The last decades have witnessed the development of methods for solving
struc- tural reliability problems, which emerged from the efforts of
numerous re- searchers all over the world. For the specific and most
common problem of determining the probability of failure of a structural
system in which the limit state function g( x) = 0 is only implicitly
known, the proposed methods can be grouped into two main categories: -
Methods based on the Taylor expansion of the performance function g(x)
about the most likely failure point (the design point), which is
determined in the solution process. These methods are known as FORM and
SORM (First- and Second Order Reliability Methods, respectively). -
Monte Carlo methods, which require repeated calls of the numerical (nor-
mally finite element) solver of the structural model using a random
real- ization of the basic variable set x each time. In the first
category of methods only SORM can be considered of a wide applicability.
However, it requires the knowledge of the first and second deriva- tives
of the performance function, whose calculation in several dimensions
either implies a high computational effort when faced with finite
difference techniques or special programs when using perturbation
techniques, which nevertheless require the use of large matrices in
their computations. In or- der to simplify this task, use has been
proposed of techniques that can be regarded as variants of the Response
Surface Method.