x and d are the random variable and design variable vectors, respectively. They

recommended Latin Hypercube sampling as the statistical design of experiments. The

number of response surface approximations constructed in optimization process is

reduced substantially by introducing design variables into the response surface

approximation formulation.

 The selection of RSA approach depends on the limit state function of the problem

and target probability of failure. The global RSA approach is more efficient than local

RSA, but it is limited to problems with relatively high probability or limit state function

that can be well approximated by regression analysis based on simple basis functions. To

avoid the extrapolation problems, RSA generally needs to be constructed around

important region or MPP to avoid large errors in the results of MCS induced by fitting

errors in RS. Therefore, an iterative RSA is desirable for general reliability analysis

problem.

 Design response surface approximations (DRS) are fitted to probability of failure to

filter out noise in MCS and facilitate optimization. Based on past experience, high-order

DRS (such as quintic polynomials) are needed in order to obtain a reasonably accurate

approximation of the probability of failure. Constructing highly accurate DRS is difficult

because the probability of failure changes by several orders of magnitude over small

distance in design space. Fitting to safety index /7=-0 (p), where p is the probability of

failure and & is the cumulative distribution function of normal distribution, improves the

accuracy of the DRS to a limited extent. The probabilistic sufficiency factor can be used

to improve the accuracy of DRS approximation.