## Hydraulic Structures Probabilistic Approaches to Maintenance

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.

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.

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