Modelling track geometry by a bivariate Gamma wear process, with application to maintenance

This paper discusses the maintenance optimization of a railway track, based on the observation of two dependent randomly increasing deterioration indicators. These two indicators are mod- elled 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. The EM algorithm is used to compute the maximum likelihood estimators. A bivariate Gamma process is then fitted to real data of railway track deterioration. Preventive maintenance scheduling is studied, ensuring that the railway track keeps a good quality with a high probability. The results are compared to those based on both indicators taken separately, and also on one single indicator (usually taken for current track maintenance). The results based on the joined information are proved to be safer than the other ones, which shows the interest of the bivariate model.