Preventive Maintenance of a Multi-State Device Subject to Internal Failure and Damage Due to External Shocks

Preventive maintenance is of interest in reliability studies, to improve the performance of a system, and to optimise profits. In this study, we model a device subject to internal failures and external shocks, and examine the influence of preventive maintenance. The internal failures can be repairable or non-repairable. External shocks produce cumulative damage until non-repairable failure occurs. The device is inspected at random times. When an inspection takes place, the level of internal degradation and the damage produced by external shocks are observed. If damage is major, the unit is assigned to preventive maintenance according to the degradation level observed. Minimal preventive maintenance is also undertaken: if internal and external degradation is observed, and only one of them is major, then the device is assigned to preventive maintenance only for the major damage, and the minor damage state is saved in memory. We model the system, solve for the stationary distribution, create measures of reliability, in transient and stationary regimes, and introduce rewards by considering profits and different costs. We show the results in algorithmic form, and they are implemented computationally with Matlab. The versatility of the model is shown by a numerical example.