“…9 Many valuable studies have been proposed to perform Nomenclature: X R , continuous random variable; M XR ξ ð Þ, the moment generating function of X R ; K XR ξ ð Þ, the cumulant generating function of X R ; f XR x R ð Þ, the probability density function of X R ; e ξ, the saddlepoint; ϕ(•), the standard normal probability density function of X R ; Φ(•), the standard normal cumulant generating function of X R ; X, the vector of local design variables; X S , the vector of shared design variables; Y ji , the vector of coupling variables which are the output of discipline j; Y ij , the vector of coupling variables which are the output of discipline i; J, the compatibility constraint; Pr(•), the reliability constraints this analysis by means of numerical simulations combining with physics of failure modeling. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] Among them, Wang et al 10 utilized a reliability index strategy and proposed an uncertainty-based optimization model for the structure design problem with bounded uncertain information. Correia et al 11 proposed a generalization probabilistic fatigue model which can include multiaxial loading conditions and mean-stress effects.…”