OPTIMAL REPLACEMENT POLICIES BASED ON NUMBER OF DOWN TIMES FOR COLD STANDBY SYSTEM WHEN THE LIFETIME AND THE REPAIR TIME ARE DEPENDENT
Keywords:
Cold standby system, Freund's bivariate exponential Model, Number of down times, Priority in use, Renewal reward theorem, Repair rate, Replacement policyAbstract
The purpose of this article is to present optimal replacement policies for a cold standby system consisting of two components and one repairman. By using the bivariate exponential model of Freund (1961) for the life time of one component and the repair time of another component, we developed methods for obtaining optimal number of down time in such a way that the long run expected reward per unit time is maximized. The results are illustrated with the help of numerical example and simulation study.
Downloads
References
Barlow, R.E. and Hunter, L.C. (1960). Optimal preventive maintenance
policies, Journal of Operation Research, 8, p. 90-100.
Block, H.W., Borges, W.S. and Savits, T.H. (1985). Age dependent minimal
repair, Journal of Applied Probability, 22, p. 370-385.
Brown, M. and Proschan, F. (1983). Imperfect repair. Journal of Applied
Probability, 20, p. 851-859.
Freund, J.E. (1961). A bivariate extension of the exponential distribution,
Journal of the American Statistical Association, 56, p. 971-77.
Hanagal, D. D. and Kanade, R. A. (2010 a). Optimal replacement policy based
on number of down times, Economic Quality Control, 25(1), p. 3-12.
Hanagal, D. D. and Kanade, R. A. (2010 b). Optimal replacement policy based
on number of down times with priority in use, Economic Quality Control,
(2), p. 243-51.
Kijima, M. (1989). Some result for repairable system with general repair,
Journal of Applied Probability, 26, p. 89-102.
Lam, Y.A. (1988). Note on optimal replacement problem, Advances in
Applied Probability, 20, p. 479-482.
Lam, Y. (1997). A maintenance for model for two unit redundant system,
Microelectronics Reliabilty, 37(3), p. 497-504.
Nakagawa, T. and Osaki, S. (1975). Stochastic behaviour of a two unit priority
standby redundant system with repair, Microelectronics Reliabilty, 14(3), p.
-313.
Rattihalli, S.R. and Hanagal, D.D. (2009). A replacement policy based on
down time for a cold standby system with dependent lifetime and repair time,
Economic Quality Control, 24(2), p. 207-12.
Ross, S.M. (1996). Stochastic Process, Second edition,Wiley, New York.
Zhang, Y.L. and Wang, G.J. (2006). A bivariate repair replacement model
using geometric processes for cold standby repairable system, Engineering
Optimization, 38, p. 609-619.
Zhang, Y.L. and Wang, G.J. (2007). A deteriorating cold standby system with
priority in system, European Journal of Operational Research, 183, p. 278-295.
Zhang, Y.L., Yam,R.C.M. and Zou, M.J. (2007). A bivariate replacement
policy for multistate repairable system, Reliability Engineering and System
Safety, 92, p. 535-542.