transportation accidents. Direct factors
Description
Value set
Human (H) Skill (H1) Health (H2) Safety awareness (H3)
Skill, experience Sickness, fatigue Safety awareness
Normal (0), abnormal (1) Normal (0), abnormal (1) Normal (0), abnormal (1)
Hazmat packing and loading (C) Packing (C1) Loading and unloading (C2)
Packing is complete Loading and unloading meet specified requirements for Hazmat
Yes (0), No (1) Yes (0), No (1)
Transport vehicles and facilities (T) Transport vehicle (T1) Protective equipment (T2) Maintenance and monitoring (T3)
Transport vehicle meets specified requirements for Hazmat transportation Transport vehicle is equipped with the required protective equipment Transport vehicle is maintained regularly
Yes (0), No (1) Yes (0), No (1) Yes (0), No (1)
Table 2 Indirect factors involved in Hazmat transportation accidents. Indirect factors
Description
Road condition (R) The type of road where the transport vehicle is operating Weather (W) Weather condition Management (M)
Management of transportation corporation
Value set Highway (0), national road (1), regional road (2) Sunny (0), rain and snow (1), foggy (2) Normal (0), abnormal (1)
Indirect factors M
3.2. Develop the structure of the Bayesian network 3.2.1. Develop the Bayesian network structure based on expert knowledge For a Bayesian network with n nodes, there are n(n 1)/2 pairs of nodes. To reduce the number of relationships that required confirmation by domain experts, we adopted certain simplifying assumptions based on the features of and causal relationships among the factors involved in Hazmat transportation accidents: Assumption 1. The parent direct factors (H, C, T) are independent each other. The indirect factors (M, R, W) are independent each other too.
Assumption 2. The child direct factors that belong to the same parent direct factor are independent each other. For example, factors H1, H2, and H3 are child factors of H. So they are independent each other.
Parent Direct factors
H2
H
H3 R
C1
C
A
C2 W
no child indirect factors) are considered to be indirect contributing causes for accidents. All 11 factors can be represented as the nodes of the Bayesian network. Thus, in the remainder of the paper, ‘‘node’’ has the same meaning as ‘‘factor’’. Tables 1 and 2 provide detailed descriptions of and value sets for the 11 factors. The direct factors have binary (yes/no, normal/abnormal) value sets, but the indirect factors potentially have more values in the value set. We collected the data from 94 Hazmat transportation accidents between 2005 and 2009 in China which was sufficiently well-documented that we could determine the values for each of the 11 parameters. Table A.1 summarizes the accident data. For example, Sample 1 in Table A.1 represents the accident in which liquid chlorine was spilled on the Beijing–Shanghai highway on 29 March 2005. Investigation revealed that the driver’s skill was inadequate (H1 = 1), the driver’s health was normal (H2 = 0), the driver’s safety awareness was low (H3 = 1), the Hazmat was packed and loaded correctly (C1 = 0, C2 = 0), the road was a highway (R = 0), the type of transport vehicle was correct (T1 = 0), the vehicle’s equipment and maintenance revealed problems (T2 = 1, T3 = 1), the weather was sunny (W = 0), and the management of the transportation corporation revealed problems (M = 1).
Child Direct factors H1
T1 T2
T
T3 Fig. 1. Factors and their relationships according to the four assumptions.
Assumption 3. Accidents only depend on parent direct factors. In other words, accidents only result from parent direct factors. Assumption 4. Indirect factors only affect child direct factors and do not directly affect parent direct factors. Based on these assumptions, we can get some relationships among the factors involved in Hazmat transportation accidents and develop the Bayesian network model shown in Fig. 1. At this stage of the analysis, there are still some pairs of nodes for which the relationships among them are not confirmed from these assumptions, and these are shown in Table A.2. The next step is to confirm their relationships based on expert knowledge using D–S evidence theory. For any pair of nodes, Vi and Vj, there is a relationship value set {Vi ? Vj, Vi Vj, Vi " Vj, Vi M Vj}, in which Vi ? Vj indicates that Vi directly causes Vj, Vi Vj indicates that Vj directly causes Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. We asked four domain experts to explore the causal relationships between the pairs of nodes. Based on their knowledge, they assigned a value representing the probability of a causal relationship between each pair of nodes in Table A.2. To reduce the subjectivity of expert opinion, we used D–S evidence theory (Fioretti, 2004) to synchronize the opinions of the experts and determine the casual relationships between the pairs of nodes. Here, we will focus on Dempster’s rule of combination, which is used to synchronize expert opinions:
8A # H; A–;; A1 ; A2 ; ; An H; mðAÞ¼K
X
m1 ðA1 Þ mn ðAn Þ
A1 ;A2 ;;An H
ð2Þ
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Table 3 Relationships between the factors involved in Hazmat transportation accidents based on expert knowledge (partial table, showing only representative examples). R ? H1
R
Exp1 Exp2 Exp3 Exp4 Mass
0 0 0 0 0
0 0 0 0 0
R ? T2
R
Exp1 Exp2 Exp3 Exp4 Mass
0 0.40 0 0 0
0 0 0 0 0
H1
T2
R " H1
R M H1
R ? H2
R
H2
1 1 1 1 1
0 0 0 0 0
1 1 1 1 1
0 0 0 0 0
R " T2
R M T2
M ? H2
M
0.80 0.60 1 1 1
0.2 0 0 0 0
0.30 0.50 0.20 0.60 0.18
0 0 0.20 0 0
H2
R " H2
R M H2
0 0 0 0 0
0 0 0 0 0
M " H2
M M H2
0 0 0 0 0
0.70 0.50 0.60 0.40 0.82
1. Vi ? Vj indicates that Vi directly causes Vj, Vi Vj indicates that Vj directly causes Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. 2. Exp = domain experts.
where : K ¼
1
P
A1 ;A2 ;;An H m1 ðA1 Þ mn ðAn Þ A1 \A2 \An ¼;
!1 Among the four
kinds of relationship, the one with the maximum mass value is adopted to represent the relationship between two nodes. The result of integrating these processes is shown in Table 3. When the causal relationship is indeterminate, as in the case of M M H2, R M H3, C1 M T1, and W M H3 in Table A.2, we used ‘‘mutual information’’ to determine the relationship between two nodes. Mutual information represents the expected information that is gained upon sending some symbol or receiving another. In Bayesian networks, if two nodes are dependent, knowing the value of one node will provide some information regarding the value of the other node. Such information can then be measured as mutual information. Therefore, the mutual information between two nodes can be used to judge whether the two nodes are dependent and how close their relationship is.
