where are the different possible actions that can be taken on the basis of the result of the
considered investigation ,
az()
z E is the expected value operator. ́ and ́ ́ refer to theprobabilistic description of the events of interest based on prior and posterior information
respectively. In Equation (3.10) the expected utility has been associated only with expected
costs and that is why the optimal decision is identified through a minimization. If utility more
generally is associated with expected benefits the optimization should be performed through
maximization.
Pre-posterior analyses form a strong decision support tool and have been intensively used for
the purpose of risk based inspection planning. However, so far pre-posterior decision analysis
has been grossly overlooked in risk assessments.
It is important to note that the probabilities for the different events represented in the prior or
posterior decision analyses may be assessed by logic tree analysis, classical reliability analysis
and structural reliability analysis or any combination of these. The risk analysis thus in effect
includes all these aspects of systems and component modelling in addition to providing the
framework for the decision making.