Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-20T08:06:06.524Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimal repair in heterogeneous populations

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

M. S. Finkelstein
M. S. Finkelstein*
Affiliation:
University of the Free State, Bloemfontein
*
∗ Postal address: Department of Mathematical Statistics, University of the Free State, PO Box 339, 9300 Bloemfontein, Republic of South Africa. Email address: finkelm@sci.uovs.ac.za
Get access Rights & Permissions [Opens in a new window]

Abstract

The notion of minimal repair is generalized to the case when the lifetime distribution function is a continuous or a discrete mixture of distributions (heterogeneous population). The statistical (black box) minimal repair and the minimal repair based on information just before the failure of an object are considered. The corresponding stochastic intensities are defined and analyzed for the point processes generated by both types of minimal repair. Some generalizations are discussed. Several simple examples are considered.

Keywords

Minimal repairstatistical minimal repairinformation-based minimal repairstochastic intensitynonhomogeneous Poisson process

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 281 - 286
Copyright
Copyright © Applied Probability Trust 2004 

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

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., and Jensen, U. (1999). Stochastic Models in Reliability (Appl. Math 41). Springer, New York.Google Scholar
Aven, T., and Jensen, U. (2000). A general minimal repair model. J. Appl. Prob. 37, 187–197.CrossRefGoogle Scholar
Bergman, B. (1985). On reliability theory and its applications. Scand. J. Statist. 12, 1–41.Google Scholar
Boland, P. J., and El-Neweihi, E. (1998). Statistical and information based (physical) minimal repair for k out of n systems. J. Appl. Prob. 35, 731–740.Google Scholar
Finkelstein, M. S. (1992). Some notes on two types of minimal repair. Adv. Appl. Prob. 24, 226–228.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. S., and Esaulova, V. (2001). Modeling a failure rate for a mixture of distribution functions. Prob. Eng. Inf. Sci. 15, 383–400.CrossRefGoogle Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. J. Appl. Prob. 26, 89–102.Google Scholar
Natvig, B. (1990). On information-based minimal repair and the reduction in remaining system lifetime due to a failure of a specific module. J. Appl. Prob. 27, 365–375.CrossRefGoogle Scholar