Table 4 Relationships between four pairs of nodes whose relationships were determined using mutual information. (Vi, Vj)
(M, H2)
(R, H3)
(C1, T1)
(W, H3)
I (Vi; Vj) Relationship
0.26 ?
0 "
0.12
0.01 "
Vj indicates that Vj directly causes Vi, Vi ? Vj indicates that Vi directly causes Vj, Vi Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain.
H1 M
R
IðX i ; X j Þ ¼
X i ;X j
3.2.2. Modify the Bayesian network structure based on a test for conditional independence The next step is to conduct a conditional independence test for the Bayesian network structure. According to assumption 4 in Section 3.2.1, indirect factors can influence direct factors via the child direct factors, so there may be conditional-independence relationships in which there is more than one path between indirect fac-
C
A
T1
T
T2
ð3Þ
For a pair of nodes, if I(Xi; Xj) is greater than a certain threshold (e), there is a causal relationship between Xi and Xj. Given the low probability of Hazmat transportation accidents, let e = 0.02. From Table A.1, we can calculate the mutual information among the pairs of nodes using Eq. (3). For pairs of nodes with a causal relationship, the direction of the causal relationship can be determined by the experts. The relationships among the abovementioned four pairs of nodes are shown in Table 4. Using this method, we can find the causal relationships among all the factors, and refine the Bayesian networks structure of Hazmat transportation accidents based on expert knowledge as shown in Fig. 2. During the process of developing the network structure, experts do not consider the conditional independence of the various factors. So it is necessary to modify the Bayesian network structure.
C1 C2
W
PðX i ; X j Þ PðX i ; X j Þ log PðX i ÞPðX j Þ
H
H3
Definition 1. The mutual information I(Xi; Xj) for nodes Xi and Xj is defined as
X
H2
T3 Fig. 2. Bayesian networks structure based on expert knowledge.
tors and child direct factors. Fig. 2 shows that these pairs of nodes include (R, C1), (R, C2), (M, T1), and (M, T3). Here, we tested for conditional independence using conditional mutual information (Cheng et al., 2002). Definition 2. The mutual information I(Xi; Xj|C) of nodes Xi and Xj given condition C is defined as:
IðX i ; X j jCÞ ¼
X X i ;X j ;C
PðX i ; X j ; CÞ log
PðX i ; X j jCÞ PðX i jCÞPðX j jCÞ
ð4Þ
where C is a set of nodes, and when I(Xi; Xj|C) is smaller than a certain threshold value of e (here, e = 0.02), we say that Xi and Xj are conditionally independent given C. The marginal and conditional probabilities in Eqs. (3) and (4) can be estimated using the relative frequencies calculated from the values in Table A.1. Geiger and Pearl (1993) proved that all conditionally independent relationships can be found from the topology of a Bayesian network using a concept called ‘‘direction-dependent separation’’, which is also referred to as ‘‘d-separation’’ (Pearl, 1988). The
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Table 5 Posterior probabilities for the direct factors involved in Hazmat transportation accidents.
H1 M
H2
H
Direct factors
H
H3 R
H1
C1
C
Posterior probability
A
C2 W
C H2
H3
T C2
T1
T2
T3
0.532 0.157 0.404 0.371 0.055 0.306 0.117 0.266 0.655
T1
C1
0.443
0.516
T
T2
Table 6 Posterior probabilities for the indirect factors involved in Hazmat transportation accidents.
T3 Fig. 3. Bayesian networks structure after conditional independence test.
following algorithm can be used to test for a conditionally independent relationship between a pair of nodes: For each arc (node1, node2) in the current graph, if any other path exists between the two nodes, then temporarily remove this arc from the current graph and use the algorithm for finding the cut-set (Cheng et al., 2002) to find a cut-set that can d-separate node1 and node2 in the revised graph. Next, use a conditional independence test to test whether node1 and node2 are conditionally independent given the new cut-set. If so, remove the arc permanently; otherwise, add this arc back to the graph. Given cut-set H, we can calculate I(R; C1|H) = 0.032, I(R; C2|H) = 0.010, I(M; T1|H) = 0.001, and I(M; T3|H) = 0.011, which means that (R, C1) is conditionally independent, and that (R, C2), (M, T1), and (M, T3) are not conditionally independent. Thus, the links between (R, C2), (M, T1), and (M, T3) can be removed from the graph. Fig. 3 shows the Bayesian network structure for Hazmat transportation accidents after eliminating links based on the results of the conditional independence test. 4. Learning the parameters of the Bayesian network When the structure of a Bayesian network has been established and the values of some of the variables can be obtained from the database of cases, the cases can then be used to estimate the parameters of the model (i.e., the conditional probabilities). This is called parameter estimation or ‘‘learning’’ (Little and Rubin, 1997; Jensen and Nielsen, 2007). The EM algorithm (Lautitzen, 1995; Jensen and Nielsen, 2007; Friedman, 2010) is a general approach for finding maximum-likelihood estimates for a set of parameters h, when researchers have an incomplete data set. The EM algorithm begins by randomly assigning a configuration h0 to h when the algorithm is used in parameter learning. Suppose that ht is the outcome after t iterations. The calculation process then follows three steps: Step 1: Suppose that Xmis is a variable with a missing value in incomplete dataset D. Let Xmis = xmis so that we can obtain a complete sample dataset by adding xmis to D. During the process, Xmis may have more assignments, the EM algorithm assigns a weight Wxmis for every possible result, Xmis, and the weighted sample is then given by:
ðD; X mis ¼ xmis Þ½W xmis
ð5Þ t
where W xmis ¼ PðX mis ¼ xmis jD; h Þ: The weight ranges from 0 to 1. The weighted sample is also called a ‘‘fractional sample’’. During the process of data fixing, each incomplete sample is replaced by a complete fractional sample, and the sample weight of the original complete sample is 1. Step 2: For the complete sample obtained in step 1, calculate the maximum likelihood by estimating ht+1 using Eq. (6):
Indirect factors
R
W
M
Posterior probability
0.798
0.191
0.372
tþ1 hijk ¼
8 ri P mtijk > > > ; mtijk > 0 ri > P > < mt k¼1 ijk
k¼1
> ri > P > > 1 > mtijk 6 0 : ri ;
ð6Þ
k¼1
Step 3: If the result meets the accuracy requirements, the algorithm ends; if not, return to step 1 and repeat the algorithm. To perform this analysis, we used the algorithm coded by Murphy (2010), and performed the learning part of the process using the sample data in Table A.1. Tables 5 and 6 summarize the results. 5. Results and discussions Based on the results of our analysis, the posterior probability for the human factors was 0.655, which was significantly higher than that for the transport vehicle and facilities (0.516) and for Hazmat packing and loading (0.443). This result shows that even when technology and equipment provide the necessary level of safety, unsuitable operation of the transportation corporation and human error are still the major factors that can cause accidents. Moreover, within the human factors group, the driver’s skill had the highest posterior probability (0.532), followed by the driver’s safety awareness (0.404). This result is realistic based on the current situation for Hazmat transportation in China. With the rapid development of transportation industry that has occurred, the number of skilled drivers is less than the number required by the industry, resulting in many inexperienced drivers who are engaged in Hazmat transportation. This is a significant problem for the Hazmat transportation industry. The transport vehicle and equipment had the second-highest posterior probability (0.516). Hazardous materials have many dangerous properties (e.g., they may be flammable, explosive, toxic, or corrosive), so the transportation of Hazmat has special requirements for the transport vehicle and equipment. For example, the selection of transport vehicles must take into account the characteristics of Hazmat, such as its nature (e.g., gas, solid, or liquid), shape, and packaging. Unfortunately, this is often neglected, especially by small and medium transportation corporations, and using an inappropriate vehicle leads to increased risk of accidents. Table 5 also shows that the packing of the Hazmat has a relatively high posterior probability (0.443). Because of the instability of Hazmat, special packing requirements are necessary. However, some transportation corporations do not follow these requirements in order to reduce their cost. In addition, the Hazmat is sometimes not tightly fixed in place. During rough driving, the package might therefore rupture, and this factor also commonly leads to accidents.
