Titel_SS06

facility. However, as the capacity of the local water reservoir is not known with certainty
another option is to get the water from another location where a suitable well already exists.

The different options are associated with different costs and different potential consequences.
The costs of establishing a well locally is assumed to be equal to 10 monetary units. If the
already existing well is used it is necessary to construct a pipeline. As the existing well is
located far away from the planned production facility the associated costs are assumed to be
equal to 100 monetary units.

Based on experience from similar geological conditions it is judged that the probability that a
local well will be able to produce the required amount of water is 0.4. Correspondingly the
probability that the well will not be able to fulfill the given requirements is 0.6.

The consequence of establishing a well locally which turns out unable to produce the required
amount of water is that a pipeline to the existing - but distant - well must be constructed. It is
assumed that in this case all the water for the production facility is supplied from this well.

The task is now to analyse such decision problems in a way making consistent use of all the
information available to the engineer, including her degree of belief in the possible states, her
subsequent observed data and her preferences among the various possible action/state pairs.

To this end, use will be made of the fact that decisions shall be based on expected values of
the corresponding consequences. This issue is addressed further in the following.

3.3 Decisions Based on Expected Values

Consider the simple case where the engineer must choose between actions and. The

consequence of action is with certainty whereas the consequence of action is

uncertain. The state of nature may be

a 1 a 2

a 2 C a 1

: 1 in which case the consequence is A and the state of

nature may be : 2 in which case the consequence is B. The decision/event tree is illustrated in

Figure 3.2.

Figure 3.2: Decision/event tree illustrating a basic decision problem.

Before the true state of nature is known the optimal decision depends upon the likelihood of
the various states of the nature : and the seriousness of the consequences , A B and C.