|
We can define the shortening of a human lifetime by a transport system ΔTHT as shown here:
|
|
(5)
|
where TH is the average human life expectancy without the impact of the
transport system, and THT the average human life expectancy with use of the transport system. We can determine the value TH from age-related statistics about life expectancy and accidents/mortality frequency in specific target groups. From the equation
|
|
(6)
|
we can derive the value for average human mortality MHM without the impact
of the transport system. Similarly, it applies for THT that:
|
|
(7)
|
where MTM is the average mortality caused by traffic. We can determine MTM using accident statistics, and calculate the mortality rate for a transport
system (or subsystem) in the context of a risk analysis.
Human Safety Potential
This approach allows us to show the risk share of a concrete subsystem in terms of the shortening of a human lifetime. An assessment regarding risk
acceptance is possible only if we take into account other subsystems or a multiple use of those systems. It is therefore useful to show the individual
share of a subsystem also in terms of its human safety potential:
|
|
(8)
|
or when assuming MHM »
MTM
:
|
|
(9)
|
We can now easily calculate the shortening of a human lifetime, provided that TH is known.
|
|
(10)
|
Illustration Using an Example
Throughout Europe, level crossings (LX) are considered to present the highest risk within the railway system. Since most victims are road users, we
need to assess the existing risk of road transport in a first step.
Figure 1 shows the age-related distribution of human mortality.
Assuming an equal use of road transport by all, we can use integration as shown in formula (6) to calculate an average life expectancy THT = 78.09 years. By analyzing the age-related accident statistics for road transport, we
can show that the sharp rise in mortality around the age of 18 (particularly among men) is caused by using cars. If we deduct mortality caused by road
transport, we can show the risk share of this transport system (illustrated in Figure 1).
These figures also show a theoretical curve for human mortality without the
influence of road transport, which we can use to calculate TH = 78.345 years (MH = 0.0128 year-1). The resulting risk of road transport in terms of shortening the human lifetime is equal to ΔTHT = 0.255 year.
Figure 1 — Human Mortality Distribution and Risk Caused by Road Transport (Germany 2001).
According to statistics, an average of 0.017 accidents per level crossing
occur in Germany (Deutsche Bahn AG). The accident statistics for any specific level crossing depend largely on its technical safety equipment
(none, signals, half barriers, etc.). Figure 2 shows a hypothetical curve of accident frequency per year for a level crossing without any technical safety
equipment. We analyzed these figures using a formal risk model [Ref. 6] for different volumes of road and rail traffic.
Using a fatality factor CF and an accident rate rAccidents (accidents/year) we can calculate a collective risk MCollective. If the road traffic volume and the
average number of occupants per car are known, we can calculate the corresponding number of users NUsers. For the risk per use of the level
crossing, RLXUse, the following then applies:
|
|
(11)
|
Taking into account repeated use of the level crossing by an individual (individual risk RLXIndividuum as the probability of death after NUses uses), we have:
|
|
(12)
|
Figure 2 — Hypothetical Curve of Accident Frequency on an Open Level Crossing.
The dependency of individual risk on the traffic flows at a level crossing
(assuming a fatality factor CF=1.5, an average number of car occupants of 1.5 people, and NUses=500 uses per year) is shown in Figure 3. (With
higher road traffic volumes, individual risk is reduced as the vehicles impact each other at the level crossing, such as with the formation of queues.)
|
)
