A methodology to clarify logical relationship among failure modes and determine system probabilities

In the vulnerability analysis, correlations among failure modes have significant effects on the estimation of failure probabilities. However, the failure modes were assumed to be independent with each other or only parts of dependencies of failure modes were considered, which might lead to inaccurate results. In the present study, a novel methodology to clarify the entire logical relationship among failure modes and determine system probabilities is developed. Firstly, based on the form-changed limit state equations (LSEs) of failure modes, the LSE surfaces or curves are plotted. Subsequently, the logical relationship among failure modes can be identified with the LSE surfaces or curves. The system consequences are further developed by the logical relationship. Bayesian network (BN) is constructed with the input of logical relationship into arcs. With BN considering logical relationship, the occurrence probabilities of failure modes are calculated and system probabilities are estimated more accurately, which are verified well with Monte Carlo simulation and analytical solution. Furthermore, the detailed compositions of occurrence probabilities of failure modes are specified by the system probabilities. The methodology is illustrated by a case study. This study can be applied to the vulnerability analysis of various hazards or disasters as long as LSEs for corresponding failure modes can be developed.