Titel_SS06

As an example consider the problem concerning the bridges described earlier. For this
problem a Bayesian Network is constructed as indicated in Figure 10.1. For matters of
convenience the variables in the Network are denoted as; Production = PR, Execution = EX,
Bridge 1 = BR1 and Bridge 2 = BR2. Furthermore, it is assumed that all variables only have
two different states, namely Good = G or Bad = B.

As a first step the probability tables and conditional probability tables for the different states
of the variables must be assigned. These are given in Table 10.1–Table 10.4.

PR

G 0.9

B 0.1

Table 10.1: Discrete probability distribution for the production quality.

EX

G 0.9

B 0.1

Table 10.2: Discrete probability distribution for the execution quality.

PR G B

EX G B G B

BR1

G 1 0.5 0.5 0

B 0 0.5 0.5 1

Table 10.3: Discrete probabilities distribution for the condition of Bridge 1, conditional on production
and execution quality.

PR G B

EX G B G B

BR2

G 1 0.5 0.5 0

B 0 0.5 0.5 1

Table 10.4: Discrete probability distribution for the condition of Bridge 2, conditional on production
and execution quality.

Now the probability distribution of the universe, i.e. all states of the Bayesian Network
considered can be established using Equation (10.1) as: