Computation of infrastructure transition probabilities using stochastic duration models

Sound infrastructure deterioration models are essential for accurately predicting future conditions that, in turn, are key inputs to effective maintenance and rehabilitation decision making. The challenge central to developing accurate deterioration models is that condition is often measured on a discrete scale, such as inspectors' ratings. Furthermore, deterioration is a stochastic process that varies widely with several factors, many of which are generally not captured by available data. Consequently, probabilistic discrete-state models are often used to characterize deterioration. Such models are based on transition probabilities that capture the nature of the evolution of condition states from one discrete time point to the next. However, current methods for determining such probabilities suffer from several serious limitations. An alternative approach addressing these limitations is presented. A probabilistic model of the time spent in a state (referred to as duration) is developed, and the approach used for estimating its parameters is described. Furthermore, the method for determining the corresponding state transition probabilities from the estimated duration models is derived. The testing for the Markovian property is also discussed, and incorporating the effects of history dependence, if found present, directly in the developed duration model is described. Finally, the overall methodology is demonstrated using a data set of reinforced concrete bridge deck observations.