Analysis of approximations for multinormal integration in system reliability computation

In the context of first-order reliability analysis, the computation of multivariate normal integrals is a key step in the analysis of the system probability of failure. Several approximate methods for multinormal integration have been developed, since the direct numerical integration in large dimensions (30–50) is not feasible. The product of conditional marginal (PCM) method was proposed as a simple and effective method for system reliability computation. Although PCM is fairly accurate in computing parallel system reliability, it can result in a large overestimation of the failure probability of series systems with highly reliable elements. The paper presents an improved version, referred to as I-PCM, to eliminate this shortcoming of the original method. The I-PCM method employs a simple modification of bivariate integrals based on the additive law of probability. Detailed error analyses and numerical examples are presented in the paper to illustrate the improved accuracy and efficiency of the proposed I-PCM method.