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)