# Hydraulic Structures Probabilistic Approaches to Maintenance

## Hydraulic Structures Probabilistic Approaches to Maintenance

Probabilistic methods allow input variables and mathematical model parameters
to have ranges instead of single numbers. This in turn provides results in the form of
ranges and outcomes. Suppose that benefits and costs of a contemplated action, each with
ranges of possible values, under some probability distribution, are entered into the
analysis. The evaluation of the difference of the variables leads to a net benefit that also
has a range with some probability distribution. This result allows determination of not
only the average value of the net benefit, but also of the probability of critical threshold
values, for example, the probability of the net benefits exceeding or not exceeding zero,
in other words the probability of this activity being an economic success of failure.

Two important extensions of traditional engineering methods that are provided by
probabilistic methods are discussed in connection with dealing with risk. The first is the
interpretation of the expected value as the insurance premium of a risk-neutral risk taker
or insurer, and the second is the inclusion of personal attitude toward risk into the
expected value and thus into the insurance premium of a risk-averse decision maker or
insurer. Insurance is an important aspect when dealing with risk and this aspect is given
some room because risk control, risk taking, and risk transfer are the essential options a
decision maker is confronted with. The increased risk awareness that flows from dealing
with probabilistic methods should lead to the selection of economical and risk-averse
alternatives. Probabilistic methods can explain the sometimes seemingly puzzling cost
overruns or even economic failures of apparently sound projects and the often
encountered divergence among parties over the results of risk assessment.