Abstract
This research is concerned with developing repair and training strategies for stand-by equipment which maximise the time until the equipment is unable to respond when it is needed. Equipment can only be used if it is in an operable state and the users have had sufficient recent training on it. Thus it is necessary to decide when to maintain/repair the equipment and when to use the equipment for training. Both actions mean the equipment is not readily available for use in an emergency. We develop discrete time Markov decision process formulations of this problem in order to investigate the form of the optimal policies which maximise the expected survival time until a catastrophic event when an emergency occurs and the equipment cannot respond. We also calculate the solution in a number of numerical examples.
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References
Barlow, R. E., & Proschan, F. (1965). Mathematical theory of reliability. New York: Wiley.
Çinlar, E. (1984). Markov and semi-Markov models of deterioration. In M. Abdel-Hamid, E. Çinlar, & J. Quinn (Eds.), Reliability theory and models (pp. 3–41). New York: Academic Press.
Çinlar, E., & Özekici, S. (1987). Reliability of complex devices in random environments. Probability in the Engineering and Informational Sciences, 3, 97–115.
Çinlar, E., Shaked, M., & Shanthikumar, J. G. (1989). On lifetimes influences by a common environment. Stochastic Processes and Their Applications, 33, 347–359.
Dekker, R. (1996). Applications of maintenance optimization models: a review and analysis. Reliability Engineering & Systems Safety, 51(3), 229–240.
Derman, C. (1963). On optimal replacement rules when changes of state are Markovian. In R. Bellmann (Ed.), Mathematical optimization techniques (pp. 201–212). Berkeley: University of California Press.
Derman, C. (1970). Finite state Markovian decision processes. Orlando: Academic Press.
Derman, C., & Sacks, J. (1960). Replacement of periodically inspected equipment (an optimal stopping rule). Naval Research Logistics Quarterly, 7, 597–607.
Derman, C., Lieberman, G. J., & Ross, S. M. (1984). On the use of replacements to extend system lifetimes. Operations Research, 32, 616–627.
Katehakis, M. N., & Derman, C. (1984). Optimal repair allocation in a series system. Mathematics of Operations Research, 9, 615–623.
Kiessler, P. C., Klutke, G.-A., & Yang, Y. (2002). Availability of periodically inspected systems subject to Markovian degradation. Journal of Applied Probability, 39, 700–711.
Kim, Y. H., & Thomas, L. C. (2004). To train or to repair? (Discussion Paper in Management M04-17). University of Southampton.
Kim, Y. H., & Thomas, L. C. (2006). Repair strategies in an uncertain environment; Markov decision approach. Journal of the Operational Research Society, 57, 957–964.
Kim, Y. H., & Thomas, L. C. (2012, to appear). Repair strategies in an uncertain environment: stochastic game approach. In T. Dohi & T. Nakagawa (Eds.), Stochastic reliability and maintenance modelling. Berlin: Springer.
Klutke, G.-A., Wortman, M., & Ayhan, H. (1996). The availability of inspected systems subject to random deterioration. Probability in the Engineering and Informational Sciences, 10, 109–118.
Lam, Y. (1995). An optimal inspection-repair-replacement policy for stand-by systems. Journal of Applied Probability, 32, 212–223.
Lam, Y. (2003). An inspection-repair-replacement model for a deteriorating system with unobservable states. Journal of Applied Probability, 40, 1031–1042.
Lefèvre, C., & Milhaud, X. (1990). On the association of the lifelengths of components subjected to a stochastic environment. Advances in Applied Probability, 22, 961–964.
McCall, J. J. (1965). Maintenance policies for stochastically failing equipment: a survey. Management Science, 11(5), 493–524.
Monahan, G. E. (1982). A survey of partially observable Markov decision processes: theory, models and algorithms. Management Science, 28, 1–16.
Özekici, S. (1995). Optimal maintenance policies in random environments. European Journal of Operational Research, 82, 283–294.
Özekici, S. (1996). Complex systems in random environments. In S. Özekici (Ed.), Reliability and maintenance of complex systems (pp. 137–157). New York: Springer.
Pierskalla, W. P., & Voelker, J. A. (1976). A survey of maintenance models: the control and surveillance of deteriorating systems. Naval Research Logistics Quarterly, 23, 353–388.
Putterman, M. L. (1994). Markov decision processes: discrete stochastic dynamic programming. New York: Wiley.
Sarkar, A., Panja, S. C., & Sarka, B. (2011). Survey of maintenance policies for the last 50 years. International Journal of Software Engineering and Its Applications, 2, 130–148.
Shaked, M., & Shanthikumar, J. G. (1989). Some replacement policies in a random environment. Probability in the Engineering and Informational Sciences, 3, 117–134.
Sherif, Y. S., & Smith, M. L. (1981). Optimal maintenance models for systems subject to failure—a review. Naval Research Logistics Quarterly, 28(1), 47–74.
Thomas, L. C. (1986). A survey of maintenance and replacement models for maintainability and reliability of multi-item systems. Reliability Engineering & System Safety, 16(4), 297–309.
Thomas, L. C., Jacobs, P. A., & Gaver, D. P. (1987). Optimal inspection policies for stand-by systems. Communications in Statistics. Stochastic Models, 3(2), 259–273.
Valdez-Flores, C., & Feldman, R. M. (1989). A survey of preventative maintenance models for stochastically deteriorating single-unit systems. Naval Research Logistics, 36, 419–446.
Wang, H. (2002). A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 139, 469–489.
Wortman, M. A., & Klutke, G.-A. (1994). On maintained systems operating in a random environment. Journal of Applied Probability, 31, 589–594.
Yang, Y., & Klutke, G.-A. (2000a). Improved inspection schemes for deteriorating equipment. Probability in the Engineering and Informational Sciences, 14, 445–460.
Yang, Y., & Klutke, G.-A. (2000b). Lifetime characteristics and inspection schemes for Lévy degradation processes. IEEE Transactions on Reliability, 49, 337–382.
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Kim, YH., Thomas, L.C. Training and repair policies for stand-by systems. Ann Oper Res 208, 469–487 (2013). https://doi.org/10.1007/s10479-012-1185-3
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DOI: https://doi.org/10.1007/s10479-012-1185-3