On the use of uniformization to estimate transition probabilities in categorical condition data

Large groups of structures like bridges, pavements and sewer systems, are often inspected visually and their condition is quantified based on a discrete scale which results in categorical data. Markov chains have traditionally been used to model the uncertain rate at which these structures progress through such a condition scale. In order to determine optimal strategies for inspections and maintenance activities, these Markov chains must be fitted to the data obtained in the field. This paper presents details on how to implement the method of uniformization for the calculation of interval transition probabilities and their sensitivity towards model parameters. The primary benefit of uniformization is that it provides a robust and efficient method for use in maximum likelihood estimation of transition probabilities or intensities in Markov chains.