Modelling the deterioration process of drainage pipelines

With the goal of modelling the deterioration of urban drainage infrastructures, a mixed multi-state deterioration process has been designed within the theoretical framework of non homogeneous Markov chains ( NHMC). The time dependent transition probabilities are conditional on the values of a set of covariates, and on the value of a pipeline specific random frailty factor. The parameters of the time dependent transition probabilities can be estimated through maximum marginal likelihood estimation using an extension of the Gompit analysis method. Although it is designed for longitudinal data analysis, the model is applicable even when pipelines are subjected to very sparse inspections. It enables the prediction of the condition state at any time, taking into account the result of a previous inspection if any. The Gompertz distribution based Mixed Multi-State Process is thus a useful support for decision making in short to long term maintenance and rehabilitation planning. An example of analysis of an actual dataset illustrates the gain in efficiency for detecting pipes needing the most urgent repairs.