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Based on our results, measures to reduce Hazmat transportation accidents should prioritize human factors. Hazmat transportation corporations should implement training programs to improve the skills of their drivers and to raise their safety awareness. Second, transportation corporations should improve their management of the transport vehicles. For example, they should choose the right type of vehicle based on the characteristics of the Hazmat, should examine the transport vehicle regularly to identify problems that require immediate action, and should periodically maintain the vehicle; in addition, they should monitor the vehicle during its travel. Last but not least, transportation corporations should improve the packing and loading of Hazmat to ensure that the packing and loading both meet the requirements of the material. Of the indirect factors (Table 6), road conditions had the greatest posterior probability (0.798), as these factors affect the driver, the vehicle, and the Hazmat packing, and poor road conditions can greatly increase the probability of an accident. Therefore, Hazmat transportation corporations must choose the proper route
according to the road conditions. At the same time, weather conditions should be carefully considered before and during Hazmat transportation. Transportation should avoid periods of bad weather, such as rain, snow and fog, or sandstorms; alternatively, drivers should take the necessary protective measures (e.g., installing winter tires during periods when the temperature decreases below freezing). The posterior probability for transportation corporation management was 0.372; even though this had a smaller impact than road conditions, this value is high enough to indicate that transportation corporations should manage their operations carefully.
6. Conclusions Bayesian networks allow researchers to investigate the influence of a range of factors, as we did for Hazmat transportation accidents in this paper. The Bayesian network was developed based on
Table A.1 Parameter values for the 94 case studies used to support the Bayesian network analysis of the factors involved in Hazmat transportation accidents. Sample
R
W
M
H1
H2
H3
C1
C2
T1
T2
T3
Sample
R
W
M
H1
H2
H3
C1
C2
T1
T2
T3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
1 0 0 0 1 2 0 0 0 0 0 2 0 0 0 2 0 2 0 2 0 0 0 0 2 2 1 0 0 2 0 0 0 2 0 0 2 0 0 1 1 0 1 1 0 0 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 1 2 0 2 0 0 0 1 0 0 0 0
0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0
0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0
0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0
1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0
0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
1 2 1 1 0 0 0 2 1 2 1 2 2 1 0 2 0 0 1 0 2 2 1 0 1 2 0 1 2 0 2 2 0 1 0 1 0 1 2 2 2 0 1 0 0 1 2
0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1
1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1
0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0
0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0
0 0
1. R = road condition, W = weather, M = management, H1 = skill, H2 = health, H3 = safety awareness, C1 = packing, C2 = loading and unloading, T1 = transport vehicle, T2 = protective equipment, T3 = maintenance and monitoring. 2. There are no public databases that report Hazmat transportation accidents in China. We therefore used accident information (e.g., time, description of accident, and source) published in the Journal of Safety and the Environment from 2005 to 2009. In addition, we gathered detailed information from newspapers and the Internet. However, we excluded some accidents that lacked sufficient information for us to determine the values of all 11 parameters. In total, we chose 94 accidents as our research subjects.
L. Zhao et al. / Safety Science 50 (2012) 1049–1055 Table A.2 The relationships among the 11 factors determined based on expert knowledge.
M R W H1 H2 H3 C1 C2 T1 T2 T3 H C T
H1
H2
H3
C1
C2
T1
T2
T3
? " "
M ? "
? M M
" ? " " " "
" ? " " " "
? " ? " " " M "
? " " " " " " "
? " " " " " " "
M " " ?
" " " ?
? "
" "
? "
"
"
" " " " "
" " " " "
" " " " "
" "
" "
" "
H
C
T
1055
Appendix A Tables A.1 and A.2 References
? ? ? " " " " "
" " " ? ? " " "
" " " " " ? ? ?
1. H1 = skill, H2 = health, H3 = safety awareness, C1 = packing, C2 = loading and unloading, T1 = transport vehicle, T2 = protective equipment, T3 = maintenance and monitoring, H = human factors, C = Hazmat packing and loading, T = transport vehicle and facilities. Vj indicates that Vj directly causes 2. Vi ? Vj indicates that Vi directly causes Vj, Vi Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. 3. The empty cells indicate that it was not necessary to confirm the relationship based on expert knowledge because of the assumption that there were no relationships between these pairs of nodes.
expert knowledge, modified based on the results of a conditional independence test, and supplied with data from 94 Hazmat transportation accidents in China. We then used the EM algorithm to calculate the posterior probability of each factor, thereby revealing the relative influence of the factors that can cause accidents. We successfully used this approach to analyze the importance of different causal factors in Hazmat transportation accidents. The conditional independence test indicated that conditional independence relationships existed within the Bayesian network developed by the experts, and resulted in modification of the Bayesian networks structure. Our studies revealed the relative importance of each of the 11 factors that we considered in our analysis of the case study data. Human factors were the most important direct factor that caused accidents. Of these factors, the driver’s skill had the greatest influence on accidents. Road conditions had the greatest indirect influence on accidents. These results are realistic given the reality of the Hazmat transportation industry in China, and provide guidance that will help transportation corporations take the necessary measures to reduce the frequency of accidents.
