State transition probabilities in bridge deterioration based on Weibull sojourn times

Abstract

Abstract This paper presents an investigation of the Markov property underlying the stochastic deterioration models for highway bridges, including transition probabilities between the condition states. Using historical data of sojourn times for the 'decay' (no improvement intervention) deterioration, hazard functions were developed and 'instantaneous' 1 year transition probabilities estimated for the sojourn times in the condition states, for various bridge categories, by type of material and roadway carried. The rate of transition out of each state was found to be not constant relative to time, as assumed for Markov chain models, but rather, increasing with the time spent in the state. Best-fit distributions of the sojourn times were determined to not be exponential (Markov chain), but Weibull, with the parameters established using the maximum likelihood estimate (MLE) method. A semi-Markov model of the bridge deterioration process was formulated and developed, including kernels of transition probabilities and time-based matrices of multi-step transition probability functions. Keywords: bridge deteriorationsojourn timesprobabilitiessemi-MarkovWeibull distribution