Analysis of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-out-of-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> system with spares, repairs, and a probabilistic rule

Chakravarthy, Srinivas R.

doi:https://doi.org/10.1155/JAMSA/2006/39093

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 039093 | https://doi.org/10.1155/JAMSA/2006/39093

Analysis of a k-out-of-N system with spares, repairs, and a probabilistic rule

Srinivas R. Chakravarthy¹

Received16 Apr 2006

Revised21 Sept 2006

Accepted21 Sept 2006

Published21 Dec 2006

Abstract

We consider a k-out-of-N reliability system with identical components having exponential lifetimes. There is a single repairman who attends to failed components on a first-come first-served basis. The repair times are assumed to be of phase type. The system has K spares that can be used according to a probabilistic rule to extend the lifetime of the system. The system is analyzed using Markov chain theory and some interesting results are obtained. A few illustrative numerical examples are discussed.

References

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Copyright

Copyright © 2006 Srinivas R. Chakravarthy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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