A comparison of two non-stationary degradation processes

Time-dependent degradation of engineering structures can be modelled in several ways. Well-known models for this type of degradation are the non-stationary gamma process and Brownian motion with non-linear drift. Accordingly, the lifetime of a structure is modelled as the first hitting time of a fixed failure level by the stochastic process under consideration. In this study we compare the lifetime distributions of both processes under different degradation scenarios. We also investigate the implications of the two stochastic processes to an age replacement policy for engineering structures in a simplified maintenance model. In this model failures are not detected immediately, but only upon replacement (either preventive or corrective). A replacement restores the system to as new condition. We find some conspicuous differences between Brownian motion and the gamma process.