Further development of matrix-based system reliability method and applications to structural systems

Abstract

In efforts to estimate the risk and reliability of a complex structure or infrastructure network, it is often required to evaluate the probability of a 'system' event, i.e. a logical function of multiple component events. Its sensitivities with respect to design parameters are also useful in decision-making processes for more reliable systems and in reliability-based design optimisation. The recently developed, matrix-based system reliability (MSR) method can compute the probabilities of general system events including series, parallel, cut-set and link-set systems, and their parameter sensitivities, by use of efficient matrix-based procedures. When the component events are statistically dependent, the method transforms the problem into an integral in the space of random variables which cause the statistical dependence, termed as the common source random variables (CSRVs). One can identify CSRVs by fitting a generalised Dunnett-Sobel (DS) model to a given correlation coefficient matrix. This article introduces two further developments of the MSR method: First, for efficient evaluation, it is proposed that the integral in the CSRV space can be performed using the first- or second-order reliability methods. Second, a new matrix-based procedure is developed to compute the sensitivity of the system failure probability with respect to the parameters that affect the correlation coefficients between the components. In addition, an extensive parametric study is performed to investigate the effect of the error in fitted generalised DS model on the accuracy of the estimates by the MSR method. The further developed MSR method is demonstrated by two examples: system reliability analysis of a three-storey Daniels system structure, and finite element reliability analysis of a bridge pylon system.