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Semi-Markov processes for reliability studies

Published online by Cambridge University Press:  15 August 2002

Christiane Cocozza-Thivent  and
Michel Roussignol
Christiane Cocozza-Thivent
Affiliation:
[email protected]
Michel Roussignol
Affiliation:
[email protected]
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Abstract

We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.

Keywords

Semi-Markov process / quasi-stationary distribution / reliability / r-recurrence.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 207 - 223
Copyright
© EDP Sciences, SMAI, 1997

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