Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
Construction, Systems and Structures: PSA Modeling and Methods for Construction, Structures and Systems
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Modeling the reliability of critical infrastructure systems such as electric power, transportation, and water supply networks is challenging for many reasons. The data often consists of counts of events, making traditional regression models inappropriate. This paper presents an overview of how generalized linear models (GLMs) and generalized linear mixed models (GLMMs) can be used to model critical infrastructure system reliability, and it gives examples of using these approaches to model electric power system reliability. GLMs are a type of regression model that accounts for the discrete nature of the failure data common in infrastructure modeling and allows for flexible modeling of explanatory variables. They are based on an assumed probability density function (PDF) for the discrete (count) data and a link function that ties the parameter(s) of this PDF to the available explanatory variables. GLMMs extend the basic GLM framework to provide additional flexibility in modeling complex variance structures in the models.
The first example presented is of the use of a Negative Binomial GLM for modeling the number of electric power outages during hurricanes due to damage to an electric distribution system. This example briefly demonstrates the potential usefulness of these types of models in estimating both (a) failures or outages in critical infrastructure systems and (b) the relative importance of different aspects of the situation in terms of their impacts on system outages and failures. The second example is of the use of a Poisson GLMM to model the impacts of a particular type of maintenance (tree trimming) on electric power system outages. This example demonstrates the use of a slightly more complex variance structure and modeling approach. While the first two examples are from past studies, the third example presents a new extension of the second example by taking a Bayesian approach to Poisson GLMMs and using a more flexible variance structure. This model demonstrates the capabilities of the GLMM approach in capturing complex variability in models of infrastructure outages and failures.