calculated inexpensively by Monte Carlo simulation or FORM and SORM using the
fitted polynomials. Therefore, RSA is particularly attractive for computationally
expensive problems (such as those requiring complex finite element analyses). The
design points where the response is evaluated are chosen by statistical design of
experiments (DOE) so as to maximize the information that can be extracted from the
resulting simulations.
Response surface approximations can be applied in different ways. One approach is
to construct local response surfaces around the MPP region that contributes most to the
probability of failure of the structure. The DOE of this approach is iteratively adjusted to
approach the MPP. Typical DOEs for this approach are Central Composite Design (CCD)
and saturated design. For example, Bucher and Bourgund (1990), and Rajashekhar and
Ellingwood (1993) constructed progressively refined local response surfaces around the
MPP. This local RSA approach can produce good probability estimates given enough
iterations.
Another approach is to construct global RSA over the entire range of random
variables (i.e., DOE around the mean values of the random variables). Fox (1993, 1994,
and 1996) used Box-Behnken DOE to construct global RSA and summarized 12 criteria
to evaluate the accuracy of response surfaces. Romero and Bankston (1998) used
progressive lattice sampling, where the initial DOE is progressively supplemented by
new design points, as the statistical design of experiments to construct global response
surfaces. With the global approach, the accuracy of the RSA around the MPP is usually
unknown, thus caution should be taken to avoid extrapolation around the MPP. Both the