Analysis of a repairable k-out-of-n:G system with repairman's multiple delayed vacations

Abstract

This paper considers a repairable k-out-of-n:G system with repairman's multiple delayed vacations where the operating times and the repair times of components are governed by exponential distributions and general distributions, respectively. After completion of repair of all broken components, the repairman remains idle for a period of time called changeover time, and then takes a vacation following an arbitrary distribution if there is no operating component breaks down during the changeover time. Applying the supplementary variable method, several reliability measures of the system including the steady-state availability, the steady-state rate of occurrence of failures and the mean time to the first failure are obtained. Meanwhile, some numerical illustrations are presented to demonstrate how the various parameters influence the behaviour of the system. Finally, a special case $(n-1)$-out-of-n:G system is discussed to validate the correctness of the theoretical results.

Keywords:

• k-out-of-n:G system
• multiple delayed vacations
• changeover time
• supplementary variable method
• reliability measures

2010 AMS Subject Classifications:

• 60K20
• 90B25

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [No.71571127, No.71171138, No.71301111].