Titel_SS06

go ahead and perform the experiment. If several different types of experiments are possible
the decision-maker must choose the experiment yielding the overall largest utility or
equivalently the smallest costs.

What needs to be considered is the situation where the experiment is planned and the
experiment result is still unknown. In this situation the expected costs disregarding the
experiment costs can be found as:

 

 

1,

11

''' 'min{''()

nn

ii ijm j

ii

Eu P z E uz P z  E ua z



 i } (12.7)

where n is the number of different possible experiment findings and m is the number of
different decision alternatives. In many reassessment decision problems the experiment
outcomes are samples from a continuous sample space in which case summation in Equation
(12.7) is exchanged with an integral. In Equation (12.8) the only new term is which

may be calculated in terms of the likelihood’s by:

Pz'

i

Pz Pz''

ii

:: : 00 P

Pz

i 1 P'

: 1 (12.8)

The framework of pre-posterior decision analysis has enormous potential as a decision
support tool in structural engineering. So far most attention has been paid to applications in
inspection and maintenance planning, but other situations where decisions have to be made on
which and how much information should be collected, i.e. one of the main problems in
assessment of existing structures can be handles within this framework. Examples of
application of the pre-posterior analysis can be found in the literature. Planning for SN fatigue
experiments is considered in Faber et al. (1993), planning of structural response
measurements is considered in Sørensen et al. (1993), planning of POD tests is considered in
Sørensen et al. (1995), planning of concrete compressive strength tests is considered in
Sørensen et al. (1999).

Example 12.3 – Optimal planning of experiments – pre-posterior analysis

To illustrate the principle in the pre-posterior analysis, consider again the simple example
with the steel bar. The decision problem is that the deterministic loading due to changes in the
operational conditions is to be increased by 10%. The yield stress of the steel bar is uncertain
and it must be ensured that the steel bar is safe with the given load increase.

The approach to the problem is that a number of materials tests are planned. If on the basis of
the tests it can be shown that the steel bar is sufficiently safe no further action is taken. If,
however, the steel bar is not sufficiently safe it will be strengthened exactly such that the
requirement to the probability of failure is fulfilled.

It is assumed that the requirement to the maximum probability of failurePfT is 1.34 10-5 which

corresponds to a safety index equal to 4.2. The loading s is deterministic and equal to

3041.5 kN.

Denoting the probability distribution function for the yield stress of the steel rod after having

performed the planned tests Fff@@( yyˆ) the required cross-sectional area after the