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Statistical and information based (physical) minimal repair for k out of n Systems

Part of: Operations research and management science Survival analysis and censored data Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Philip J. Boland  and
Emad El-Neweihi
Philip J. Boland*
Affiliation:
University College, Dublin
Emad El-Neweihi*
Affiliation:
University of Illinois at Chicago
*
∗Postal address: University College, Dublin, Department of Statistics, Belfield, Dublin 4, Ireland.
∗∗Postal address: University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, Chicago, IL 60607–7045, USA. Email address: neweihi@uic.edu.
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Abstract

The ‘minimal’ repair of a system can take several forms. Statistical or black box minimal repair at failure time t is equivalent to replacing the system with another functioning one of the same age, but without knowledge of precisely what went wrong with the system. Its major attribute is its mathematical tractability. In physical minimal repair, at system failure time t, we minimally repair the ‘component’ which brought the system down at time t. The work of Arjas and Norros, Finkelstein, and Natvig is reviewed. The concept of a rate function for minimal repairs of the statistical and physical types are discussed and developed. It is shown that the number of physical minimal repairs is stochastically larger than the number of statistical minimal repairs for k out of n systems with similar components. Some majorization results are given for physical minimal repair for two component parallel systems with exponential components.

Keywords

Minimal repairstatistical minimal repairblack box minimal repairphysical minimal repairstochastic orderhazard rate orderk out of n systems

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 731 - 740
Copyright
Copyright © Applied Probability Trust 1998 

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References

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