Optimal preventive replacement policies for a system with discrete scheduled times

Abstract

In reality, most operating systems are repaired or replaced when they have failed. For such systems, it would be reliable to maintain them in a control-limit consideration of repairs or operations. This article addresses a system scheduling policy for preventive replacement with discrete control limits of minimal repair and random work. An operating system which works at random times for multiple jobs (N tandem jobs or N parallel jobs) is considered. The system subjects to two failure mechanisms and maintained imperfectly: type-I (minor) failure rectified by a minimal repair and type-II (catastrophic) failure removed by a corrective replacement. To control the deterioration process, the preventive replacement is planned to undergo before catastrophic failure at number n of minimal repairs or the completion of N multiple jobs. The objective is to determine the optimal discrete scheduling replacement parameters (n* or N*) that minimizes the mean cost rate function in a finite time horizon. Model analysis relating to the existence and uniqueness of optimal solutions is provided. A Numerical example is presented for illustrative purposes.

Keywords:

• Replacement
• random work
• optimization
• imperfect maintenance
• minimal repair
• reliability

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.

Additional information

Funding

This research was supported by the Ministry of Science and Technology of Taiwan, ROC, under Grant No. MOST109-2410-H-147-002.