Acknowledgments This study was supported by grants from the National Natural Science Foundation of China (Nos. 90924030 and 70673012) and the ‘‘Shuguang’’ project of the Shanghai Education Commission (No. 09SG38). We thank the journal’s anonymous reviewers for their valuable comments and suggestions, which helped to improve our paper.
Andrews, J.D., Moss, T.R., 2002. Reliability and Risk Assessment, second ed. American Society of Mechanical Engineers, New York, NY. Bird, F., Germain, G. 1990. Practical Loss Control Leadership, Revised ed. International Loss Control Institute, Duluth, GA, 446 p. Cheng, J., Bell, D., Liu, W.R., 2002. Learning Bayesian networks from data: an efficient approach based on information theory. Artificial Intelligence 137 (1-2), 43–90. Fioretti, G., 2004. Evidence theory: a mathematical framework for unpredictable hypotheses. Metroeconomica 55 (4), 345–366. Friedman, N., 2010 The Bayesian Structural EM algorithm.. (20.05.10). Geiger, D., Pearl, J., 1993. Logical and algorithmic properties of conditional independence. The Annals of Statistics 21 (4), 2001–2021. Hamada, M., Martz, H.F., Reese, C.S., Graves, T., Johnson, V., Wilson, A.G., 2004. A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation. Reliability Engineering and System Safety 86 (3), 297–305. Jensen, F.V., Nielsen, T.D., 2007. Bayesian Networks and Decision Graphs, second ed. Springer-Verlag, New York, NY, pp. 201–206. Kjaerulff, U.B., Madsen, A.L., 2008. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Springer, New York, NY, 144 p. Lautitzen, S.L., 1995. The EM algorithm for graphical association models with missing data. Computational Statistics & Data Analysis 19, 191–201. Little, R., Rubin, D., 1997. Statistical Analysis with Missing Data. John Wiley & Sons, New York, NY. Maglogiannis, I., Zafiropoulos, E., Platis, A., Lambrinoudakis, C., 2006. Risk analysis of a patient monitoring system using Bayesian Network modeling. Journal of Biomedical Informatics 39, 637–647. Marsh, W., Bearfield, G., 2004. Using Bayesian networks to model accident causation in the UK railway industry. In: International Conference on Probabilistic Safety Assessment and Management, PSAM7, Berlin. Murphy, J., 2010. Bayes Net Toolbox for Matlab.
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Safety Science journal homepage: www.elsevier.com/locate/ssci
Analysis of factors that influence hazardous material transportation accidents based on Bayesian networks: A case study in China Laijun Zhao a, Xulei Wang a,b,⇑, Ying Qian a a b
Shanghai University, School of Management, Shanghai 200444, PR China Qingdao Agriculture University, College of Economics and Management, Qingdao 266109, PR China
a r t i c l e
i n f o
Article history: Received 24 September 2010 Received in revised form 3 November 2011 Accepted 4 December 2011 Available online 27 December 2011 Keywords: Hazardous materials (Hazmat) Transportation Bayesian networks Dempster–Shafer evidence theory Expectation–maximization algorithm
a b s t r a c t In this study, we applied Bayesian networks to prioritize the factors that influence hazardous material (Hazmat) transportation accidents. The Bayesian network structure was built based on expert knowledge using Dempster–Shafer evidence theory, and the structure was modified based on a test for conditional independence. We collected and analyzed 94 cases of Chinese Hazmat transportation accidents to compute the posterior probability of each factor using the expectation–maximization learning algorithm. We found that the three most influential factors in Hazmat transportation accidents were human factors, the transport vehicle and facilities, and packing and loading of the Hazmat. These findings provide an empirically supported theoretical basis for Hazmat transportation corporations to take corrective and preventative measures to reduce the risk of accidents. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, many accidents caused by hazardous materials (Hazmat) transportation have resulted in catastrophic losses of human life and damage to the environment in China. Such accidents have attracted increasing attention from the general public and the government, and a growing amount of research about accident prevention has been conducted (Wang et al., 2005; Zhao et al., 2009; Yang et al., 2010). Analysis of the factors that influence Hazmat transportation accidents is an important issue in accident prevention because it can provide transportation corporations with actionable information on the causes of accidents. As a result, corrective and preventative measures can be implemented to exercise greater control over these factors. The most common methods that are used to analyze the factors that influence Hazmat transportation accidents, such as statistical methods and fault tree analysis, consider all factors to be independent rather than related (Wang et al., 2005; Oggero et al., 2006; Samuel et al., 2009; Trépanier et al., 2009; Zhao et al., 2009; Yang et al., 2010). In reality, multiple factors contribute to a Hazmat transportation accident, and these factors are often interrelated (Bird and Germain, 1990). Thus, it is necessary to consider the interplay of factors when analyzing such accidents. As a tool for ⇑ Corresponding author at: Shanghai University, School of Management, 99 Shangda Road, BaoShan District, Shanghai 200444, PR China. Tel.: +86 21 6613 7925; fax: +86 21 6613 4284. E-mail address: [email protected] (X. Wang). 0925-7535/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2011.12.003
studying uncertainty, Bayesian networks combine graph theory with probability theory, and can represent both the uncertainty and the interplay among the variables (Pearl, 1988, 2003). In this approach, probabilistic inference can be conducted to predict the values of some variables based on the observed values of other variables, and the predicted value is referred to as the ‘‘posterior probability’’. The posterior probability serves as a universally sufficient statistic for detection applications because it captures the relationships and interplay among the variables that describe a situation (Pearl, 2003). If we apply Bayesian networks to analyze Hazmat transportation accidents, we can assign the probability of the accident to be 1 (i.e., 100% probability because the accident has already occurred), and the posterior probability of each factor can then represent its influence on the accident. Based on this analysis, we can identify the most important factors that contributed to the accident and find relationships among these factors. The results of this analysis will help transportation corporations take the measures required to reduce the risk of an accident. A Bayesian network can be constructed manually, (semi-)automatically from the data, or by a combination of a manual and datadriven processes (Kjaerulff and Madsen, 2008). The last approach first develops the structure of the Bayesian network by taking advantage of the knowledge of domain experts, and then learns the parameters of the Bayesian network from a database using a learning algorithm such as the maximum-likelihood estimation algorithm or the expectation–maximization (EM) algorithm. This approach is sufficiently easy that it can be used in practice. Moreover, the network structure can be easily understood and the
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expert knowledge can be easily incorporated in the model. However, this method has two limitations: expert knowledge is subjective and limited, which results in poor reliability when building the network’s structure, and conditional independence among the variables is ignored when the experts confirm the causal relationship among variables. Overcoming these limitations is the key issue when constructing Bayesian networks using this approach. The remainder of this paper is organized as follows: Section 2 presents a literature review on the analysis of factors that influence Hazmat transportation accidents and Bayesian networks. Section 3 identifies key factors involved in Hazmat transportation accidents and builds a Bayesian network structure based on expert knowledge using Dempster–Shafer (D–S) evidence theory. Moreover, the structure of Bayesian network is modified according to the conditional independence test. Section 4 computes the posterior probability of the factors using the EM algorithm to find the influence of the different factors on transportation accidents. Section 5 analyzes the results and describes their implications for China’s Hazmat transportation corporations. Section 6 provides our conclusions.
