Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T18:01:48.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic Intensity for Minimal Repairs in Heterogeneous Populations

Part of: Operations research and management science 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: jhcha@ewha.ac.kr
∗∗ Postal address: Department of Mathematical Statistics, University of the Free State, 339 Bloemfontein 9300, South Africa. Email address: finkelm@ufs.ac.za
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 this note we revisit the discussion on minimal repair in heterogeneous populations in Finkelstein (2004). We consider the corresponding stochastic intensities (intensity processes) for items in heterogeneous populations given available information on their operational history, i.e. the failure (repair) times and the time since the last failure (repair). Based on the improved definitions, the setup of Finkelstein (2004) is modified and the main results are corrected in accordance with the updating procedure for the conditional frailty distribution.

Keywords

Heterogeneous populationminimal repairfrailtyintensity processupdating procedure

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 868 - 876
Copyright
Copyright © Applied Probability Trust 2011 

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.Google 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. (2004). Minimal repair in heterogeneous populations. J. Appl. Prob. 41, 281–286.Google Scholar
Finkelstein, M. (2008). Failure Rate Modelling for Reliability and Risk. Springer, London.Google Scholar
Natvig, B. (1990). On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. J. Appl. Prob. 27, 365–375.Google Scholar