Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

Abstract

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).

Keywords:

• geometric process
• minimal repair
• replacement
• average cost rate
• cold standby system

Acknowledgements

The authors would like to thank the editor and the reviewers for their valuable comments and suggestions, which have considerably improved the presentation of the paper.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China [grant number 11271067], [grant number 61174136]; the Natural Science Foundation of Jiangsu Province of China [grant number BK2011598].

Notes on contributors

Guan Jun Wang

Guan Jun Wang is an associate professor at the Department of Mathematics, Southeast University. He received his MS degree from Lanzhou University in 1999, and the PhD degree from Southeast University in 2009, both in mathematics. His research interests are in applied probability, maintenance theory and stochastic operations research. He has published some articles in International Journal of Systems Science, IEEE Transactions on Reliability, Engineering Optimization, Computers and Mathematics with applications, European Journal of Operations Research and others.

Yuan Lin Zhang

Yuan Lin Zhang is a professor at the Department of Mathematics, Southeast University. His research interests include applied probability, stochastic operations research and insurance mathematics and risk theory. He has published five books and more than 80 articles in Applied Mathematics and Computation, Applied Mathematical Modelling, Computers and Mathematics with Applications, Computers and Operations Research, European Journal of Operational Research, Engineering Optimization, IEEE Transactions on Reliability, International Journal of Systems Science, Journal of Applied Probability, Journal of Engineering Manufacture, Journal of the Operational Research Society, Microelectronics and Reliability, Naval Research Logistics, Reliability Engineering and System Safety and others. Professor Zhang is a fellow of Royal Statistical Society of UK, and a member of Institute of Mathematical Statistics of USA.