2. Previous related work Most previous studies that analyzed the factors responsible for Hazmat transportation accidents used a statistical method. The researchers largely confined themselves to the collection, analysis, and interpretation of data derived from accident reports or an accident database. For example, Oggero et al. (2006) studied 1932 accidents that occurred during the transport of Hazmat by road and rail from the beginning of the 20th century to July 2004, and concluded that the following major factors were responsible for the accidents: external factors such as the weather, human factors such as operator error, and mechanical failures. Wang et al. (2005) studied Hazmat transportation accidents in China and concluded that six groups of factors were responsible for these accidents: human, vehicle, packing, transportation facilities, road conditions, and environmental conditions. Zhao et al. (2009) studied 650 Hazmat transportation accidents from 2005 to 2008 to analyze the influencing factors and found results similar to those of Wang et al. (2005). Although statistical methods can analyze the relationships between an accident and the factors that influence it, they cannot account for the interplay among different factors and fail to reflect the fact that an accident is usually the result of more than one factor (Bird and Germain, 1990). To avoid this problem, tree-based methods such as fault-tree analysis, event-tree analysis, and cause-consequence analysis are often used to identify the influencing factors (Roland and Moriarty, 1990; Hamada et al., 2004). However, tree-based methods are based on three assumptions: (1) accidents are binary events, (2) events are statistically independent, and (3) the relationship among events can be represented by means of ‘‘logical gates’’ (Singer, 1990; Andrews and Moss, 2002; Rao et al., 2009). These assumptions restrict the use of these methods to static, logic-based modeling. The tree-based methods are therefore not suitable to describe influencing factors with more than two potential states and make it difficult to represent the relationships among factors. For Hazmat transportation accidents, some factors may have more than two states; for example, weather conditions and road conditions have a wide range of possible states. In addition, the relationships among the factors responsible for an accident cannot be easily represented by means of logical gates. Thus, tree-based methods are not suitable for analyzing the factors that influence Hazmat transportation accidents. A more promising approach involves the use of Bayesian networks, which have previously been applied in accident analysis.
For example, Trucco et al. (2008) developed a Bayesian belief network to model the maritime transport system. Their model represented various factors and their mutual influences by means of a set of dependent variables. Marsh and Bearfield (2004) described a method of modeling the organizational causes of accidents using Bayesian networks, and demonstrated how such a model can be used for risk assessment based on examples from a model of the causes of Signals Passed at Danger (SPAD) incidents in the UK railway system. Maglogiannis et al. (2006) developed a Bayesian network model to concisely represent all the interactions among undesirable events in a risk analysis for health information systems, and the Bayesian network model identified and prioritized the most critical events. The structures of the abovementioned Bayesian networks were often developed based on the causal relationships determined by domain experts. However, due to the subjectivity of the opinions of domain experts, the Bayesian network’s structure may be inconsistent with the actual situation. Moreover, the domain experts in these studies did not consider the possibility of conditional independence relationships between nodes, which can lead to an incorrect description of the relationships between nodes in the network structure. 3. A Bayesian network structure for Hazmat transportation accidents For detailed information about Bayesian networks, refer to the work of Pearl (1988, 2003). Here, we present only a basic mathematical description. Given a directed acyclic graph, f = (V, E), where V denotes a set of nodes and E denotes a set of directed edges, we can describe a joint probability distribution, P, over the set of variables X = {X1, X2, . . ., Xn}, which can be factorized as follows:
PfX 1 ; X 2 ; . . . X n g ¼ Pi PðX i jp½X i Þ
ð1Þ
where p[Xi] denotes the set of parent variables of variable Xi for each node m 2 V. The nodes in V are in one-to-one correspondence with the variables Xi. For a node without any parent nodes, the conditional probability is the same as the prior probability. 3.1. Define the variables and their structures Based on a review of the literature (Oggero et al., 2006; Samuel et al., 2009; Trépanier et al., 2009; Zhao et al., 2009) and a survey of transportation corporations, we identified 11 direct and indirect factors related to Hazmat transportation accidents (Tables 1 and 2). According to the theory of accident causation (Bird and Germain, 1990), the root causes of accidents can be grouped as ‘‘immediate’’ or ‘‘contributing’’. The immediate causes are unsafe acts by a worker and unsafe working conditions. The contributing causes include management-related factors, environmental conditions, and the physical or mental condition of the worker. Here, we have defined human factors (H), Hazmat packing and loading (C), and transport vehicles and facilities (T) as direct factors responsible for accidents. Human factors include skill level (H1), health (H2), and safety awareness (H3). Hazmat packing and loading includes packing (C1), and loading and unloading (C2). Transport vehicles and facilities (T) include transport vehicles (T1), protective equipment (T2), and maintenance and monitoring (T3). H, C, and T are parent direct factors, and H1, H2, H3, C1, C2, T1, T2, and T3 are child direct factors. The indirect factors are road conditions (R), weather conditions (W), and management (M). Road conditions and weather might increase the probability of accidents through their impact on humans, transport vehicles, and the hazardous material itself. Both humans and materials are subject to management impacts. Therefore, road conditions, weather, and management (which have
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L. Zhao et al. / Safety Science 50 (2012) 1049–1055 Table 1 Direct factors involved in Hazmat transportation accidents. Direct factors
Description
Value set
Human (H) Skill (H1) Health (H2) Safety awareness (H3)
Skill, experience Sickness, fatigue Safety awareness
Normal (0), abnormal (1) Normal (0), abnormal (1) Normal (0), abnormal (1)
Hazmat packing and loading (C) Packing (C1) Loading and unloading (C2)
Packing is complete Loading and unloading meet specified requirements for Hazmat
Yes (0), No (1) Yes (0), No (1)
Transport vehicles and facilities (T) Transport vehicle (T1) Protective equipment (T2) Maintenance and monitoring (T3)
Transport vehicle meets specified requirements for Hazmat transportation Transport vehicle is equipped with the required protective equipment Transport vehicle is maintained regularly
Yes (0), No (1) Yes (0), No (1) Yes (0), No (1)
Table 2 Indirect factors involved in Hazmat transportation accidents. Indirect factors
Description
Road condition (R) The type of road where the transport vehicle is operating Weather (W) Weather condition Management (M)
Management of transportation corporation
Value set Highway (0), national road (1), regional road (2) Sunny (0), rain and snow (1), foggy (2) Normal (0), abnormal (1)
Indirect factors M
3.2. Develop the structure of the Bayesian network 3.2.1. Develop the Bayesian network structure based on expert knowledge For a Bayesian network with n nodes, there are n(n 1)/2 pairs of nodes. To reduce the number of relationships that required confirmation by domain experts, we adopted certain simplifying assumptions based on the features of and causal relationships among the factors involved in Hazmat transportation accidents: Assumption 1. The parent direct factors (H, C, T) are independent each other. The indirect factors (M, R, W) are independent each other too.
