Failure interaction model based on extreme shock and Markov processes

Reliability models have overtaken the stochastic dependence that may exist between multiple failure modes of the same system. A few relevant models involve the calculation of interaction coefficients, which are difficult to interpret and quantify from maintenance logs. This paper develops a model that integrates failure interactions as successive random events. It uses an interrelated draw concept to model the dependent failure modes as consequences of extreme shocks. The model quantifies the probabilities of both sides’ failure mode effects on the reliability indexes’ system. A Markov process method is used to estimate the mean time-to-failure of a culvert system subject to two cracking and displacement dependent failure modes. The model developed reproduces the interaction phenomena within the culvert beside the interpretability of its results. A sensitivity analysis demonstrates that the intensity of the shock process strengthens its interactivity in most cases.