consistent basis for the assessment of compensation costs can also be established using the
LQI. Taking basis again in Equation (13.9) the Societal Value of a Statistical Life (SVSL) can
be assessed through:
g
SVSL E
q(13.16)
where E is the so-called age averaged discounted life expectancy at birth, see Rackwitz et al.
(ASTRA, 2007) for details. If an effective discounting of 2% per annum is applied E can be
determined equal to 28.3 and the corresponding SVSL is close to 6 million SFr. This value
should thus be included in the formulation of the benefit function as the consequence of each
lost life which may follow due to a given decision alternative.
Example 13.1 – Optimization of the design of a steel rod
Consider a steel rod under pure tension. The rod will fail if the applied stress exceeds the steel
yield stress. The yield strength R of the rod and the loading strength on the rod S are
assumed to be uncertain and modelled by uncorrelated Normal distributed variables. The
mean value of the load is assumed to be 200 MPa with a coefficient of variation of vS0.2.
The coefficient of variation of the yield strength of the steel vR is 0.1. Furthermore it is:
200
400.1S
S
R
R
RMPa
MPavThe objective is to answer to the question of which yield strength is sufficient and which yield
strength maximizes the utility of the owner?
To answer these questions some boundary conditions need to be known. It is assumed that the
mean value of persons NPE affected by a failure is 15. The probability of dying given a rod
failure is equal to one. The cost for steel depends on the yield strength. The costs are assumed
to be 115 times the mean value of the yield strength
kR. Hence it is:y
1
15
115
PE
Rk
N
Cp CHFThe failure rate of the steel rod is calculated by (see Figure 13.10, A):
ln 1 0.1 (^22)
!!
" "
" ,
"#"
$%$%
S
Sp
mp
p## (13.17)
The LQI acceptance according to Equation (13.15) criteria is given by:
() ()
y 0
xPEdm p q dC p
dp C N k g dp