Assumption 2. The child direct factors that belong to the same parent direct factor are independent each other. For example, factors H1, H2, and H3 are child factors of H. So they are independent each other.
Parent Direct factors
H2
H
H3 R
C1
C
A
C2 W
no child indirect factors) are considered to be indirect contributing causes for accidents. All 11 factors can be represented as the nodes of the Bayesian network. Thus, in the remainder of the paper, ‘‘node’’ has the same meaning as ‘‘factor’’. Tables 1 and 2 provide detailed descriptions of and value sets for the 11 factors. The direct factors have binary (yes/no, normal/abnormal) value sets, but the indirect factors potentially have more values in the value set. We collected the data from 94 Hazmat transportation accidents between 2005 and 2009 in China which was sufficiently well-documented that we could determine the values for each of the 11 parameters. Table A.1 summarizes the accident data. For example, Sample 1 in Table A.1 represents the accident in which liquid chlorine was spilled on the Beijing–Shanghai highway on 29 March 2005. Investigation revealed that the driver’s skill was inadequate (H1 = 1), the driver’s health was normal (H2 = 0), the driver’s safety awareness was low (H3 = 1), the Hazmat was packed and loaded correctly (C1 = 0, C2 = 0), the road was a highway (R = 0), the type of transport vehicle was correct (T1 = 0), the vehicle’s equipment and maintenance revealed problems (T2 = 1, T3 = 1), the weather was sunny (W = 0), and the management of the transportation corporation revealed problems (M = 1).
Child Direct factors H1
T1 T2
T
T3 Fig. 1. Factors and their relationships according to the four assumptions.
Assumption 3. Accidents only depend on parent direct factors. In other words, accidents only result from parent direct factors. Assumption 4. Indirect factors only affect child direct factors and do not directly affect parent direct factors. Based on these assumptions, we can get some relationships among the factors involved in Hazmat transportation accidents and develop the Bayesian network model shown in Fig. 1. At this stage of the analysis, there are still some pairs of nodes for which the relationships among them are not confirmed from these assumptions, and these are shown in Table A.2. The next step is to confirm their relationships based on expert knowledge using D–S evidence theory. For any pair of nodes, Vi and Vj, there is a relationship value set {Vi ? Vj, Vi Vj, Vi " Vj, Vi M Vj}, in which Vi ? Vj indicates that Vi directly causes Vj, Vi Vj indicates that Vj directly causes Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. We asked four domain experts to explore the causal relationships between the pairs of nodes. Based on their knowledge, they assigned a value representing the probability of a causal relationship between each pair of nodes in Table A.2. To reduce the subjectivity of expert opinion, we used D–S evidence theory (Fioretti, 2004) to synchronize the opinions of the experts and determine the casual relationships between the pairs of nodes. Here, we will focus on Dempster’s rule of combination, which is used to synchronize expert opinions:
8A # H; A–;; A1 ; A2 ; ; An H; mðAÞ¼K
X
m1 ðA1 Þ mn ðAn Þ
A1 ;A2 ;;An H
ð2Þ
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Table 3 Relationships between the factors involved in Hazmat transportation accidents based on expert knowledge (partial table, showing only representative examples). R ? H1
R
Exp1 Exp2 Exp3 Exp4 Mass
0 0 0 0 0
0 0 0 0 0
R ? T2
R
Exp1 Exp2 Exp3 Exp4 Mass
0 0.40 0 0 0
0 0 0 0 0
H1
T2
R " H1
R M H1
R ? H2
R
H2
1 1 1 1 1
0 0 0 0 0
1 1 1 1 1
0 0 0 0 0
R " T2
R M T2
M ? H2
M
0.80 0.60 1 1 1
0.2 0 0 0 0
0.30 0.50 0.20 0.60 0.18
0 0 0.20 0 0
H2
R " H2
R M H2
0 0 0 0 0
0 0 0 0 0
M " H2
M M H2
0 0 0 0 0
0.70 0.50 0.60 0.40 0.82
1. Vi ? Vj indicates that Vi directly causes Vj, Vi Vj indicates that Vj directly causes Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. 2. Exp = domain experts.
where : K ¼
1
P
A1 ;A2 ;;An H m1 ðA1 Þ mn ðAn Þ A1 \A2 \An ¼;
!1 Among the four
kinds of relationship, the one with the maximum mass value is adopted to represent the relationship between two nodes. The result of integrating these processes is shown in Table 3. When the causal relationship is indeterminate, as in the case of M M H2, R M H3, C1 M T1, and W M H3 in Table A.2, we used ‘‘mutual information’’ to determine the relationship between two nodes. Mutual information represents the expected information that is gained upon sending some symbol or receiving another. In Bayesian networks, if two nodes are dependent, knowing the value of one node will provide some information regarding the value of the other node. Such information can then be measured as mutual information. Therefore, the mutual information between two nodes can be used to judge whether the two nodes are dependent and how close their relationship is.
Table 4 Relationships between four pairs of nodes whose relationships were determined using mutual information. (Vi, Vj)
(M, H2)
(R, H3)
(C1, T1)
(W, H3)
I (Vi; Vj) Relationship
0.26 ?
0 "
0.12
0.01 "
Vj indicates that Vj directly causes Vi, Vi ? Vj indicates that Vi directly causes Vj, Vi Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain.
