Progressive advanced-mean-value method for CDF and reliability analysis

The Advanced Mean Value (AMV) method, developed more than a decade ago, can provide a quick response CDF (Cumulative Distribution Function) and reliability analysis with reasonable results for many practical applications. The method is particularly useful for analysing computationally demanding numerical models. However, the accuracy of AMV depends on the characteristics of the response function and cannot be estimated without additional analyses. The lack of an error estimate has been a significant drawback that prevents the method from being used by non-experts. This paper presents a progressive AMV CDF-analysis procedure that can detect whether the solution has converged or requires additional analyses. The methodology is demonstrated using a simple analytical problem and a real-world reliability application problem that involves a large finite-element model.