ACCIDENT RISK FOR TRAIN DRIVING
5.1 Train operations and work shift regulations of the TRA
The TRA is the only institution in Taiwan providing 24 hour service for both passenger
and freight railway operations with 219 stations and 1,097.2 kilometers of track. The TRA has
1,250 drivers who alternately drive both passenger and freight trains, and each is assigned to
one of five dispatching units (Taiwan Railways Annual Report, 2006). Drivers are assigned to
freight trains for at least two consecutive weeks after finishing a specific number of work
shifts driving passenger trains. A driver’s work schedule is arranged and strictly controlled
under regulations issued by TRA. The work shift regulations include:
(1) driving distance for each shift must be less than 300 kilometers;
(2) each shift must not exceed 6 hours from 6 a.m. to 10 p.m.;
(3) each shift must not exceed 5 hours from 10 p.m. to 6 a.m.;
(4) drivers’ rest duration between consecutive shifts must be longer than 6 hours; and
(5) drivers must have at least one off-duty day a week (duration must exceed 24 hours).
5.2 Data collection
5.2.1 Driver responsible accidents
According to the TRA’s operation rules, a train accident is defined as an event causing
more than 10 minutes delay in operations, and the related personnel are responsible for
reporting it to the Accident Investigation Prevention Committee (AIPC). Details of the
accident report include, among other things, the characteristics of train driver(s) and his/their
corresponding work shift information. The AIPC then investigates possible causes of the
accident and determines whether the personnel are responsible for its occurrence; thus, they
are further classified into human- or non-human-error accidents. Given this, a driver’s
consecutive driving hours before the accident can be determined by combining his work shift
record with the accident report.
The records of accidents that occurred during 1996-2006 were collected and used in this
study. Among the total of 10,990 TRA accidents, 10,371 were reported as non-human errors
and 619 were human error accidents. Furthermore, among those human error accidents, 193
accidents were attributed to train driver errors, which accounted for 31% of all human error
accidents. Based on the study purpose, only the driver-responsible accidents are counted in
the study. According to the statistics of accident occurrence time, 172 driver-responsible
accidents occurred at the on-board driving stage, 12 at the pre-starting stage, and only 9 at the
post-arrival stage. For the purpose of studying the effect of consecutive driving on accident
risk, a total of 172 on-board driving accidents were examined in this study, which included
122 passenger train accidents and 50 freight train accidents.
5.2.2 Driving exposure to the risk of accident
As mentioned in Chapter 2.3.2, the on-board driving stage is defined as the operating
duration from the starting station to the ending station for each train driver. The driving task
for a train driver at this stage is relatively continuous and a driver needs more concentration
and alertness to operate safely. In addition, “trunk line driving and shunting” at the on-board
driving stage is a relatively continuous job for train drivers during their work shifts, and
usually influences train operations, occupies the main tracks, and leaves available driving
records for train drivers. Therefore, only the on-board driving time was calculated and was
selected as the exposure measure in this study.
On average, there were 1,072 working shifts per day and approximately 4.3 million
working shifts were collected to calculate the on-board driving hours during 1996-2006. A
passenger train driver had a mean of 2 hours and 45 minutes of on-board driving, while a
freight train driver had a higher average of 3 hours and 20 minutes. In addition, the variation
in on-board driving time for passenger train drivers (SD = 89 min) was larger than that for
freight train drivers (SD = 42 min). This demonstrated that the length of on-board driving for
Distributing all drivers’ work shifts from the eleven observed years into different time
slots, the accumulated on-board driving hours in each time slot for both types of train driving
are shown in Figure 5-1. The total on-board driving hours for passenger trains was 9.88
million hours while the total on-board driving hours for freight trains was 2.57 million hours,
which comprised only 20.6% of total on-board driving hours. The distribution of driving
exposures for different time slots also showed that passenger train drivers had greater
variability in their on-board driving hours as the pattern deviates more from a uniform
distribution than that of freight train drivers.
