Reliability analysis of multidisciplinary systems by using chi-squared distributions

To improve the accuracy of reliability analysis in the multidisciplinary systems, a novel multidisciplinary reliability analysis method using a quadratic polynomial approximation and the chi-squared distributions is proposed in this paper. This method integrates the system analysis, sensitivity analysis, polynomial approximation and reliability analysis. The limit-state function is described by a quadratic polynomial function which can be transformed into a linear polynomial with the combination of chi-square variables by using an orthogonal transformation. Then, the probability of failure is a numerical integration of the joint Probability Density Function (PDF) over the linear failure area. By using the quadratic approximation and the chi-squared distributions, the proposed method is more accurate than the First Order Reliability Method (FORM). The effectiveness of the proposed method is demonstrated with two numerical examples.