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