Reliability analysis of a k-out-of-n:G system with general repair times and replaceable repair equipment

Abstract

This paper studies a k-out-of-n:G repairable system with one replaceable repair equipment, where the lifetimes and repair times of components follow exponential distributions and arbitrary distributions, respectively. When one component breaks down, it is repaired by the repair equipment. Further, the repair equipment may fail during the repair period and then be replaced by a new one. The replacement time of the repair equipment is a generally distributed random variable. Employing the semi-Markov process theory and the Laplace (Laplace–Stieltjes) transform, the mean time to the first failure, the steady-state system availability, the rate of occurrence of failures of the system, the probability that the repair equipment is being replaced and the rate of occurrence of failures of the repair equipment are derived. Meanwhile, some numerical illustrations are reported to demonstrate how the various parameters of the model influence the behaviour of the system. Finally, a special case -out-of-n:G repairable system is discussed to validate the correctness of the theoretical results.

Keywords:

• k-out-of-n:G system
• replaceable repair equipment
• semi-Markov process
• reliability measures

Acknowledgements

The authors acknowledge anonymous reviewers for their constructive comments which are very helpful in improving the presentation of this paper.

Notes

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under [grant number 71571127], [grant number 71301111]; the Doctoral Research Foundation of Southwest University of Science and Technology under [grant number 15zx7141].