123 Chapter 6 Comparing Homogeneous and Inhomogeneous Time Markov Chains for Modelling Deterioration in Sewer Pipe Networks Paper published at L. A. Jimenez-Roa, T. Heskes, T. Tinga, M. Stoelinga, “Comparing Homogeneous and Inhomogeneous Time Markov Chains for Modelling Deterioration in Sewer Pipe Networks”, in 34th European Safety and Reliability Conference, ESREL 2024: Advances in Reliability, Safety and Security, 2024, arxiv.org/abs/2407.12557. Abstract Sewer systems are essential for social and economic welfare. Managing these systems requires robust predictive models for deterioration behaviour. This study focuses on probability-based approaches, particularly Markov chains, for their ability to associate random variables with deterioration. Literature predominantly uses homogeneous and inhomogeneous Markov chains for this purpose. However, their e!ectiveness in sewer main deterioration modelling is still debatable. Some studies support homogeneous Markov chains, while others challenge their utility. We examine this issue using a large-scale sewer network in the Netherlands, incorporating historical inspection data. We model deterioration with homogeneous discrete and continuous time Markov chains, and Inhomogeneous-time Markov Chains (IHTMCs) using Gompertz, Weibull, Log-Logistic and Log-Normal density functions. Our analysis suggests that, despite their higher computational requirements, IHTMCs are more versatile for modelling the non-linear stochastic characteristics related to sewer main deterioration, particularly the Gompertz distribution. However, they pose a risk of over-fitting, necessitating significant improvements in parameter inference processes to e!ectively address this issue.
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