Hybrid reliability analysis method for systems with random and non-parameterized p-boxes based on weight coefficients

This paper establishes a hybrid variable system failure probability optimization model based on sampling methods and weighting coefficients. By introducing auxiliary input variables, important sampling functions, and p-box, failure samples are mapped from the random variable space to the p-box variable space. The new weight coefficients are constructed, including important sampling weights and interval weights. Combining discretization methods and Monte Carlo simulation (MCS), the interval weights are transformed into variables, and constraints conforming to the p-box variable distribution are constructed. After calculating the weighting coefficients for all failure samples, the new failure probability optimization model is built. This model is independent of the performance functions and does not involve cyclic optimization, with computational complexity only related to the dimensions. Six cases are used for method comparison, validating that the new method exhibits higher efficiency and accuracy.