Multi-level maintenance strategy of deteriorating systems subject to two-stage inspection

Preventive maintenance, including time-based and condition-based maintenance, plays an important role in reducing system economic losses caused by unexpected failures. This paper studies a multi-level preventive maintenance strategy for a three-state industrial system subject to two competing failure processes. The first is a continuous degradation process characterized by the general path model, and the second is a shock process arriving according to a non-homogenous Poisson process. The degradation/hazard rate of the system undergoes an abrupt increase upon the initialization of the defective state, and the magnitude of the damage caused by a shock load is correlated to two factors: (a) operational age; (b) degradation speed. The system is preventively replaced at a pre-determined operational age, before which a finite number of inspections are executed according to a two-stage interval partition. The objective of this paper is to minimize the expected cost per unit time via the optimization of the replacement age, the control limit and two inspection intervals. A case study on a peristaltic pump is provided to illustrate the application of the maintenance model.