Volume 41, Number 4, October-December 2007
|Page(s)||399 - 410|
|Published online||11 October 2007|
The expected cumulative operational time for finite semi-Markov systems and estimation
École Nationale Supérieure d'Arts et Métiers, Marjane II,
Meknès Ismailia, B.P. 4024 Béni M'Hamed, Meknès, Maroc; email@example.com
2 Office National des Chemins de Fer, Agdal, Rabat, Maroc
3 École Mohammadia d'Ingénieurs, Agdal, B.P. 765, Rabat, Maroc
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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