Computing intensity and cost consuming are two important difficulties in reliability-based design optimization (RBDO).the single-looping optimization (SLO) methods and the double-looping optimization (DLO) methods cannot deal with them.Some based on the inverse most probable point (MPP) transforms the probabilistic constraints to deterministic constraints

but they cannot decouple the two procedures including reliability analysis and optimization

in additional

there are too large errors because of using the first order reliability methods(FORM) in the methods to be adaptive in aero-engine design.The nominal limit state factor method was proposed that can decouple the two procedures of reliability analysis and optimization and can make the reliability analysis become a pre-procedure before optimization.Moreover

the uni-variate dimension reduction method was used to obtain accurate probability of failure that only requires the results of FORM in previous reliability analysis.Finally

an example on structure optimization for turbine disk was given to illustrate that the proposed methods are more efficient than the DLP method and are close to the deterministic optimization in efficiency.