New linear programming-based bound method for structural system reliability

A small-scale LP bound (SSLP bound) method is proposed for structural system reliability testing. A mixed system is considered that consists of r failure sequences in series, each of which consists of failure modes in parallel. If the original space is a standard normal space, the most probable point (MPP) in the joint failure domain is on the intersection surface. The joint failure probabilities (JFP) of these three surrogate linear limit state functions by Monte Carlo simulation is 0.00141, the JFP of the primary three nonlinear limit state functions by the Monte Carlo simulation is 0.00140. Three numerical examples and an engineering example involving an inside flap structure of an aircraft demonstrate the efficiency and precision of the proposed methods.