Goodness-of-fit procedure for gamma processes

Gamma processes are commonly used for modelling the accumulative deterioration of systems, in many fields. However, given a series of observations, it is not always easy to affirm that the choice of a gamma process modelling is a good choice. In particular, it would be of great interest to have a statistical test, i.e. a goodness-of-fit test, to answer this question. In this paper, a practical procedure combining three statistical tests is firstly proposed, whose aim is to reject the gamma process modelling as soon as the observations are clearly in contradiction with the basic properties of a homogeneous gamma process, observed with periodic inspections: stationarity, independence and gamma distribution for the increments. The procedure is then extended to non-homogeneous gamma process and aperiodic inspection times. The efficiency of the approach is investigated through numerical simulations, and on real data.