Moment method for reliability sensitivity with multiple failure modes and correlated variables

For structural system with multiple failure modes and correlated variables, a numerical simulation method is given to analyze reliability sensitivity. Furthermore, the moment based reliability sensitivity method for a single failure mode with correlated variables is extended to the multiple failure modes, and the moment based reliability sensitivity method is presented for series and parallel system with correlated variables. In presented method, the correlated variables are transformed into uncorrelated variables equivalently, and the performance functions in the correlated variables space are transformed into those in the equivalent uncorrelated variables space, in which the reliability sensitivity of the system failure probability with respect to the distribution parameters of the uncorrelated variables can be solved by the moment method for the uncorrelated variables. Finally the equivalent relationship between the correlated variables and the uncorrelated variables, the chain rule for derivative are employed to obtain the reliability sensitivity of the system failure probability with respect to the means of the correlated variables. Numerical examples are used to demonstrate the rationality of the presented method.