Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T13:10:44.288Z Has data issue: false hasContentIssue false
  • English
  • Français

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.; [email protected]
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.
Get access

Abstract

This paper studies the machine repairproblem consisting of M operating machines with S sparemachines, and R servers (repairmen) who leave for a vacation ofrandom length when there are no failed machines queuing up forrepair in the repair facility. At the end of the vacation theservers return to the repair facility and operate one of threevacation policies: single vacation, multiple vacation, and hybridsingle/multiple vacation. The Markov process and thematrix-geometric approach are used to develop the steady-stateprobabilities of the number of failed machines in the system aswell as the performance measures. A cost model is developed toobtain the optimal values of the number of spares and the numberof servers while maintaining a minimum specified level of systemavailability. Some numerical experiments are performed and someconclusions 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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.