information (degree of belief) about the yield strength of the steel, subsequent use of observed
data and preferences among the various possible decision / state pairs.
du:No strengtheningStrengtheningSurvivalSurvivalFailureFailure0 $100000 $1000 $101000 $Decision Event ConsequenceFigure 12.5: Decision / event tree.
Assessment of utility/benefit
In regard to the modelling of preferences in decision analysis this topic has been addressed in
previous lectures and thus no specific details are given here. It is only noted that in decision
analysis terms the optimal decisions may be identified as the decisions maximising the
expected value of a utility function, a function expressing the decision-makers stated
preferences in terms of the consequences, see Lecture 3.
In decision analysis for structural assessment and maintenance planning the consequences
may normally be expressed in monetary terms. Having identified all utility (cost and incomes)
generating events in the decision problem, the next step is, for each decision alternative to
associate to these events the corresponding marginal utilities. Marginal, meaning that the
utility is associated only with the considered event. Thereafter, the expected utility associated
with each decision alternative may be evaluated by the sum over the products of the marginal
utilities and the corresponding probabilities of the utility generating events.
As an example consider the situation where the marginal utilities are associated with the
events of failure, repair and inspection. In this case the expected utility (costs) EC t Tinst() for
one particular decision alternative may be expressed as:
EC t Tinst() PC PCII f fC PRREC I EC 89 f EC r
(12.5)
where ECI,EC f and ECr are the expected cost of inspection, expected cost of failure
and expected cost of repair, respectively. It is important to note that the costs entering
Equation (12.5) are represented by their mean values in consistency with the decision theory.