Bayesian analysis and prediction of failures in underground trains

Based upon failure data (date and odometer reading) in the early operating time, a public transportation company is interested in checking the actual reliability of the door opening system of its subway trains before their warranty expires. We consider non-homogeneous Poisson processes with a double scale because both time and kilometres are recorded for each failure. Different choices to model the relation between operated time and kilometres run are possible: in this paper the kilometres run are incorporated within the intensity function as a random function of time, modeled as a gamma process. Furthermore a periodic component is introduced to deal with the seasonality in the data. Bayesian inference is then carried out via Monte Carlo simulation, obtaining prediction intervals for the expected number of failures during periods of desired length, using only part of the data. The predictions are then compared with the observed data.