Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T00:05:01.990Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Terminating Shock Process with Independent Wear Increments

Part of: Applications Special processes

Published online by Cambridge University Press:  14 July 2016

Ji Hwan Cha  and
Maxim Finkelstein
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Maxim Finkelstein*
Affiliation:
University of the Free State and Max Planck Institute for Demographic Research
*
∗Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: [email protected]
∗∗Postal address: Department of Mathematical Statistics, University of the Free State, PO Box 339, Bloemfontein 9300, Republic of South Africa. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. In this paper we combine an extreme shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a generalization of the well-known Brown–Proschan model that describes repair actions for repairable systems. For a system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate function. Some meaningful interpretations and examples are discussed.

Keywords

Brown–Proschan modelextreme shock modelcumulative shock modelvirtual agewear

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 62P30: Applications in engineering and industry
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 353 - 362
Copyright
Copyright © Applied Probability Trust 2009 

References

Beichelt, F. E. and Fischer, K. (1980). General failure model applied to preventive maintenance policies. IEEE Trans. Reliab. 29, 39–41.Google Scholar
Block, H. W., Borges, W. S. and Savits, T. H. (1985). Age-dependent minimal repair. J. Appl. Prob. 22, 370–386.CrossRefGoogle Scholar
Brown, M. and Proschan, F. (1983). Imperfect repair. J. Appl. Prob. 20, 851–859.Google Scholar
Cha, J. H. (2001). Burn-in procedures for a generalized model. J. Appl. Prob. 38, 542–553.CrossRefGoogle Scholar
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Cox, D. R. and Isham, V. (1980). Point Processes. Chapman and Hall, New York.Google Scholar
Finkelstein, M. S. (1999). Wearing-out components in variable environment. Reliab. Eng. System Safety 66, 235–242.Google Scholar
Finkelstein, M. S. (2007). On some ageing properties of general repair processes. J. Appl. Prob. 44, 506–513.CrossRefGoogle Scholar
Finkelstein, M. S. (2008). Failure Rate Modelling for Risk and Reliability. Springer, London.Google Scholar
Gut, A. and Husler, J. (2005). Realistic variation of shock models. Statist. Prob. Lett. 74, 187–204.Google Scholar
Nachlas, J. A. (2005). Reliability Engineering. CRC Press, Boca Raton, FL.Google Scholar
Sumita, U. and Shanthikumar, J. G. (1985). A class of correlated cumulative shocks models. Adv. Appl. Prob. 17, 347–366.Google Scholar