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On a Markov chain approach for the study of reliability structures

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

M. V. Koutras
M. V. Koutras*
Affiliation:
University of Athens
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece.
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Abstract

In this paper we consider a class of reliability structures which can be efficiently described through (imbedded in) finite Markov chains. Some general results are provided for the reliability evaluation and generating functions of such systems. Finally, it is shown that a great variety of well known reliability structures can be accommodated in this general framework, and certain properties of those structures are obtained on using their Markov chain imbedding description.

Keywords

MARKOV IMBEDDINGMARKOV CHAINTRANSITION PROBABILITY MATRIXRELIABILITY GENERATING FUNCTIONCONSECUTIVE SYSTEMS

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 357 - 367
Copyright
Copyright © Applied Probability Trust 1996 

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