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

Brahim Ouhbi; Ali Boudi; Mohamed Tkiouat

RAIRO - Operations Research (2007)

  • Volume: 41, Issue: 4, page 399-410
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Ouhbi, Brahim, Boudi, Ali, and Tkiouat, Mohamed. "The expected cumulative operational time for finite semi-Markov systems and estimation." RAIRO - Operations Research 41.4 (2007): 399-410. <http://eudml.org/doc/250101>.

@article{Ouhbi2007,
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. },
author = {Ouhbi, Brahim, Boudi, Ali, Tkiouat, Mohamed},
journal = {RAIRO - Operations Research},
keywords = {Expected cumulative operational time; Semi-Markov process; Non-parametric Estimation; semi-Markov process},
language = {eng},
month = {10},
number = {4},
pages = {399-410},
publisher = {EDP Sciences},
title = {The expected cumulative operational time for finite semi-Markov systems and estimation},
url = {http://eudml.org/doc/250101},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Ouhbi, Brahim
AU - Boudi, Ali
AU - Tkiouat, Mohamed
TI - The expected cumulative operational time for finite semi-Markov systems and estimation
JO - RAIRO - Operations Research
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 4
SP - 399
EP - 410
AB - 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.
LA - eng
KW - Expected cumulative operational time; Semi-Markov process; Non-parametric Estimation; semi-Markov process
UR - http://eudml.org/doc/250101
ER -

References

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  10. R. Pyke and R. Schaufele, The existence and uniqueness of stationary measures for Markov renewal processes. Ann. Math. Stat.37 (1966) 1439–1462.  Zbl0154.42901
  11. R. Pyke, Markov renewal processes: definitions and preliminary properties. Ann. Math. Stat.32 (1961) 1231–1241.  Zbl0267.60089
  12. R.M. Smith, K.S. Trivedi and A.V. Ramesh, Performability analysis : measures, an algorithm, and a case study. IEEE Trans. Comput.C-37 (1988) 406–417.  
  13. A. Scenski, Cumulative operational time analysis of finite semi-Markov reliability models. Reliab. Eng. Syst. Saf.44 (1994) 17–25.  
  14. S. Ross, Applied probability models with optimization applications. Dover New York (1992).  Zbl1191.60001
  15. G. Rubino and B. Sericola, Interval availability analysis using operational periods. Perform. Eval.14 (1992) 257–272.  Zbl0757.90026
  16. J. Janssen and N. Limnios Eds., Semi-Markov models and Applications. Kluwer Academic, Dordrecht (1999).  

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