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Figure 3 — Individual Risk at an Open Level Crossing.
We can calculate the mortality of an individual within t time units (years) as
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(13)
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This random number is clearly subject to a negative exponential distribution. The rate of distribution λ
is equal to the mortality MLX that results for an individual from use of the level crossing.
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 [deaths per person per year]
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(14)
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We can thus use the equation
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 [years]
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(15)
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to determine the shortening of a human lifetime. We have calculated the
shortening of a lifetime as resulting from use of an open level crossing (500 times per year throughout a lifetime) as follows: 0.272 years (0.25 trains/hr);
0.601 years (2 trains/hr); 0.979 years (4 trains/hr). For our analysis, we used the maximum values of individual risk for the respective train density,
equivalent to a road traffic volume of 0.1-1 cars/hr. Figure 4 shows the
shortening of a lifetime resulting from use of a level crossing compared to other risks to human life.
Figure 4 — The Risk of Level Crossings in Comparison.
Summary and Outlook
The approach we have introduced for quantifying risk supports an intuitive formation of risk awareness in people. This is an essential requirement for
determining risk acceptance in society.
To be able to assess and compare the risks inherent in different transport
systems, and to use this information in the context of approval procedures, we would also need to quantify the factor “human self-determination” and
integrate it with the relevant safety potential, possibly also taking into account the “felt” (subjective) sense of risk. By contrasting safety and availability
potentials, we can achieve comparability of transport systems as a whole in terms of their reliability. Such a comparison can also be applied in
requirement specifications and in the design and approval of technical equipment, or to help passengers in their selection of a specific transport system.
About the Authors
Prof. Dr.-Ing. Eckehard Schnieder
is Professor for Traffic Safety and Automation Engineering Head of the Institute of Traffic Safety and Automation
Engineering at Technical University in Braunschweig, Germany, where he is also a Member of the Board of Centre of Transportation and head of several
university senate commissions. He is credited with more than 350 contributions to conferences and journals. A licensed expert of the German
Federal Railway Authority, he is a member of several national and international scientific societies.
Ing. Roman Slovák is currently a Research Assistant for Traffic Safety and
Automation Engineering. The author of more than 20 contributions to conferences, journals and books, his specialization is in risk and hazard
analysis of railway operation control systems using stochastic Petri nets, modelling of railway systems, and validation of formal software specifications using railway models.
Dipl.-Ing. Stefan Wegele is a Research Assistant for Traffic Safety and
Automation Engineering and a Dipl.-Ing. (Mechanical Engineering) at Technical University of Braunschweig, and is the author of more than 15
contributions to conferences, journals and books. His professional focus is on control engineering, optimization of railway scheduling by genetic algorithms,
and stochastic model analysis.
References
- EN 50126: “Railway applications — The specification and
demonstration of reliability, availability, maintainability and safety (RAMS).” Brussels: CENELEC, 1998.
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University of Sheffield. Sheffield: Rail Safety & Standards Board, 2004.
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