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# Machine Repair Problem with Spares and N-Policy Vacation

Author Affiliations

• 1 School of Mathematics, Statistics and Computational Sciences Central University of Rajasthan, Kishangarh Ajmer, INDIA

Res. J. Recent Sci., Volume 1, Issue (4), Pages 72-78, April,2 (2012)

## Abstract

In this paper we have taken a machine repairable system with spares and two repairmen where “the partial server vacation” is applied. In our system, the first repairman never takes vacations and always available for serving the failed units. The second repairman goes to vacation of random length when number of failed units is less than N. At the end of vacation period, this repairman returns back if there are N or more failed units/machine accumulated in the system. Otherwise this repairman goes for another vacation. Vacation time is exponentially distributed. By using of Markov process theory, we develop the steady state probabilities equations using transition diagram and solve these equations recursively. We present derivations of some queuing and reliability measures. A cost model is developed to determine the optimum value of N while the system availability is maintained at certain level. Sensitivity analysis is also investigated. In this paper we not only analyze the queuing problems but also analyze the reliability characteristics of the system.

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