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Machine Repair Problem in Production Systems with Spares and Server Vacations

Published online by Cambridge University Press:  28 January 2009

Jau-Chuan Ke ,
Ssu-Lang Lee  and
Cheng-Hwai Liou
Jau-Chuan Ke
Affiliation:
Department of Applied Statistics, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan, R.O.C.; jauchuan@ntit.edu.tw
Ssu-Lang Lee
Affiliation:
Department of Accounting, National Taichung Institute of Technology, Taichung 404, Taiwan, R.O.C.
Cheng-Hwai Liou
Affiliation:
Department of Accounting, National Taichung Institute of Technology, Taichung 404, Taiwan, R.O.C.
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Abstract

This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrix-geometric approach are used to develop the steady-state probabilities of the number of failed machines in the system as well as the performance measures. A cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability. Some numerical experiments are performed and some conclusions are drawn.

Keywords

Hybrid multiple/single vacationmachine repair problemmatrix-geometric approachmultiple vacationssingle vacation.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 1 , January 2009 , pp. 35 - 54
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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References

W. Feller, An introduction to probability theory and its applications, Vol. I. John Wiley and Sons, New York (1967).
Toft, F.J. and Boothroyd, H., A queueing model for spare coal faces. Oper. Res. Quart. 10 (1959) 245–251. CrossRef
B.D. Sivazlian and K.-H. Wang, Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectron. Reliab. 29 (1989) 25–35.
Wang, K.-H., Cost analysis of the M/M/R machine repair problem with mixed standby spares. Microelectron. Reliab. 33 (1993) 1293–1301. CrossRef
K.-H. Wang and H.-C. Lee, Cost analysis of the cold-standby M/M/R machine repair problem with multiple modes of failure. Microelectron. Reliab. 38. (1998) 435–441.
Jain, M., Rakhee and S. Maheshwari, N-policy for a machine repair system with spares and reneging. Appl. Math. Model. 28 (2004) 513–531. CrossRef
Ashcroft, H., The productivity of several machines under the care of one operator. J. R. Stat. Soc. B 12 (1950) 145–151.
Elsayed, E.A., An optimum repair policy for the machine interference problem. J. Oper. Res. Soc. 32 (1981) 793–801. CrossRef
Hilliard, J.E., An approach to cost analysis of maintenance float systems. IIE Trans. 8 (1976) 128–133.
Gross, D., Kahn, H.D. and Marsh, J.D., Queueing models for spares provisioning. Nav. Res. Logist. Quart. 24 (1977) 521–536. CrossRef
Gross, D., Miller, D.R. and Soland, R.M., A closed queueing network model for multi-echelon repairable item provisioning. IIE Trans. 15 (1983) 344–352. CrossRef
Wang, K.H., Ke, J.B. and Profit, J.C. Ke analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Comput. Oper. Res. 34 (2007) 835–847. CrossRef
Doshi, B.T., Queueing system with vacations-a survey. Queueing Syst. 1 (1986) 29–66. CrossRef
H. Takagi, Queueing analysis: A foundation of performance evaluation, Vol. I. Vacation and priority systems, Part I. North-Holland, Amsterdam (1991).
Gupta, S.M., Machine interference problem with warm spares, server vacations and exhaustive service. Perform. Eval. 29 (1997) 195–211. CrossRef
Jain, M., Rakhee and M. Singh, Bilevel control of degraded machining system with warm standbys, setup and vacation. Appl. Math. Model 28 (2004) 1015–1026. CrossRef
Vacation, J.C. Ke policies for machine interference problem with an un-reliable server and state-dependent service rate. J. Chinese Institute Industrial Engineers 23 (2006) 100–114.
Ibe, O.C. and Trivedi, K.S., Stochastic Petri net analysis of finite population vacation queueing systems. Queueing Syst. 8 (1991) 111–128. CrossRef
Chelst, K., Tilles, A.Z. and Pipis, J.S., A coal unloader: a finite queueing system with breakdowns. Interfaces 11 (1981) 12–24. CrossRef
D. Gross and C.M. Harris, Fundamentals of queueing theory. 3rd ed., John Wiley and Sons, New York (1998).
M.F. Neuts, Matrix geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore (1981).
Benson, F. and Cox, D.R., The productivity of machines requiring attention at random interval. J. R. Stat. Soc. B 13 (1951) 65–82.