| Issue |
RAIRO-Oper. Res.
Volume 41, Number 4, October-December 2007
|
|
|---|---|---|
| Page(s) | 399 - 410 | |
| DOI | https://doi.org/10.1051/ro:2007029 | |
| Published online | 11 October 2007 | |
The expected cumulative operational time for finite semi-Markov systems and estimation
1
École Nationale Supérieure d'Arts et Métiers, Marjane II,
Meknès Ismailia, B.P. 4024 Béni M'Hamed, Meknès, Maroc; ouhbib@yahoo.co.uk
2
Office National des Chemins de Fer, Agdal, Rabat, Maroc
3
École Mohammadia d'Ingénieurs, Agdal,
B.P. 765, Rabat, Maroc
Received:
11
May
2005
Accepted:
6
February
2007
In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
Mathematics Subject Classification: 60K20
Key words: Expected cumulative operational time / Semi-Markov process / Non-parametric Estimation
© EDP Sciences, ROADEF, SMAI, 2007
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