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Imperfect maintenance in a generalized competing risks framework

Part of: Operations research and management science Stochastic processes Survival analysis and censored data Special processes

Published online by Cambridge University Press:  14 July 2016

Laurent Doyen  and
Olivier Gaudoin
Laurent Doyen*
Affiliation:
Université Pierre Mendès France Grenoble 2
Olivier Gaudoin*
Affiliation:
Institut National Polytechnique de Grenoble
*
∗ Postal address: Laboratoire LABSAD, Université Pierre Mendès France Grenoble 2, BP 47-38 040 Grenoble Cedex 9, France. Email address: laurent.doyen@iut2.upmf-grenoble.fr
∗∗ Postal address: Laboratoire LMC, Institut National Polytechnique de Grenoble, BP 53-38 041 Grenoble Cedex 9, France. Email address: olivier.gaudoin@imag.fr
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Abstract

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In this paper we present a general framework for the modelling of the process of corrective and condition-based preventive maintenance actions for complex repairable systems. A new class of models is proposed, the generalized virtual age models. On the one hand, these models generalize Kijima's virtual age models to the case where both preventive and corrective maintenances are present. On the other hand, they generalize the usual competing risks models to imperfect maintenance actions which do not renew the system. A generalized virtual age model is defined by both a sequence of effective ages which characterizes the effects of both types of maintenance according to a classical virtual age model, and a usual competing risks model which characterizes the dependency between the two types of maintenance. Several particular cases of the general model are derived.

Keywords

Point processreliabilityimperfect maintenancecompeting risksvirtual age

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.) 60G55: Point processes
Secondary: 90B25: Reliability, availability, maintenance, inspection 62N05: Reliability and life testing

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 825 - 839
Copyright
© Applied Probability Trust 2006 

References

Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.CrossRefGoogle Scholar
Bedford, T. and Lindqvist, B. H. (2004). The identifiable problem for repairable systems subject to competing risks. Adv. Appl. Prob. 36, 774–790.CrossRefGoogle Scholar
Brown, J. F., Mahoney, J. F. and Sivalzian, B. D. (1998). Hysteresis repair in discounted replacement problems. IIE Trans. 15, 156–165.CrossRefGoogle Scholar
Brown, M. and Proschan, F. (1983). Imperfect repair. J. Appl. Prob. 20, 851–859.CrossRefGoogle Scholar
Bunea, C. and Bedford, T. (2002). The effect of model uncertainty on maintenance optimization. IEEE Trans. Reliab. 51, 486–493.CrossRefGoogle Scholar
Cooke, R. and Bedford, T. (2002). Reliability databases in perspective. IEEE Trans. Reliab. 51, 294–310.CrossRefGoogle Scholar
Cooke, R. M. (1993). The total time test statistic and age-dependent censoring. Statist. Prob. Lett. 18, 307–312.CrossRefGoogle Scholar
Crowder, M. J. (2001). Classical Competing Risks. CRC, Boca Raton, FL.CrossRefGoogle Scholar
Doyen, L. (2004). Modélisation et évaluation de l'efficacité de la maintenance des systèmes réparables. , Institut National Polytechnique de Grenoble. Available at http://tel.ccsd.cnrs.fr/documents/archives0/00/00/77/22/index.html.Google Scholar
Doyen, L. and Gaudoin, G. (2004). Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliab. Eng. System Safety 84, 45–56.CrossRefGoogle Scholar
Jack, N. (1998). Age-reduction models for imperfect maintenance. IMA J. Math. Appl. Business Industry 9, 347–354.Google Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. J. Appl. Prob. 26, 89–102.CrossRefGoogle Scholar
Kijima, M., Morimura, H. and Suzuki, Y. (1988). Periodical replacement problem without assuming minimal repair. Operat. Res. 37, 194–203.CrossRefGoogle Scholar
Langseth, H. and Lindqvist, B. H. (2003). A maintenance model for components exposed to several failure mechanisms and imperfect repair. In Mathematical and Statistical Methods in Reliability, eds Doksum, K. and Lindqvist, B. H., World Scientific, River Edge, NJ, pp. 415–430.CrossRefGoogle Scholar
Langseth, H. and Lindqvist, B. H. (2006). Competing risks for repairable systems: a data study. J. Statist. Planning Infer. 136, 1687–1700.CrossRefGoogle Scholar
Lindqvist, B. H., Støve, B. and Langseth, H. (2006). Modelling of dependence between critical failure and preventive maintenance: the repair alert model. J. Statist. Planning Infer. 136, 1701–1717.CrossRefGoogle Scholar
Pham, H. and Wang, H. (1996). Imperfect maintenance. Europ. J. Operat. Res. 94, 425–438.CrossRefGoogle Scholar
Tsiatis, A. (1975). A nonidentifiability aspect of the problem of competing risks. Proc. Nat. Acad. Sci. USA 72, 20–22.CrossRefGoogle ScholarPubMed