Hostname: page-component-7f64f4797f-zzvtc Total loading time: 0 Render date: 2025-11-03T06:35:06.327Z Has data issue: false hasContentIssue false
  • English
  • Français

On information-based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module

Published online by Cambridge University Press:  14 July 2016

Bent Natvig
Bent Natvig*
Affiliation:
University of Oslo
*
∗ Postal address: Institute of Mathematics, University of Oslo, P.O. Box 1053, Blindem, 0316 Oslo 3, Norway.
Get access Rights & Permissions [Opens in a new window]

Abstract

The first part of this paper is inspired by a somewhat surprising result in Arjas and Norros (1989). Here we give some results comparing remaining system lifetime just after a ‘black box' minimal repair of a system and after a natural minimal repair based on information on the component level. In the second part we consider the reduction in remaining system lifetime due to the failure of a specific module and explore the relation to the reduction in remaining system lifetime due to the failure of a component inside the module. This former reduction also equals the increase in remaining system lifetime due to a minimal repair of the module at its time of failure. The expected value of this reduction/increase is proportional to the so-called Natvig measure of the importance of the module.

Keywords

INFORMATIONSTOCHASTIC COMPARISONIMPORTANCE OF MODULESNATVIG MEASURE

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 365 - 375
Copyright
Copyright © Applied Probability Trust 1990 

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.)

Article purchase

Temporarily unavailable

References

Arjas, E. (1989) Survival models and martingale dynamics. Rejoinder to a discussion contribution by Bent Natvig. Scand. J. Statist. 16, 224–225.Google Scholar
Arjas, E. and Norros, I. (1987) A martingale approach to reliability theory: on the role of filtration in the model specification. First Finnish-Soviet Seminar on Probability and Mathematical Statistics, Lahti, Finland.Google Scholar
Arjas, E. and Norros, I. (1989) Change of life distribution via a hazard transformation: an inequality with application to minimal repair. Math. Operat. Res. 14, 355–361.Google Scholar
Aven, T. (1983) Optimal replacement under a minimal repair strategy – a general failure model Adv. Appl. Prob. 15, 198–211.CrossRefGoogle Scholar
Barlow, R. E. and Hunter, L. (1960) Optimum preventive maintenance policies. Operat. Res. 1, 90–100.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975a) Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975b) Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153–173.CrossRefGoogle Scholar
Bergman, B. (1985) On reliability theory and its applications. Scand. J. Statist. 12, 1–41.Google Scholar
Birnbaum, Z. W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis II, ed. Krishnaiah, P. R. Academic Press, New York, 581–592.Google Scholar
Egeland, T. (1988) Computing in the solarium. Technical Report, University of Oslo.Google Scholar
Griffith, W. and Sheu, S.-H. (1989) Multivariate imperfect repair model.Google Scholar
Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319–330.Google Scholar
Natvig, B. (1982) On the reduction in remaining system lifetime due to the failure of a specific component. J. Appl. Prob. 19, 642–652. Correction. J. Appl. Prob. 20, 713.Google Scholar
Natvig, B. (1985) New light on measures of importance of system components. Scand. J. Statist. 12, 43–54.Google Scholar
Natvig, B. (1988) On information based minimal repair and the reduction in remaining system lifetime due to the failure of a specific module. Technical Report, University of Oslo.Google Scholar
Norros, I. (1986) Notes on Natvig's measure of importance of system components. J. Appl. Prob. 23, 736–747.CrossRefGoogle Scholar
Norros, I. (1987) The ‘minimal repair’, elimination and extemalization of a totally inaccessible stopping time. Dept of Mathematics, University of Helsinki.Google Scholar
Xie, M. (1987) Some Contributions to Reliability Analysis. Ph.D. Dissertation. Dept of Mechanical Engineering, Linköping University.Google Scholar