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.