The expected cumulative operational time for finite semi-Markov systems and estimation
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 399-410.

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.

DOI : 10.1051/ro:2007029
Classification : 60K20
Mots-clés : expected cumulative operational time, semi-Markov process, non-parametric estimation 
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     author = {Ouhbi, Brahim and Boudi, Ali and Tkiouat, Mohamed},
     title = {The expected cumulative operational time for finite {semi-Markov} systems and estimation},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Ouhbi, Brahim; Boudi, Ali; Tkiouat, Mohamed. The expected cumulative operational time for finite semi-Markov systems and estimation. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 399-410. doi : 10.1051/ro:2007029. http://archive.numdam.org/articles/10.1051/ro:2007029/

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