EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Issue RAIRO Oper. Res.
Volume 41, Number 4, October-December 2007
Page(s) 399 - 410
DOI 10.1051/ro:2007029
Published online 11 October 2007

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 Tkiouat3

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 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


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.