Optimization of continuous and discrete scheduled times for a cumulative damage system with age-dependent maintenance

Abstract

This paper presents a preventive replacement problem when a system is operating successive works with random times and suffering stochastic shocks. The works cause random amount additive damage to the system, and the system fails whenever the cumulative damage reaches a failure level threshold. As an external shock occurs, the system experiences one of the two types of shocks with age-dependent maintenance mechanism: type-I (minor) shock is rectified by a minimal repair, or type-II (catastrophic) shock causes the system to fail. To control the deterioration process, preventive replacement is scheduled to replace the system at a continuous age T or at a discrete number N of working cycles, whichever occurs first, and corrective replacement is performed immediately whenever the system fails due to either shock or damage. The optimal preventive replacement schedule that minimizes the expected cost rate is discussed analytically and computed numerically. The proposed model provides a general framework for analyzing maintenance policies and extends several existing results.

Keywords:

• Preventive replacement
• working time
• cumulative damage model
• minimal repair
• imperfect maintenance
• optimization

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60K05
• Secondary 90B25
• 62N05

Acknowledgments

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. This research was supported by the Ministry of Science and Technology of Taiwan, ROC, under Grant No. MOST 105-2410-H-147-006 and MOST 105-2410-H-147-007.