H1 M
R
IðX i ; X j Þ ¼
X i ;X j
3.2.2. Modify the Bayesian network structure based on a test for conditional independence The next step is to conduct a conditional independence test for the Bayesian network structure. According to assumption 4 in Section 3.2.1, indirect factors can influence direct factors via the child direct factors, so there may be conditional-independence relationships in which there is more than one path between indirect fac-
C
A
T1
T
T2
ð3Þ
For a pair of nodes, if I(Xi; Xj) is greater than a certain threshold (e), there is a causal relationship between Xi and Xj. Given the low probability of Hazmat transportation accidents, let e = 0.02. From Table A.1, we can calculate the mutual information among the pairs of nodes using Eq. (3). For pairs of nodes with a causal relationship, the direction of the causal relationship can be determined by the experts. The relationships among the abovementioned four pairs of nodes are shown in Table 4. Using this method, we can find the causal relationships among all the factors, and refine the Bayesian networks structure of Hazmat transportation accidents based on expert knowledge as shown in Fig. 2. During the process of developing the network structure, experts do not consider the conditional independence of the various factors. So it is necessary to modify the Bayesian network structure.
C1 C2
W
PðX i ; X j Þ PðX i ; X j Þ log PðX i ÞPðX j Þ
H
H3
Definition 1. The mutual information I(Xi; Xj) for nodes Xi and Xj is defined as
X
H2
T3 Fig. 2. Bayesian networks structure based on expert knowledge.
tors and child direct factors. Fig. 2 shows that these pairs of nodes include (R, C1), (R, C2), (M, T1), and (M, T3). Here, we tested for conditional independence using conditional mutual information (Cheng et al., 2002). Definition 2. The mutual information I(Xi; Xj|C) of nodes Xi and Xj given condition C is defined as:
IðX i ; X j jCÞ ¼
X X i ;X j ;C
PðX i ; X j ; CÞ log
PðX i ; X j jCÞ PðX i jCÞPðX j jCÞ
ð4Þ
where C is a set of nodes, and when I(Xi; Xj|C) is smaller than a certain threshold value of e (here, e = 0.02), we say that Xi and Xj are conditionally independent given C. The marginal and conditional probabilities in Eqs. (3) and (4) can be estimated using the relative frequencies calculated from the values in Table A.1. Geiger and Pearl (1993) proved that all conditionally independent relationships can be found from the topology of a Bayesian network using a concept called ‘‘direction-dependent separation’’, which is also referred to as ‘‘d-separation’’ (Pearl, 1988). The
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Table 5 Posterior probabilities for the direct factors involved in Hazmat transportation accidents.
H1 M
H2
H
Direct factors
H
H3 R
H1
C1
C
Posterior probability
A
C2 W
C H2
H3
T C2
T1
T2
T3
0.532 0.157 0.404 0.371 0.055 0.306 0.117 0.266 0.655
T1
C1
0.443
0.516
T
T2
Table 6 Posterior probabilities for the indirect factors involved in Hazmat transportation accidents.
T3 Fig. 3. Bayesian networks structure after conditional independence test.
following algorithm can be used to test for a conditionally independent relationship between a pair of nodes: For each arc (node1, node2) in the current graph, if any other path exists between the two nodes, then temporarily remove this arc from the current graph and use the algorithm for finding the cut-set (Cheng et al., 2002) to find a cut-set that can d-separate node1 and node2 in the revised graph. Next, use a conditional independence test to test whether node1 and node2 are conditionally independent given the new cut-set. If so, remove the arc permanently; otherwise, add this arc back to the graph. Given cut-set H, we can calculate I(R; C1|H) = 0.032, I(R; C2|H) = 0.010, I(M; T1|H) = 0.001, and I(M; T3|H) = 0.011, which means that (R, C1) is conditionally independent, and that (R, C2), (M, T1), and (M, T3) are not conditionally independent. Thus, the links between (R, C2), (M, T1), and (M, T3) can be removed from the graph. Fig. 3 shows the Bayesian network structure for Hazmat transportation accidents after eliminating links based on the results of the conditional independence test. 4. Learning the parameters of the Bayesian network When the structure of a Bayesian network has been established and the values of some of the variables can be obtained from the database of cases, the cases can then be used to estimate the parameters of the model (i.e., the conditional probabilities). This is called parameter estimation or ‘‘learning’’ (Little and Rubin, 1997; Jensen and Nielsen, 2007). The EM algorithm (Lautitzen, 1995; Jensen and Nielsen, 2007; Friedman, 2010) is a general approach for finding maximum-likelihood estimates for a set of parameters h, when researchers have an incomplete data set. The EM algorithm begins by randomly assigning a configuration h0 to h when the algorithm is used in parameter learning. Suppose that ht is the outcome after t iterations. The calculation process then follows three steps: Step 1: Suppose that Xmis is a variable with a missing value in incomplete dataset D. Let Xmis = xmis so that we can obtain a complete sample dataset by adding xmis to D. During the process, Xmis may have more assignments, the EM algorithm assigns a weight Wxmis for every possible result, Xmis, and the weighted sample is then given by:
ðD; X mis ¼ xmis Þ½W xmis
ð5Þ t
where W xmis ¼ PðX mis ¼ xmis jD; h Þ: The weight ranges from 0 to 1. The weighted sample is also called a ‘‘fractional sample’’. During the process of data fixing, each incomplete sample is replaced by a complete fractional sample, and the sample weight of the original complete sample is 1. Step 2: For the complete sample obtained in step 1, calculate the maximum likelihood by estimating ht+1 using Eq. (6):
Indirect factors
R
W
M
Posterior probability
0.798
0.191
0.372
tþ1 hijk ¼
8 ri P mtijk > > > ; mtijk > 0 ri > P > < mt k¼1 ijk
k¼1
> ri > P > > 1 > mtijk 6 0 : ri ;
ð6Þ
k¼1
Step 3: If the result meets the accuracy requirements, the algorithm ends; if not, return to step 1 and repeat the algorithm. To perform this analysis, we used the algorithm coded by Murphy (2010), and performed the learning part of the process using the sample data in Table A.1. Tables 5 and 6 summarize the results. 5. Results and discussions Based on the results of our analysis, the posterior probability for the human factors was 0.655, which was significantly higher than that for the transport vehicle and facilities (0.516) and for Hazmat packing and loading (0.443). This result shows that even when technology and equipment provide the necessary level of safety, unsuitable operation of the transportation corporation and human error are still the major factors that can cause accidents. Moreover, within the human factors group, the driver’s skill had the highest posterior probability (0.532), followed by the driver’s safety awareness (0.404). This result is realistic based on the current situation for Hazmat transportation in China. With the rapid development of transportation industry that has occurred, the number of skilled drivers is less than the number required by the industry, resulting in many inexperienced drivers who are engaged in Hazmat transportation. This is a significant problem for the Hazmat transportation industry. The transport vehicle and equipment had the second-highest posterior probability (0.516). Hazardous materials have many dangerous properties (e.g., they may be flammable, explosive, toxic, or corrosive), so the transportation of Hazmat has special requirements for the transport vehicle and equipment. For example, the selection of transport vehicles must take into account the characteristics of Hazmat, such as its nature (e.g., gas, solid, or liquid), shape, and packaging. Unfortunately, this is often neglected, especially by small and medium transportation corporations, and using an inappropriate vehicle leads to increased risk of accidents. Table 5 also shows that the packing of the Hazmat has a relatively high posterior probability (0.443). Because of the instability of Hazmat, special packing requirements are necessary. However, some transportation corporations do not follow these requirements in order to reduce their cost. In addition, the Hazmat is sometimes not tightly fixed in place. During rough driving, the package might therefore rupture, and this factor also commonly leads to accidents.