0
Driving exposure (million hours)
Passenger Freight
Fig. 5-1 passenger and freight train driving exposure for different consecutive driving hours
5.3 Accident rates for different time slots of consecutive train driving hours
Dividing the number of total accidents that occurred in the observation period by the
total driving hours, we find that TRA experienced an average accident rate of 13.82 accidents
per million driving hours from 1996 through 2006. If we further investigate the accident rates
for freight and passenger train driving separately, we will find the freight and passenger train
driving experienced 19.45 and 12.35 accidents per million driving hours, respectively, over
the observation period. Freight train driving had a 58% higher accident risk than passenger
train driving, which is consistent with the expectancy discussed in the previous section.
Furthermore, based on the collected data, the accident rates for each time slot could be
measured by dividing the number of accidents that occurred in one time slot by its
corresponding driving exposure (i.e., the on-board driving hours in the same time slot),
indicating the accident risk for that time slot. That is, the accident rate for the ith time slot can
be expressed as
ARi=Ai/Hi (1)
where ARi is the accident rate for the ith time slot, Ai is the number of accidents that occurred
in the ith time slot, and Hi is the accumulated driving hours in the ith time slot.
According to the above definition, the accident rates for different time slots for the
consecutive driving of all trains, passenger trains and freight trains, are computed and
illustrated in Figure 5-2. We find the accident rates for all train driving had a distinct peak
after one hour of consecutive driving, followed by a relatively low level, which subsequently
increased again. This study result is consistent with the findings of both Wharf (1993) and
Kecklund et al’s (1999) studies.
However, if the accident rates for different time slots are investigated separately for
freight and passenger train driving, a significant difference in accident rates over time will be
found between the two types of train driving, as can be seen in Figure 5-2. That is, the
accident rates for freight train driving were significantly higher than those for passenger train
driving during the first hour of driving, but this phenomenon disappeared after one hour of
driving.
A further investigation indicates the average accident rate during the first hour of freight
train driving was 34.04 accidents per million driving hours, which was about 3.2 times the
average accident rate for passenger train driving (10.78 accidents per million driving hours)
during the first hour. But these statistically significant differences in accident rates between
the two types of train driving were not found at α= 0.05 after one hour of driving. Further
investigation indicates that, among the 24 freight train accidents that occurred in the first hour
of initial driving, 20 accidents (83%) occurred in the marshalling yards. That result is
consistent with the expectancy that freight train driving will experience higher accident risk
for shunting in the marshalling yards than running on the main lines.
Fig. 5-2 The accident rate over consecutive driving hours for train driving
0 10 20 30 40 50 60
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Consecutive driving hours
Accidents per million driving hours
Passenger train driving Freight train driving All train driving
Figure 5-2 also indicates that the accident rate for freight train driving reached its peak
after one hour of driving (i.e., the 4th time slot) and then dropped to the lowest accident rate
for all time slots. Afterward, the accident rate increased again across consecutive driving
hours. This result is similar to the findings of previous railway studies in that train drivers had
a distinct peak of accident risk during the second and third hours of duty followed by a
relatively low level, and then an increase again (Kecklund et al., 1999; Wharf, 1993). The
only difference with the current study is the time of occurrence of this early peak of accident
risk, which reflects the fact that pre-driving hours were included in the on-duty hours in
previous studies, but not included in this study.
Interestingly, the peak accident rate in the early driving hours was not found for
passenger trains. The accident rates for passenger train driving seemed to increase gradually
as the driving hours were accumulated, which is consistent with the hypothesis that prolonged
driving induces fatigue and then increases the accident risk for train driving. This
phenomenon could also be found for freight train driving if we neglect the early peak of
accident risk during the first hour of on-board driving. Therefore, the study results shown in
Figure 5-2 seem to indicate the effect of consecutive driving on accident risk actually exists
for both passenger and freight train driving, even within a short mission of 4.5 on-board
driving hours. However, an extra accident risk was found for freight train driving in the first
hour, which reveals a distinct early peak accident rate. This extra accident risk for freight train
driving in the first hour could be explained by volume of shunting in the marshalling yards,
which is expected to have a higher accident risk based on the complicated track layout and
semi-automatic traffic guidance for TRA.
5.4 Modeling the accident risk for consecutive driving
Given the accident rates for different time slots over consecutive train driving hours, it is
possible to explore the effect of continuous driving on the accident risk for train operations.
