The Trade-off Between Expected Risk and the Potential for Large Accidents

Abstract

Complex modern technologies often have the potential, though with very low probabilities, to cause accidents which could affect a large number of people at the same time. This is a topic of great concern to the public. Therefore, several authors have proposed safety goals which give different weights to such large consequences. However, it is difficult to decide which rules should be applied, and it is even more difficult to obtain the weighting factors. This paper proposes that such rules and weighting factors may be obtained from historical data analysis.

Generally, it can be observed that with time the expected value of the risks of technologies are reduced. However, this achievement often has to be paid for creating the potential for LP/HC accidents. Such a trend can, for example, be observed with airplane accidents. This study analyzed such accidents between 1947 to 1980. If the largest number of fatalities in a single accident in each year is plotted against the average number of fatalities per passenger-km (i. e., the expected value) in that year, it is found that an inverse exponential relationship exists.

This finding can also be expressed in the form that the product of the expected value and the weighted largest number of fatalities in each year was constant

$$ EV{({C_{\max }} - b)^c} = a $$

where

• EV = expected value of risk in a given year

• C_max = largest number of fatalities in a give year

• a, b, c = constants obtained from the historical trend.

This paper presents the relevant data for airplane accidents and describes the methematical relationship obtained. These results are being discussed with regard to their implications for safety decisions.