decision analysis involves the analysis of decision event trees which is quite involving in size
and complexity. However, available tools for the analysis of BPN’s usually include a feature
for decision analysis too. Such tools are often referred to as decision graph analysis or
influence diagram analysis. Without going into the theoretical background behind the
functionality of these tools it is just stated here that the algorithms applied for implementation
of these tools rest firmly on the theoretical basis for decision analysis introduced in Lecture 3.
The use of these tools is normally quite intuitive and for the purpose of introducing these tools
and to illustrate their considerable strength in decision analysis a simple example is analyses
in the following. This example is also described in Benjamin and Cornell (1971) in which the
reader may find the equivalent analysis performed in hand calculations.
Consider the following simple pile driving decision problem. The problem is stated as
follows. In connection with the construction of a bridge a pile has to be driven as a part of the
foundation structure. However, there is no information in regard to the depth of the stratum
and the engineer has a choice between two actions:
a 0 : Select a 40 ft pile to drive
a 1 : Select a 50 ft pile to drive
The possible states of nature are the following two:
: 0 : The depth of the stratum is 40 ft
: 1 : The depth of the stratum is 50 ft
Economical risks are associated with both decisions. If the engineer chooses the 40 ft pile and
the stratum depth is 50 ft then the pile has to be spliced with a cost of 400 monetary units. If
on the other hand the engineer selects a 50 ft pile and it turns out that the stratum depth is only
40 ft the pile has to be cut of at ground level with a cost of 100 monetary units. If the engineer
chooses a pile of the same length as the depth of the stratum there are no cost consequences.
The prior assessment of probabilities is based on experience from pile driving several hundred
feet away from the present site together with large-scale geological maps. The prior
probabilities for the two possible stratum depths are
P ́: 0 = 0.70
P ́: 1 = 0.30
A Bayesian probabilistic net for the analysis of this decision problem is illustrated in Figure
10.10.