In this paper, a new reliability analysis method for engineering structures is developed based on probability and probability box (p-box) models. Random variable distributions are used to deal with the uncertain parameters with sufficient information, while the p-box models are employed to deal with the uncertain-but-bounded variables. Due to the existence of the p-box parameters, a limit-state band will result and a complex nesting optimization problem will be involved in this reliability analysis. To reduce the computational burden, an efficient decoupling strategy is developed to solve the ...