Generalization of the proportional hazards model for maintenance modelling and optimization

A non-observable monotonically deteriorating system is considered. The observed data are the maintenance times and the kinds of maintenance performed. The aim of this paper is to propose a model of the dependency between all kinds of maintenance by considering imperfect maintenance efficiency. Furthermore, we present an additional planned preventive maintenance policy that reduces a finite horizon average total maintenance cost. To deal with such a problem a competing risks model is considered. A general class of models, denoted generalized proportional hazards, is presented and a particular model is derived. An estimation method is detailed for the proposed model. Finally, by numerical implementation, a maintenance policy that leads to the lowest finite horizon average total maintenance cost is proposed.