If extreme realisations of the total costs are associated with a marginal utility this should be
included in the utility function as a separate term.
Decision analysis with given information
When the utility function has been defined and the probabilities of the various states of nature
corresponding to different consequences have been estimated the decision analysis is reduced
to the calculation of the expected utilities corresponding to the different action alternatives.
At this stage the probabilistic description ( )P: of the state of nature : is usually called a prior
description and denoted P@( ):.
Example 12.1 - Reassessment decision analysis with given information – prior analysis
To illustrate the prior decision analysis in the context of reassessment of structures the
example with the steel bar is considered again. The decision problem is stated as follows. The
engineer has a choice between two actions:
a 0 : Do nothing
a 1 : Strengthen the steel bar
The possible states of nature are the following:
: 0 : The strength of the steel bar is larger than the loading
: 1 : The strength of the steel bar is smaller than the loading
The prior assessment of probabilities is based on the prior information available about the
yield stress of the steel. It is assumed that the load effect s is equal to 2765 kN. The resistance
R is assumed to be Normal distributed with mean value equal to 3500 kN and a coefficient of
variation equal to 10%. The prior probabilities can then be determined e.g. by FORM/SORM
analysis as:
PaPRs PR@
: 00 & &( 0) ( 1.1 2765 0) 1 1.15 10^2Pa@@
:: 10 1( )1.1510Pa0 0 ^2PaPRs PR@
: 01 &&(1.1 0) ( 2765 0) 1 1.33 10^4Pa@@
:: 11 1( )1.3310Pa0 1 ^4Based on the prior information alone it is easily seen that the expected utility E'uamounts
to: