safety index P, which replaces the probability by using the inverse standard normal

transformation,

 P7= -95' (P) (3-6)

Safety index is the distance measured as the number of standard deviations from the

mean of a normal distribution that gives the same probability. Fitting DRS to safety index

showed limited improvement of accuracy (Chapter 6), and it has the same problems of

accuracy as the probability of failure when based on Monte Carlo simulations.

 Box-Cox transformation (Myers and Montgomery 1995) on the probability of

failure was also tested, but showed very limited improvement. A probabilistic sufficiency

factor approach is developed as an inverse reliability measure to improve the accuracy of

DRS, estimate additional resources required to satisfy the reliability constraint, and

convert RBDO to sequential deterministic optimization (Chapter 6 and 7).

 Analysis and Design Response Surface Approach

 Figure 3-1 summarizes the ARS/DRS-based RBDO approach. First the DOE of

ARS is performed and ARS is constructed. Then DOE of DRS is performed, which

should stay in the range of design variables of the DOE for the ARS, and DRS is

constructed. Design optimization is then performed on the DRS. If the design does not

converge, the DOE of the DRS can be moved toward the intermediate optimum and its

range can be shrunk to improve the accuracy of DRS. If the intermediate optimum is near

the boundary of the ARS, the DOE of the ARS needs to be moved to cover the potential

optimum region better. The entire process is repeated until the optimization converges

and the reliability of the optimum stabilizes.