# Semi-Markov processes for reliability studies

Christiane Cocozza-Thivent; Michel Roussignol

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 207-223
- ISSN: 1292-8100

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topCocozza-Thivent, Christiane, and Roussignol, Michel. "Semi-Markov processes for reliability studies." ESAIM: Probability and Statistics 1 (2010): 207-223. <http://eudml.org/doc/197758>.

@article{Cocozza2010,

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.
},

author = {Cocozza-Thivent, Christiane, Roussignol, Michel},

journal = {ESAIM: Probability and Statistics},

keywords = {Semi-Markov process / quasi-stationary distribution / reliability /
r-recurrence.},

language = {eng},

month = {3},

pages = {207-223},

publisher = {EDP Sciences},

title = {Semi-Markov processes for reliability studies},

url = {http://eudml.org/doc/197758},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Cocozza-Thivent, Christiane

AU - Roussignol, Michel

TI - Semi-Markov processes for reliability studies

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 207

EP - 223

AB -
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.

LA - eng

KW - Semi-Markov process / quasi-stationary distribution / reliability /
r-recurrence.

UR - http://eudml.org/doc/197758

ER -

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