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L. Zhao et al. / Safety Science 50 (2012) 1049–1055
Based on our results, measures to reduce Hazmat transportation accidents should prioritize human factors. Hazmat transportation corporations should implement training programs to improve the skills of their drivers and to raise their safety awareness. Second, transportation corporations should improve their management of the transport vehicles. For example, they should choose the right type of vehicle based on the characteristics of the Hazmat, should examine the transport vehicle regularly to identify problems that require immediate action, and should periodically maintain the vehicle; in addition, they should monitor the vehicle during its travel. Last but not least, transportation corporations should improve the packing and loading of Hazmat to ensure that the packing and loading both meet the requirements of the material. Of the indirect factors (Table 6), road conditions had the greatest posterior probability (0.798), as these factors affect the driver, the vehicle, and the Hazmat packing, and poor road conditions can greatly increase the probability of an accident. Therefore, Hazmat transportation corporations must choose the proper route
according to the road conditions. At the same time, weather conditions should be carefully considered before and during Hazmat transportation. Transportation should avoid periods of bad weather, such as rain, snow and fog, or sandstorms; alternatively, drivers should take the necessary protective measures (e.g., installing winter tires during periods when the temperature decreases below freezing). The posterior probability for transportation corporation management was 0.372; even though this had a smaller impact than road conditions, this value is high enough to indicate that transportation corporations should manage their operations carefully.
6. Conclusions Bayesian networks allow researchers to investigate the influence of a range of factors, as we did for Hazmat transportation accidents in this paper. The Bayesian network was developed based on
Table A.1 Parameter values for the 94 case studies used to support the Bayesian network analysis of the factors involved in Hazmat transportation accidents. Sample
R
W
M
H1
H2
H3
C1
C2
T1
T2
T3
Sample
R
W
M
H1
H2
H3
C1
C2
T1
T2
T3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
1 0 0 0 1 2 0 0 0 0 0 2 0 0 0 2 0 2 0 2 0 0 0 0 2 2 1 0 0 2 0 0 0 2 0 0 2 0 0 1 1 0 1 1 0 0 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 1 1 2 0 2 0 0 0 1 0 0 0 0
0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0
0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0
0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0
1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0
0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
1 2 1 1 0 0 0 2 1 2 1 2 2 1 0 2 0 0 1 0 2 2 1 0 1 2 0 1 2 0 2 2 0 1 0 1 0 1 2 2 2 0 1 0 0 1 2
0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1
1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1
0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0
0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0
0 0
1. R = road condition, W = weather, M = management, H1 = skill, H2 = health, H3 = safety awareness, C1 = packing, C2 = loading and unloading, T1 = transport vehicle, T2 = protective equipment, T3 = maintenance and monitoring. 2. There are no public databases that report Hazmat transportation accidents in China. We therefore used accident information (e.g., time, description of accident, and source) published in the Journal of Safety and the Environment from 2005 to 2009. In addition, we gathered detailed information from newspapers and the Internet. However, we excluded some accidents that lacked sufficient information for us to determine the values of all 11 parameters. In total, we chose 94 accidents as our research subjects.
L. Zhao et al. / Safety Science 50 (2012) 1049–1055 Table A.2 The relationships among the 11 factors determined based on expert knowledge.
M R W H1 H2 H3 C1 C2 T1 T2 T3 H C T
H1
H2
H3
C1
C2
T1
T2
T3
? " "
M ? "
? M M
" ? " " " "
" ? " " " "
? " ? " " " M "
? " " " " " " "
? " " " " " " "
M " " ?
" " " ?
? "
" "
? "
"
"
" " " " "
" " " " "
" " " " "
" "
" "
" "
H
C
T
1055
Appendix A Tables A.1 and A.2 References
? ? ? " " " " "
" " " ? ? " " "
" " " " " ? ? ?
1. H1 = skill, H2 = health, H3 = safety awareness, C1 = packing, C2 = loading and unloading, T1 = transport vehicle, T2 = protective equipment, T3 = maintenance and monitoring, H = human factors, C = Hazmat packing and loading, T = transport vehicle and facilities. Vj indicates that Vj directly causes 2. Vi ? Vj indicates that Vi directly causes Vj, Vi Vi, Vi " Vj indicates that there is no direct causal relationship between Vi and Vj, and Vi M Vj indicates that the causal relationship between Vi and Vj is not certain. 3. The empty cells indicate that it was not necessary to confirm the relationship based on expert knowledge because of the assumption that there were no relationships between these pairs of nodes.
expert knowledge, modified based on the results of a conditional independence test, and supplied with data from 94 Hazmat transportation accidents in China. We then used the EM algorithm to calculate the posterior probability of each factor, thereby revealing the relative influence of the factors that can cause accidents. We successfully used this approach to analyze the importance of different causal factors in Hazmat transportation accidents. The conditional independence test indicated that conditional independence relationships existed within the Bayesian network developed by the experts, and resulted in modification of the Bayesian networks structure. Our studies revealed the relative importance of each of the 11 factors that we considered in our analysis of the case study data. Human factors were the most important direct factor that caused accidents. Of these factors, the driver’s skill had the greatest influence on accidents. Road conditions had the greatest indirect influence on accidents. These results are realistic given the reality of the Hazmat transportation industry in China, and provide guidance that will help transportation corporations take the necessary measures to reduce the frequency of accidents.
Acknowledgments This study was supported by grants from the National Natural Science Foundation of China (Nos. 90924030 and 70673012) and the ‘‘Shuguang’’ project of the Shanghai Education Commission (No. 09SG38). We thank the journal’s anonymous reviewers for their valuable comments and suggestions, which helped to improve our paper.
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