RAIRO Oper. Res. 41 (2007) 399-410
DOI: 10.1051/ro:2007029

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

Brahim Ouhbi¹, Ali Boudi² and Mohamed Tkiouat<sup>3

1</sup>  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 May 11, 2005. Accepted February 6, 2007. Published online 11 October 2007.)

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.

Mathematics Subject Classification. 60K20

Key words: Expected cumulative operational time, Semi-Markov process, Non-parametric Estimation


© EDP Sciences, ROADEF, SMAI 2007