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On Some Ageing Properties of General Repair Processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Maxim Finkelstein
Maxim Finkelstein*
Affiliation:
University of the Free State and Max Planck Institute for Demographic Research
*
∗ Postal address: Department of Mathematical Statistics, University of the Free State, PO Box 339, 9300 Bloemfontein, South Africa. Email address: finkelm.sci@ufs.ac.za
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Abstract

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We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.

Keywords

General renewal processvirtual agedegradationageing distributionsfailure ratemean remaining lifetimerepairable systems

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 506 - 513
Copyright
Copyright © Applied Probability Trust 2007 

References

Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability (Appl. Math. (New York) 41). Springer, New York.Google Scholar
Baxter, L. A., Kijima, M. and Tortorella, M. (1996). A point process model for the reliability of the maintained system subject to general repair. Stoch. Models 12, 37–65.Google Scholar
Finkelstein, M. S. (1988). Engineering systems with imperfect repair. Nadejnost i Control Kachestva 8, 7–12 (in Russian).Google Scholar
Finkelstein, M. S. (1992). A restoration process with dependent cycles. Automatic Remote Control 53, 115–1120.Google Scholar
Finkelstein, M. S. (2000). Modeling a process of non-ideal repair. In Recent Advances in Reliability Theory, eds Limnios, N. and Nikulin, M., Birkhäuser, Boston, MA, pp. 41–53.Google Scholar
Finkelstein, M. and Esaulova, V. (2006). Asymptotic behavior of a general class of mixture failure rates. Adv. Appl. Prob. 38, 244–262.Google Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. J. Appl. Prob. 26, 89–102.CrossRefGoogle Scholar
Last, G. and Szekli, R. (1998). Asymptotic and monotonicity properties of some repairable systems. Adv. Appl. Prob. 30, 1089–1110.Google 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
Thatcher, A. R. (1999). The long-term pattern of adult mortality and the highest attained age. J. R. Statist. Soc. A 162, 5–43.Google Scholar
Yashin, A., Iachine, I. A. and Begun, A. S. (2000). Mortality modeling: a review. Math. Population Studies 8, 305–332.Google Scholar