Infrastructure deterioration modeling with an inhomogeneous continuous time Markov chain: A latent state approach with analytic transition probabilities

Abstract

Markov chains have been widely used to characterize performance deterioration of infrastructure assets, to model maintenance effectiveness, and to find the optimal intervention strategies. For long-lived assets such as bridges, the time-homogeneity assumptions of Markov chains should be carefully checked. For this purpose, this research proposes a regime-switching continuous-time Markov chain of which the state transition probabilities depend on another, latent, Markov chain that characterizes the overall aging regime of an asset. With the aid of a state-augmentation technique, closed-form solutions for the transition probabilities are analytically derived, making the statistical analysis simple. A case study is presented using the open Ontario Bridge Condition data for provincial highway bridges. The case study demonstrates that the proposed method allows to (1) estimate a statistically superior model to the homogeneous Markov chain and (2) obtain results with comparable accuracy in approximately 48% of the computation time of the state-of-the-art inhomogeneous Markov chain.