Evaluation of Multinormal Integral and Sensitivity by Matrix-Based System Reliability Method

Abstract

In efforts to estimate the system-level risk and reliability of an engineering system, it is often required to evaluate multinormal integrals efficiently and accurately. Their sensitivities with respect to design parameters are also important in decision-making processes for more reliable systems. This paper proposes to use the recently developed matrix-based system reliability (MSR) method for evaluating multinormal integrals and their sensitivities with respect to design parameters. While most of the existing multinormal calculation methods are applicable to parallel or series system events only, the proposed approach can compute the probabilities of any general system events. The correlation coefficient matrix of the normal random variables is fitted by a generalized Dunnett-Sobel correlation model. This transforms the multinormal problem into an integral in the space of statistically independent standard normal random variables, termed as common source random variables (CSRVs). If many CSRVs are needed for accurate representation of the given correlation coefficient matrix, first- and second-order reliability methods (FORM/SORM) can be used for efficient numerical integration. The paper demonstrates the proposed approach through numerical examples.