* Determining a mathematical model that best fits the data generated from the design
 points of DOE by performing statistical test of hypotheses of the model
 parameters(Khuri and Cornell 1996 and Myers et al. 2002)

* Predicting response for given sets of experimental factors or variables by the
 constructed response surface approximation. Due to the close form nature of the
 approximation, RSA is particularly attractive for engineering problems that require
 a large number of computationally expensive analyses, such as structural
 optimization and reliability analysis.

 The accuracy of RSA is measured by error statistics such as the adjusted coefficient

of multiple determination (R2adj), root mean square error predictor (RMSE), and

coefficient of variation (COV =RMSE/Mean of Response). An R2adj close to one and a

small COV close to zero usually indicate good accuracy. The RSAs in this dissertation

were all constructed by JMP software (SAS Institute., 2000). The above error statistics

are readily available from JMP after RSA construction. Khuri and Cornell (1996)

presented a detailed discussion on response surface approximation.

 This chapter presents the response surface approach developed for reliability-

based design optimization.

 Stochastic Response Surface (SRS) Approximation for Reliability Analysis

 Among the available methods to perform reliability analysis, moment-based

methods (e.g., FORM/SORM) are not well suited for the composite structures in

cryogenic environments because of the existence of multiple failure modes. Direct Monte

Carlo simulation requires a relatively large number of analyses to calculate probability of

failure, which is computationally expensive. Stochastic response surface approximation is

employed here to solve the above problems.

 To apply RSA to a reliability analysis problem, the limit state function g(x)

(usually the stress of displacement in the structures) is approximated by