Titel_SS06

mp()

p

dp

maximum acceptable
failure rate

acceptable decisions

y

xPE

dC p q

CN kg

y

xPE

Cpq

CN kg

Figure 13.9: Illustration of the use of the SWTP criterion as basis for assessing acceptable decisions and
corresponding acceptable failure rates for engineered facilities.

In Figure 13.9 it is illustrated how the failure rate m(p) as well as the normalized risk

reduction costs
y()
xPE

Cpq

CN kg

depends on p. In the illustration it has been assumed that the cost of

risk reduction is linear in the decision parameter p. This might resemble the situation where p
corresponds to a cross-sectional dimension of a structural component. The failure rate m(p) on
the other hand is in general a rather non-linear function of p. According to the SWTP criterion

the decision parameter should be increased as long as dm p()
dp

is larger than

y()

xPE

q dC p

CN kg dp

.

The point p where the two gradients are identical corresponds to the decision alternative with
the highest acceptable failure rate. Any value of p larger than this value can be considered
acceptable in respect to the SWTP criterion.

In case there the decision options are of a discrete nature the failure rate m(p) as well as the

normalized risk reduction costs
y()
xPE

Cpq

CN kg

are not differentiable, however, the same

consideration still holds. Discrete actions of risk reduction shall be engaged as long as the
normalized costs of these are smaller than the corresponding reduction in failure rate.

The Societal Value of a Statistical Life

In the previous section it was shown how on the basis of the LQI a criterion in regard to the
acceptability of life risks can be derived. This criterion serves as a limitation of possible
feasible decision alternatives, i.e. the decision alternatives which are associated with an
economical benefit, see also Lecture 3, Figure 3.1. However, due to the fact that modern law
requires that dependents of people killed in accidents are compensated it is necessary to
include these compensation costs in the formulation of the benefit function to be optimized.
Several different approaches are taken in practice when it comes to the assessment of
compensation costs. The legal systems in especially North America and Europe differ
significantly on this issue and the resulting compensations can be very different. However, a