A preventive maintenance policy for a continuously monitored system with correlated wear indicators

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Lévy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive maintenance policy is proposed, which involves a delayed replacement, triggered by the reaching of some preventive zone for the system deterioration level. The preventive maintenance policy is assessed through a cost function on an infinite horizon time. The cost function is provided in full form, and tools are provided for its numerical computation. The influence of different parameters on the cost function is studied, both from a theoretical and/or numerical point of view.

► System: submitted to accumulating deterioration and continuous monitoring.
► Measure of the deterioration: two dependent increasing wear indicators, modelled by a bivariate increasing Lévy process.
► Failure zone: upper set (once the system has reached the failure zone, it cannot leave it any more without any repair).
► Perfect repair, with delay in the repair.
► Preventive zone: upper set, which includes the failure zone.