124 Chapter 6. Comparing Homogeneous and Inhomogeneous Time Markov Chains for Modelling Deterioration in Sewer Pipe Networks 6.1 Introduction Sewer networks are essential for societal and economic welfare but face management challenges such as budget constraints, environmental changes, and complex deterioration processes. Predictive tools for deterioration are becoming crucial as these systems reach the end of their design life, aiding in e"cient maintenance and logistics (Marc Ribalta and Rubión, 2023). Robust models for sewer main deterioration are critical for balancing maintenance costs and system performance, enabling proactive maintenance, informed decision-making, and strategic planning (Caradot, Sonnenberg, Kropp, et al., 2017). In this work, we focus on Markov chains, which are probabilistic models with the ability to predict future distributions associated with deterioration processes. Markov chains have several advantages: (i) they convert condition data into ordinal numbers such as severity levels, commonly used in industry to assess the condition of infrastructure assets (Tran, Lokuge, Setunge, et al., 2022); (ii) capture the stochastic nature of deterioration processes in sewer mains; (iii) their outputs can indicate the proportions of pipes in specific conditions, crucial for optimising maintenance planning. Two primary types of Markov chains, homogeneous and inhomogeneous-time, are prevalent in the literature for modelling deterioration in sewer networks (see Table II.3). However, the optimal Markov chain type remains debated. Proponents of homogeneous-time Markov chains, such as Micevski, Kuczera, and Coombes, 2002, argue for their su"ciency, while proponents of inhomogeneous-time Markov chains, such as Egger, Scheidegger, Reichert, et al., 2013, question homogeneoustime Markov chains e"cacy. This gap is what we cover with this work since no studies have directly compared these models using the same dataset and discussed their suitability. Understanding this is crucial for sewer asset managers implementing maintenance strategies, as di!erent assumptions about the deterioration model can have distinct implications for maintenance policies. For this, we employ homogeneous-time Markov chains, and for inhomogeneous chains, we use Gompertz, Weibull, Log-Logistic and Log-Normal functions, commonly used in reliability engineering. Our study, using a large-scale sewer network case study in the Netherlands (see Section II.4.3), evaluates calibration complexity and model performance using cross-validation and various goodness-of-fit metrics. We employ the non-parametric Turnbull estimator (Turnbull, 1976) for handling the interval-censored data in the inspection dataset, serving as a reference. Contributions. Our key contributions with this work are: - Presenting evidence that inhomogeneous-time Markov chains, despite their complexity, are more versatile and e!ective to model non-linear stochastic behaviours in long-lived assets like sewer networks.
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