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A general minimal repair model

Part of:Special processesOperations research and management science

Published online by Cambridge University Press:  14 July 2016

Terje Aven and
Uwe Jensen
Terje Aven*
Affiliation:
Stavanger University College
Uwe Jensen*
Affiliation:
University of Ulm
*
∗ Postal address: Stavanger University College, Ullandhaug, 4091, Stavanger, Norway. Email address: terje.aven@tn.his.no
∗∗ Postal address: Department of Stochastics, University of Ulm, 89069 Ulm, Germany
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Abstract

Minimal repairs have been given considerable attention in the reliability literature. Instead of replacing a failed system by a new one, such a minimal repair restores the system to the state it had just before failure. But the state just before failure depends on the information which is available about the system. Different information levels are possible. This paper gives a general definition characterizing point processes which describe time points of minimal repairs with respect to a certain information level. Some examples demonstrate the wide range of applications.

Keywords

Reliabilityminimal repair processshock modelsdifferent information levels

MSC classification

Primary:60K10: Applications (reliability, demand theory, etc.)
Secondary:90B25: Reliability, availability, maintenance, inspection

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000, pp. 187 - 197
Copyright
Copyright © 2000 by The Applied Probability Trust 

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References

Arjas, E. (1989). Survival models and martingale dynamics. Scand. J. Statist. 16, 177–225.Google Scholar
Arjas, E., and Norros, I. (1989). Change of life distribution via hazard transformation: an inequality with application to minimal repair. Math. Operat. Res. 14, 355–361.Google Scholar
Aven, T. (1996). Condition based replacement times—a counting process approach. Reliability Engg. and Syst. Safety [spec. issue, Maintenance and Reliability] 51, 275–292.CrossRefGoogle Scholar
Aven, T. (1987). A counting process approach to replacement models. Optimization 18, 285–296.CrossRefGoogle Scholar
Aven, T. (1983). Optimal replacement under a minimal repair strategy—a general failure model. Adv. Appl. Prob. 15, 198–211.Google Scholar
Aven, T., and Jensen, U. (1999). Stochastic Models in Reliability. Springer, New York.Google Scholar
Barlow, R., and Hunter, L. (1960). Optimum preventive maintenance policies. Operat. Res. 8, 90–100.Google Scholar
Beichelt, F. (1993). A unifying treatment of replacement policies with minimal repair. Nav. Res. Log. Quart. 40, 51–67.Google Scholar
Bergman, B. (1985). On reliability theory and its applications. Scand. J. Statist. 12, 1–41.Google Scholar
Block, H., Borges, W., and Savits, T. (1985). Age-dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
Brémaud, P. (1981). Point Processes and Queues. Martingale Dynamics. Springer, New York.Google Scholar
Finkelstein, M. S. (1992). Some notes on two types of minimal repair. Adv. Appl. Prob. 24, 226–228.Google Scholar
Natvig, B. (1990). On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. J. Appl. Prob. 27, 365–375.Google Scholar
Phelps, R. (1983). Optimal policy for minimal repair. J. Operat. Res. 34, 425–427.CrossRefGoogle Scholar
Shaked, M., and Shanthikumar, G. (1986). Multivariate imperfect repair. Operat. Res. 34, 437–448.Google Scholar
Sheu, S., and Griffith, W. S. (1992). Multivariate imperfect repair. J. Appl. Prob. 29, 947–956.CrossRefGoogle Scholar
Stadje, W., and Zuckerman, D. (1991). Optimal maintenance strategies for repairable systems with general degree of repair. J. Appl. Prob. 28, 384–396.Google Scholar