Some previous studies indicated the relationship between accident rates and consecutive truck
(or automobile) driving hours fit an exponential model (Chang and Hwang, 1991; FMCSA,
2000; Folkard 1997) or a quadratic model (Kecklund et al., 1999; Wharf, 1993). Therefore,
four different regression models are considered to formulate the relationship between accident
rates and consecutive driving hours for train driving, according to the trends of accident rates
over different time slots demonstrated in Figure 5-3. These four models are expressed as
follows:
Model 1 (Linear): AR = a + bt (2)
Model 2 (Log linear): ln(AR)= a + bt or AR=exp(a +bt ) (3)
Model 3 (Quadratic): AR= a+ bt + c t2 (4)
Model 4 (Modified Quadratic): AR= a+ c t2 (5)
where a , b and c are the parameters to be estimated and t is the cumulative on-board driving
hours. Models 1, 2, and 4 are used to formulate the increasing trend of accident risk for
consecutive train driving hours, while Model 3 is especially considered to catch the trend
shown in Figure 5-2, which had a distinct peak of accident risk during the first hour of driving
followed by a relatively low level, which then increased again
Table 5-1 Accident rates and relevant statistics for different types of regression models
Model types Accident rate (Accidents
per million driving hours) a (p-value) b (p-value) c (p-value) R2 All trains
* The best model among the four candidate models.
** It is suggested to be the best model in terms of its explanatory power, though the parameter b is only marginally significant with a p-value of 0.16.
These four candidate models were applied to model the trends of accident risk resulting
from consecutive driving for all trains, passenger trains, and freight trains separately.
According to the model estimation results summarized in Table 5-1, Model 3 is suggested to
be the best model for all train driving in terms of its explanatory power, though the parameter
b is only marginally significant with a p-value of 0.16. For passenger train driving, Model 4 is
the best model to describe the increasing accident risk over time for consecutive driving. As
to freight train driving, Model 3 is obviously better than the other three models to catch the
trend of accident risk over time for consecutive driving. However, the explanatory ability of
any of the four candidate models is not good enough for freight train driving.
Apparently, the models for passenger train driving had much better fit than those of
freight train driving due to the lack of a distinct risk peak in the first hour of driving. It was
found that the pattern of increasing accident risk caused by consecutive driving for passenger
trains is similar to that for automobiles or trucks. Conversely, although the accident rates over
time for consecutive freight train driving are not significantly different from those of
consecutive passenger train driving after one hour of driving, the abnormally high accident
risk in the first hour of driving makes the continuous models unable to clearly depict the
pattern of accident risk over time for freight train operation. Therefore, a combined model,
which handles the additional accident risk for freight train driving in the first hour through a
dummy variable and combines the accident rates of both passenger and freight train driving, is
formulated as follows:
AR = a+ bt + c t2 + D (dt + et2) (6)
where D is the dummy variable and D = 1 for freight train driving in the first hour, and D = 0
otherwise. A stepwise regression procedure using backward-elimination was employed to find
the best model for Equation 6, and the estimated results are summarized in Table 5-2. The
explanatory ability of the best model, with R2 = 0.842, was significantly improved as
compared to the single models for passenger and freight train driving, respectively.
Table 5-2 The estimated results for the combined model of accident risk over time
Parameter a (p-value) b (p-value) c (p-value) d (p-value) e (p-value) R2
Step 1 13.08(0.00) -3.48(0.11) 1.37(0.00) 33.83(0.04) 14.16(0.47) 0.854 Step 2 12.37(0.00) -2.91(0.15) 1.27(0.00) 44.85(0.00) 0.852
*Step 3 9.73(0.00) 0.67(0.00) 46.40(0.00) 0.842
* The best model estimated by the stepwise regression procedure.
According to the estimation results of the best combined model shown in Table 5.2,
the accident rates over consecutive driving hours for both passenger and freight trains are
illustrated in Figure 5-3. It indicates the accident risk for passenger train driving increases
with the accumulated driving hours, and shows the accident risk will double after four
consecutive hours of driving, as compared with the accident risk of driving during the first
hour. As to the extra accident risk for freight train driving, it is found to increase sharply with
accumulated driving time during the first hour. That is, the accident rates for freight train
driving were 3.3 and 5.5 times of those of passenger train driving after half an hour and one
hour, respectively, of consecutive driving. This might be a function of the increasing train
length accompanied by the accumulated driving hours in the marshalling yard that increases
the difficulty of shunting and, therefore, increases the risk of accident. In addition, the
accident rates for freight train driving went sharply down to the risk levels of passenger train
driving after one hour of on-board driving in the marshalling yards for shutting.
