Reliability sensitivity analysis based on directional simulation for systems of multiple design points/failure modes with normal correlated variables

For the reliability problem of systems of multiple design points or multiple failure modes with normal correlated variables, two reliability sensitivity analysis methods based on directional simulation are presented. First, the normal correlated variables are transformed into equivalent independent standard normal variables. Second, two reliability sensitivity methods based on directional simulation are employed for multiple design point or multiple failure mode systems with independent standard normal variables. Third, the reliability sensitivity of independent standard normal variables, the partial derivatives of the distribution parameters of independent standard normal variables, can be transformed into those of normal correlated variables by means of equivalent transformation. The variances of reliability estimators and sensitivity estimators are analyzed to realize convergence. Compared with the classical Monte Carlo numerical simulation, the results of numerical examples and engineering examples can validate the feasibility and validity of the proposed methods.