| Article ID: | iaor20083361 |
| Country: | France |
| Volume: | 41 |
| Issue: | 4 |
| Start Page Number: | 399 |
| End Page Number: | 410 |
| Publication Date: | Oct 2007 |
| Journal: | RAIRO Operations Research |
| Authors: | Ouhbi Brahim, Boudi Ali, Tkiouat Mohamed |
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.