Evaluation of multivariate normal integrals for general systems by sequential compounding

摘要

System reliability analysis often requires efficient and accurate evaluation of a multivariate normal integral. Despite recent advances in system reliability analysis methods, it is still a challenging task especially when the definition of the system event is complex; the system has a large number of components; and/ or the component events have significant statistical dependence. This paper presents a new method developed for evaluating multivariate normal integrals defined for general system events including series, parallel, cut-set and link-set systems. The method compounds two components coupled by union or intersection sequentially until the system becomes a single compound event. Efficient numerical procedures are developed for obtaining the reliability index of the new compound event, and the correlation coefficients between the compound event and the remaining component events, at each step of the sequential compounding. The accuracy and efficiency of the proposed method, and its applicability to various types and sizes of multivariate normal integrals are demonstrated by numerical examples.