Optimal bivariate spare ordering policy for a system with imperfect maintenance

Abstract

In this paper, we investigate an ordering-replacement modelling framework for a system deteriorating with two failure types: a repairable failure (Type-I failure) and an unrepairable failure (Type-II failure). Repairable failures are followed by minimal repair, whereas unrepairable failures are removed by a corrective replacement. A spare unit ordered regularly is associated with the system's operation time T and the number N of successive working times for preventive replacement, or ordered in emergency at any unrepairable failure for corrective replacement, whichever is first to happen. Three kinds of objectives – system availability, expected cost rate, and cost-effectiveness – are optimised to seek for the optimal spare unit ordering schedule (T*, N*), respectively. The existence and uniqueness of each optimal ordering policy are derived analytically and computed numerically.

KEYWORDS:

• Spare unit ordering
• replacement
• minimal repair
• random working time
• optimisation

Acknowledgment

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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors can confirm that the data for tables are provided with the paper and no data from the literature was used.

Additional information

Funding

This research was supported by the National Science and Technology Council of Taiwan, ROC [grant numbers NSTC 111-2410-H-147-001 and NSTC 111-2410-H-147-002].

Notes on contributors

Chin-Chih Chang

Chin-Chih Chang is a Professor of the Department of Distribution Management at Takming University of Science and Technology. He received his M.Sc. (1988) in Statistics from the National Chengchi University, and his Ph.D. (2009) in Industrial Management from the National Taiwan University of Science and Technology. His current research interests include reliability engineering, maintenance policy, and statistics.

Yen-Luan Chen

Yen-Luan Chen is an Associate Professor of the Department of Marketing Management at Takming University of Science and Technology. She received her M.Sc. (1988) in Statistics from National Chengchi University, and her Ph.D. (2009) in Business Administration from the National Taiwan University of Science and Technology. Her recent research interests include strategic management, reliability engineering, and statistics.