Derivation of Transition Probability Matrices for Pavement Deterioration Modeling

The derivation of transition matrices has traditionally been effected using one of two methods. The standard approach is to observe, from historical data, the way in which a road network deteriorates from one year to the next, and use this to estimate the transition matrix probabilities. Alternatively, a panel of experienced engineers can be used to estimate the probabilities using expert opinion. This paper proposes and describes the development of three further methods for the determination of transition probabilities. The first method assumes that the historical condition data for each of the sites in the network is readily available. The second utilizes the regression curve obtained from the original data, and the third assumes that the yearly distributions of condition are available to assit in the process. In each case, an objective function aims at minimizing the difference between each of the method functions obtained from the original data and the corresponding functions obtained from the transition probabilities. An analysis of the results concluded that although the transition matrix fitted curve for the third method was not always as close to the regression curve as in the other methods, it did yield a distribution not only closer, but comparable, to the original distributions in all tested cases. The third method has therefore been taken forward and encapsulated in an analytical tool to assist the engineer in the formulation of transition matrices.