Multi-stage stochastic programming for predictive maintenance scheduling with probabilistic Remaining Useful Life prognostics

Predictive maintenance for modern machines requires a dynamic process of decision making, where updated information about the health of machines steers the maintenance decisions. For this, it is important to consider the uncertainty associated with the health of the machines. In this paper, we propose a multi-stage stochastic program to schedule maintenance for machines that are continuously monitored by sensors. First, we model the uncertainty associated with the health of the machines by means of probabilistic Remaining Useful Life (RUL) prognostics. With this, the proposed stochastic program schedules maintenance for multiple machines sharing a limited capacity and spare parts. These machines can only be maintained if these resources are available. For failed machines, this may require rescheduling the maintenance of other machines. To reduce the computational time, we formulate the multi-stage stochastic program such that the constraint matrix is totally unimodular, and we can therefore solve it using nested Benders decomposition. We apply our approach to a case study on aircraft engines, planning maintenance 12 weeks ahead. We simulate the maintenance schedule over a period of 10 years. Based on this case study, the results show that our approach reduces the expected costs by 1.4% compared to a non-stochastic approach.