Return Period for Extreme Events
The return period TR for an extreme event may be defined by:
max
,1
R (1 XT( ))
TnT T
Fx(2.84)
where is the reference period for the cumulative distribution function of the extreme events
. If as an example the annual probability of an extreme load event is 0.02 the return
period for this load event is 50 years.
T
FXTmax, ()x2.11 Introduction to Engineering Model Building
An important task in risk and reliability analysis is to establish probabilistic models for the
further statistical treatment of uncertain variables.
In the literature a large number of probabilistic models for load and resistance variables may
be found. E.g. in the Probabilistic Model Code by the Joint Committee on Structural Safety
(2001) where probabilistic models may be found for the description of the strength and
stiffness characteristics of steel and concrete materials, soil characteristics and for the
description of load and load effects covering many engineering application areas. However it
is not always the case that an appropriate probabilistic model for the considered problem is
available. Moreover in other engineering fields such as in environmental engineering and
hydrology standardization of the probabilistic modelling is far less progressed. In such
situations it is necessary that methodologies and tools are readily available for the statistical
assessment of frequentistic information (e.g. observations and test results) and the formulation
of probabilistic models of uncertain variables.
In practice two situations may thus be distinguished namely, the situation where a new
probabilistic model is formulated from the very beginning and the situation where an already
existing probabilistic model is updated on the basis of new information, e.g. observations or
experiment results. The formulation of probabilistic models may be based on data
(frequentistic information) alone, but most often data are not available to the extent where this
is possible. In such cases it is usually possible to base the model building on physical
arguments, experience and judgement (subjective information). If also some data are available
the subjective information may be combined with the frequentistic information and the
resulting probabilistic model is in effect of a Bayesian nature.
It should be emphasised that on the one hand the probabilistic model should aim for simplicity
and, on the other hand the model should be accurate enough to allow for including important
information collected during the lifetime of the considered technical system, and thereby
facilitate the updating of the probabilistic model. In this way uncertainty models, which
initially are based entirely on subjective information will, as new information is collected,
eventually be based on objective information.
In essence the model building process consists of five steps, namely