# Performance analysis and optimization of a machine repair problem with warm spares and two heterogeneous repairmen

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## Abstract

In this paper, we study a machine repair problem with warm spares and two heterogeneous repairmen from the view points of both queueing and reliability. In this system, the first repairman is always available for serving the failed units, while the second repairman leaves for a vacation of random length when the number of failed units is less than *N*. We obtain expressions for the steady-state probabilities of the system by solving the steady-state probability equations iteratively. Then, we obtain some performance measures for the system. We also obtain some performance measures of reliability for the system such as the steady-state availability, the steady-state failure frequency and the mean time between the system failures. Moreover, we present derivations of the mean time taken until the first failure of the system. A cost model is developed to determine the optimum value *N* while the system availability is maintained at a certain level. A sensitivity analysis is also performed.

## Keywords

Repairable system Warm spare Vacation Availability Failure frequency Performance optimization## Notes

### Acknowledgements

The authors wish to thank the anonymous referee’s comments leading to a much improved presentation. This work was supported in part by the National Natural Science Foundation of China (No. 70671088), and was supported in part by GRANT-IN-AID FOR SCIENTIFIC RESEARCH (No. 21500086) and MEXT, Japan.

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