Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling

This article discusses the intervention scheduling of a railway track, based on the observation of two dependent randomly increasing deterioration indicators. These two indicators are modelled through a bivariate Gamma process constructed by trivariate reduction. Empirical and maximum likelihood estimators are given for the process parameters and tested on simulated data. An expectation-maximisation (EM) algorithm is used to compute the maximum likelihood estimators. A bivariate Gamma process is then fitted to real data of railway track deterioration. Intervention scheduling is defined, ensuring that the railway track remains of good quality with a high probability. The results are compared to those based on both indicators taken separately, and also on one single indicator. The policy based on the joint information is proved to be safer than the other ones, which shows the potential of the bivariate model.