Keywords: Markov chain models, transition probability matrix, variation, sensitivity, regression modelling, facility conditions, facility deterioration, civil infrastructure, pavements, roads, bridges, transition probabilities, condition transitions, Monte Carlo simulation
Markov chain applications in modelling facility condition deterioration
Condition states of civil infrastructure such as pavements and bridges are usually indexed on discrete scales. Historical condition data is modelled using Markov chain to estimate transition probabilities from one condition state to another, the rate of change and the time spent in any given state. The usefulness of such models is a function of the completeness of the available records and underlying assumptions of homogeneity. However, complete sets of condition data are not always easily available. In addition, the transition probabilities between states are assumed to be homogeneous, even though they tend not to be. Therefore, the objective of this study is two–fold: First, to maximise the usage of limited available data in estimating transition probabilities between condition states; and second to assess the sensitivity of model predictions to variations in transition probabilities between condition states. The paper presents a novel method to estimate transition probabilities based on the simulation of long term behaviour of a Markov chain model. Next, building on existing research, a Monte Carlo simulation of a non–homogeneous Markov chain model is used to explicitly consider heterogeneity in transition probabilities.