local RSA approach can produce satisfactory results given enough iterations. Another
approach is to construct global RSA over the entire range of random variables, i.e.,
design of experiment around the mean values of the random variables. Fox (1993, 1994,
1996) used Box-Behnken design to construct global response surfaces and summarized
12 criteria to evaluate the accuracy of RSA. Romero and Bankston (1998) employed
progressive lattice sampling as the design of experiments to construct global RSA. With
this approach, the accuracy of response surface approximation around the MPP is
unknown, and caution must be taken to avoid extrapolation near the MPP. Both
approaches can be used to perform reliability analysis for computationally expensive
problems. The selection of RSA approach depends on the limit state function of the
problem. The global RSA is simpler and efficient to use than local response surface
approximation for problems with limit state function that can be well approximated
globally.
However, the reliability analysis needs to be performed and hence the RSA needs
to be constructed at every design point visited by the optimizer, which requires a fairly
large number of response surface constructions and thus limit state evaluations. The local
RSA approach is even more computationally expensive than the global approach in the
design environment. Qu et al. (2000) developed a global analysis response surface (ARS)
approach in unified space of design and random variables to reduce the number of RSA
substantially and achieve higher efficiency than the previous approach. This analysis
response surface can be written as
g(x,d)= Z(x, d)Tb (6-18)