Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T00:18:31.000Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling of repairable systems

Part of: Stochastic processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
Get access Rights & Permissions [Opens in a new window]

Abstract

The reliability of many stochastic repairable systems depends on several characteristics that are time dependent. In this paper, we develop general repair models for a repairable system by using auxiliary stochastic processes which describe physical characteristics of the system and derive various properties of resulting models. We also obtain an inference procedure to assess the number of failures and expected number of failures for our proposed models by observing auxiliary processes.

Clearly, our inference procedure is different from the traditional approach, where successive times of occurrence of failures are observed.

Keywords

NON-HOMOGENEOUS POISSON PROCESSBROWNIAN MOTION, ORNSTEIN–UHLENBECK PROCESS

MSC classification

Secondary: 60G55: Point processes 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993 , pp. 926 - 938
Copyright
Copyright © Applied Probability Trust 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ammann, L. P. (1979) Simultaneous life testing in a random environment. Stoch. Proc. Appl. 9, 195–205.CrossRefGoogle Scholar
Ascher, H. and Feingold, H. (1984) Repairable Systems Reliability. Marcel Dekker, New York.Google Scholar
Barlow, R. E and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Ebrahimi, N. (1990) Ordering of repairable systems. J. Appl. Prob. 27, 193–201.CrossRefGoogle Scholar
Ebrahimi, N. and Ramalingam, T. (1991) Assessing system reliability using non-stationary models. Submitted for publication.Google Scholar
Karlin, S. and Taylor, H. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
Kijima, M. (1989) Some results for repairable systems with general repair. J. Appl. Prob. 26, 89–103.CrossRefGoogle Scholar
Marshall, A. and Olkin, I. (1979) Inequalities: Theory of Majorization and its Applications. Academic Press, New York.Google Scholar
Mitrinovic, D. S. (1970) Analytic Inequalities. Springer-Verlag, Berlin.CrossRefGoogle Scholar