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

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