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The expected cumulative operational time for finite semi-Markov systems and estimation

Published online by Cambridge University Press:  11 October 2007

Brahim Ouhbi ,
Ali Boudi  and
Mohamed Tkiouat
Brahim Ouhbi
Affiliation:
École Nationale Supérieure d'Arts et Métiers, Marjane II, Meknès Ismailia, B.P. 4024 Béni M'Hamed, Meknès, Maroc; ouhbib@yahoo.co.uk
Ali Boudi
Affiliation:
Office National des Chemins de Fer, Agdal, Rabat, Maroc
Mohamed Tkiouat
Affiliation:
École Mohammadia d'Ingénieurs, Agdal, B.P. 765, Rabat, Maroc
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Abstract

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.

Keywords

Expected cumulative operational timeSemi-Markov processNon-parametric Estimation
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 4 , October 2007 , pp. 399 - 410
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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