Performance analysis of machine repair system with single working vacation

Abstract

This paper studies a machine repair problem with repairman’s single working vacation in which repairman works with a lower repair rate rather than completely terminating repair during vacation period. Employing Markov process theory and matrix analytical method, various system performance measures are obtained in transient and stationary regimes. Moreover, we deduce the system reliability, the mean time to failure, the repairman’s busy period and the waiting time of failed machine by using the probabilistic properties of phase type distribution. Further, some numerical examples are provided. Finally, a cost model is developed to determine the optimum value of operating machines.

Keywords:

• machine repair system
• single working vacation
• matrix analytical method
• performance measure
• cost function

Acknowledgments

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

Disclosure statement

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

Additional information

Funding

The research was supported by the Longshan Academic Talent Research supporting program of SWUST (No. 17LZXY20), and the Doctoral Research Foundation of Southwest University of Science and Technology (No. 16zx7108, 15zx7141).