Optimal condition-based maintenance policy with delay for systems subject to competing failures under continuous monitoring

Delay in maintenance operations occurs for many systems in real engineering applications. Random delays increase the variability in maintenance modeling, making the optimization of maintenance policy more complicated. In this paper, a delayed condition-based maintenance (CBM) problem for systems under continuous monitoring is studied. The system is assumed to be affected by competing degradation failures and fatal shocks. The degradation path is modeled by a gamma process, while random fatal shocks are modeled by a non-homogeneous Poisson process, of which the failure intensity has a change point that depends on the degradation level. It is assumed that when the degradation level reaches the alarm threshold, the maintenance operation delays for a random duration of time before its implementation. The main objective here is to choose an appropriate alarm threshold to minimize the expected cost rate. We derive the asymptotic cost rate in the analytical form. The proposed modeling and decision framework are validated and illustrated by numerical examples along with sensitivity analysis. The results show the necessity to determine the distribution for delay time precisely and the framework also helps decision maker to identify the source of the cost that is most worthwhile to be controlled in practice.