Mean points of failure and safety domains: Estimation and application

A conceptual representation of the mean points of failure and safety domains in reliability problems is presented, and a practical approach for approximating the mean points based on the first-order reliability method (FORM) is proposed. The effectiveness of the approach is demonstrated with two nonlinear examples. The mean points of failure and safety domains and the approach for approximating them are then used to develop an innovative method for estimating transition probabilities between failure and safety domains in discrete time-variant reliability problems. The performance of the new method is demonstrated in example problems. It is shown that, from a practical viewpoint, the method is quite effective. Although the example problems are stationary univariate systems, the method shows promise for being applicable for more complex cases, such as non-stationary multivariate systems.