Imprecise reliability analysis of complex interconnected networks

The effect of natural and man made disasters on critical infrastructures are substantial, as evident from recent history. Break downs of critical systems such as electrical power grids, water supply networks, communication networks or transportation can have dire consequences on the availability of aid in such a crisis. That is why, reliability analyses of these networks are of paramount importance. Two important factors must taken into consideration during reliability analysis. First, the networks are subject to complex interdependencies and must not be treated as individual units. Second, the reliability analysis is typically based on some form of data and or expert knowledge. However, this information is rarely precise or even available. Therefore, it is important to account for different kinds of uncertainties, namely aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty represents the natural randomness in a process, while epistemic uncertainty represents vaguness or lack of knowledge in the model. In this work we present an approach to the numerical reliability analysis of complex networks and systems extending a previously developed method based on Monte Carlo simulation and survival signature. The extended method treats both kinds of uncertainties, thus, yielding better results. We show how Monte Carlo simulation controls aleatory uncertainty and apply sets of distributions (probability boxes) to treat epistemic uncertainties in component failures. In this framework, dependencies are modelled using copulas. Copulas possess the unique property of decoupling the odelling of the univariate margins from the modelling of the dependence structure for continuous multivariate distributions. Analoguous to the p-boxes we use sets of copulas to include imprecision in the dependencies. Finally, the method is applied to an example system of coupled networks. A secondary task during the reliability analysis is the accurate modelling of component failures and dependencies. Typically, this is done based on data or expert assessments. However, both are subject to two kinds of imprecisions, namely, aleatory and epistemic uncertainty (Beer et al. 2013). Aleatory uncertainty represents the randomness inherent in a process, such as component degradation and external forces affecting the system (natural hazards, earthquakes, etc.), while epistemic uncertainty describes the uncertainty in the model due to a lack of or vagueness of knowledge about the system. The latter is usually regarded as reducible through acquiring of additional data and information. In this work we expand our previously developed technique by inclusion of imprecision. The method is based on Monte Carlo simulation and as such already deals with aleatory uncertainty. In this extension the modelling of component failures is refined by applying probability-boxes (p-boxes) to account for epistemic uncertainty. Feng et al. 2016 have shown the advantages of using p-boxes