Optimum imperfect maintenance policy with cumulative damage model for a used system subject to number-dependent shocks

Abstract

This paper presents a model to define the optimal maintenance policy of a system that deteriorates as a result of initial variable damage and random shocks. A system is subject to two types of shocks according to a non-homogeneous Poisson process with number-dependent probability. Type-I shocks are minor and cause a random amount of damage to the system, whereas type-II shocks are catastrophic and each such occurrence causes the system to fail. The system undergoes a preventive maintenance at age T or immediately after the nth type-I shock, and a corrective maintenance at the age when the total damage exceeds a threshold level or immediately after any type-II shock, whichever occurs first. Maintenance procedures restore the system to a pristine state with a random initial damage and the adopted maintenance technique is regarded as imperfect. The optimal preventive maintenance schedules that minimise the total average cost over time are determined analytically and computed numerically.

Keywords:

• preventive maintenance
• imperfect maintenance
• optimisation
• used system
• cumulative damage model
• reliability

Acknowledgements

The author would like to thank the referees for their insightful comments and suggestions, which greatly enhanced the clarity of the article. All of the suggestions were incorporated directly in the text.

Additional information

Funding

This research was supported by the Ministry of Science and Technology of Taiwan, ROC [grant number MOST103-2410-H-147-006].