A Copula Approach in the Point Estimate Method for Reliability Engineering

In order to arrive at realistic results in statistical analysis, it is often advisable to consider involved uncertainties as random variables. An important aspect in this context is the evaluation of the importance of parameter uncertainty. Because of the complexity of computational models, the point estimate method is usually adopted as an easy‐run approach for approximating the statistical moments of a system/model in a reliability analysis. The efficiency of this method highly depends on the correlation coefficient. However, the complex nature of parameters in computational problems often exhibits a nonlinear relationship. This paper aims to develop an original and efficient point estimate method based on the copula approach for reliability engineering problems. The paper discusses the use of the copula theory in the point estimate method for computing the statistical moments of a function involving random variables. The study performs two engineering applications to demonstrate the benefits of this approach. The performance of this proposed method can significantly improve the quality of the results in using the point estimate method when a nonlinear relationship exists between the parameters.