Fig. 5-3 The estimated accident rate model over consecutive driving hours for passenger and freight train driving
0 10 20 30 40 50 60
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Consecutive driving hours
Accidents per million driving hours Estimated model for passenger train driving
Estimated model for freight train driving during the first hour
5.5 Discussion
This study investigated train-driver-responsible accidents by examining their accumulated
on-board driving hours and the associated increasing trend of accident risk over time caused
by consecutive driving. Differentiation of accident risk between passenger and freight train
driving helps us to investigate the distinct early peak problem of accident risk for rail
operation raised by previous literature. Some findings and their implications follow.
5.5.1 Accelerating accident risk of train driving compared with truck driving
The accident risk for train driving was found to double after four hours of consecutive
accident risk for train driving seems to occur earlier than that of automobile driving
(Amundsen and Sagberg, 2003; Chang and Hwang, 1991; Elvik et al., 1997; Mackie and
Miller, 1978). Mackie and Miller (1978) investigated 750 truck crashes and found crash
occurrences began to increase after five hours of driving, and the risk during the second five
hours was twice that of the first five. Elvik et al. (1997) reported truck accident risk
significantly increases after eight hours of consecutive driving and there is a tendency for
increasing risk when driving more than 9-11 hours (Amundsen and Sagberg, 2003). In
addition, Chang and Hwang (1991) studied the effect of prolonged driving on accident risk for
a U.S. trucking company and found the risk after five hours driving was double that of the
first hour. Greater fatigue generated by higher working pressure and a more monotonous
driving environment are considered to be two important reasons for an accelerated accident
risk for consecutive driving during train operations.
Train driving is a dynamic control and decision-making task (Kecklund et al., 2001;
Reinach and Raslear, 2001). The complexity of the operating environment and the work
requirements (i.e., higher density of switches and signals, stations, track works, and grade
crossings speed restrictions) affect the degree of salient environmental information that must
be identified, processed, committed to memory, and used to take appropriate actions.
Especially important is the fact that the train driver’s job is largely governed by timetables
and technical conditions (e.g., type of train and track layouts) that restrict the driver’s ability
to decide how the job should be done. Therefore, these harsher working requirements for train
driving may result in accelerated fatigue for train drivers and, thus, increase train accident risk
faster than it would for automobile driving.
Furthermore, highly automated duties, such as automatic train controls, can be perceived
as boring and monotonous tasks. In particular, when driving during the night everything is
dark and the driver cannot see anything but the signals. The working environment increases
the monotony of train driving except when near signals or stations, and a monotonous and
non-stimulating environment is likely to provoke sleepiness. Johnson (1982) found that tasks
that are more monotonous and lacking in interest are more likely to make people fall asleep.
In addition, performing monotonous tasks may gradually cause a decline in behavior
performance (Thiffault, and Bergern, 2003), reduce levels of alertness, and increase crash risk
(Horne and Reyner, 1995). The monotonous driving environment is, therefore, expected to be
another reason for accelerating the accident risk of consecutive train driving.
5.5.2 The early peak of accident risk for freight train driving
In this study, freight train driving was found to be associated with a risk peak within the
first hour of initial driving. This early peak phenomenon of accident risk was also found in
previous railway studies, but lacked further investigation for its possible causes. Compared
with passenger train driving, freight train driving is usually associated with higher working
complexity. These working characteristics might lead to an earlier peak of accident risk for
freight train driving.
Shunting in the marshalling yard is an unsafe activity, not only because the yard’s track
layout is more complicated than that of the main lines but also because circulation of freight
trains in the yard is guided by a semi-automatic interlock system for TRA. Differing from
passenger train driving, which is directed by an automatic interlock system in the main lines,
the operation of shunting requires more attention by yard staff and freight train drivers. These
operation characteristics for freight train driving in the marshalling yards are thought to be the
reasons for TRA to experience higher accident risk for shunting in the marshalling yards.
A higher proportion of night work shifts for freight train driving is also expected to
increase the accident risk for shunting in the marshalling yards. However, antithetically,
increase the accident risk for shunting in the marshalling yards. However, antithetically,