Maintenance planning estimations and policies optimization for single-unit systems using Hawkes processes

ABSTRACT Maintenance planning and optimizations are very important issues in both theory and practice. In this paper, Hawkes processes, a tool for description of self-excited failure effects, are used to model the failure processes of single-unit systems under the assumption of neglected repair times. For such degraded single-unit systems, some maintenance planning estimations such as the distribution, mean and variance of failures or repairs by time , reliability, mean cost of maintenance, mean and variance of system lifetime are presented under the maximal entropy assumption on repair effects. Meanwhile, two optimization problems are developed by considering the lifetime mean of the single-unit system and total maintenance cost as objective functions and constraints alternatively. We have proved that both optimization problems can reduce to two simplified optimal cases, respectively, and their optimal policies are increasing stepwise sequences of increasing rates of failure rates, which greatly reduce the scope of optimal solutions. The relationships between the estimations and the optimizations are discussed. Furthermore, the detailed optimal maintenance policies for a special case are given as well including an algorithm.