6th International Young Scientist Congress (IYSC-2020) will be Postponed to 8th and 9th May 2021 Due to COVID-19. 10th International Science Congress (ISC-2020).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

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)


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.


  1. Hsies Y.C. and Wang K.H., Reliability of a repairable system with spares and removable repairmen. Microelectronics and Reliability 35, 197-208 (1995)
  2. Jain M., Rakhee and Maheshwari S., N-policy for a machine repair system with spares and reneging, Applied Mathematical Modelling, 28, 513-531(2004)
  3. Wang K.H. and Sivazlian B.D., Reliability of a system with warm standby and repairmen, Microelectronics and Reliability, 29, 849-860 (1989)
  4. Wang K.H. and Ke J., Probabilistic analysis of a repairable system with warm standby plus balking and reneging, Applied Mathematical Modelling, 27, 327-336 (2003)
  5. Gupta S.M., Machine interference problem with warm spares, server vacation and exhoutive service, Performance Evaluation, 29, 195-211(1997)
  6. Jain M. and Singh M., Bilevel control of degraded machining system with warm standby stup and vacation, Applied Mathematical Modelling, 28, 1015-1026 (2004)
  7. Kee J.C. and Wang K.H., Vacation policies for machine repair problem with two type spares, Appld. Math. Modeling, 31(5), 880-894 (2007)
  8. Jain M. and Upadhyaya S., Threshold N-policy for degraded machining system with multiple types of spares and multiple vacations, Quality Technology and Quantitative Management 6(2), 185-203 (2009)
  9. Zhong Yu, Mingwu Liu and Yongkai Ma, Steady-State Queue Length Analysis of a Batch Arrival Queue under N-Policy with Single Vacation and Setput Times, Intelligent Information Management, 2(6), June (2010)
  10. Zhang Z.G. and Tian N., Analysis of Queuing system with synchronous vacations of partial servers, Perfrmance Evaluation, 52, 269-282 (2003)
  11. Yue Dequan, Yue Wuyi and Qi Hongjuan, Analysis of a Machine Repair System with Warm Spares and N- Policy Vacations, ISORA,190-198 (2008)