Modelling and inference for a degradation process with partial maintenance effects

This paper proposes a new way of modelling imperfect maintenance in degradation models, by assuming that maintenance affects only a part of the degradation process. More precisely, the global degradation process is the sum of two dependent Wiener processes with drift. Maintenance has an effect of the ARD(1)-type on only one of these processes: it reduces the degradation level of a quantity which is proportional to the amount of degradation of this process accumulated since previous maintenance. Two particular cases of the model are considered: perturbed ARD(1) and partial replacement models. The usual ARD(1) model is also a specific case of this new model. The system is regularly inspected in order to measure the global degradation level. Two observation schemes are considered. In the complete scheme, the degradation levels are measured both between maintenance actions and at maintenance times (just before and just after). In the general scheme, the degradation levels are measured only between maintenance actions. The maximum likelihood estimation of the model parameters is studied for both observation schemes in both particular models. The quality of the estimators is assessed through a simulation study.