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

Published online by Cambridge University Press:  11 October 2007

Brahim Ouhbi ,
Ali Boudi  and
Mohamed Tkiouat
Brahim Ouhbi
Affiliation:
École Nationale Supérieure d'Arts et Métiers, Marjane II, Meknès Ismailia, B.P. 4024 Béni M'Hamed, Meknès, Maroc; [email protected]
Ali Boudi
Affiliation:
Office National des Chemins de Fer, Agdal, Rabat, Maroc
Mohamed Tkiouat
Affiliation:
École Mohammadia d'Ingénieurs, Agdal, B.P. 765, Rabat, Maroc
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Abstract

In this paper we, firstly, present a recursive formula of theempirical estimator of the semi-Markov kernel. Then a non-parametricestimator of the expected cumulative operational time forsemi-Markov systems is proposed. The asymptotic properties of thisestimator, as the uniform strongly consistency and normality aregiven. As an illustration example, we give a numerical application.

Keywords

Expected cumulative operational timeSemi-Markov processNon-parametricEstimation
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 4 , October 2007 , pp. 399 - 410
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

A. Boudi, Sur le contrôle adaptatif des populations de chaines de Markov finies. Thèse de 3ème cycle, Faculté des Sciences, Rabat, Morocco (1996).
A. Huzurbazar, Flowgraph models for multistate Time-to-Event Data. Wiley, New York (2005).
Kulkarni, V.G., Nicola, V.F. and Trivedi, K.S., The completion time of a job on multimode systems. Adv. Appl. Probab. 19 (1987) 932–954. CrossRef
N. Limnios and G. Oprişan, Semi-Markov Processes and Reliability. Birkhäuser, Boston (2001).
Limnios, N., Ouhbi, B. and Sadek, A., Empirical Estimator of Stationary Distribution For Semi-Markov Processes. Commun. Stat. Theory Methods 34 (2003) 987–995. CrossRef
Ouhbi, B. and Limnios, N., Non-parametric estimation for semi-Markov processes based on its hazard rate. Stat. Inference Stoch. Process. 2 (1999) 151–173. CrossRef
Ouhbi, B. and Limnios, N., Non-parametric estimation for semi-Markov kernels with application to reliability analysis. Appl. Stoch. Models Data Anal. 12 (1996) 209–220. 3.0.CO;2-T>CrossRef
Ouhbi, B. and Limnios, N., The Rate of Occurrence of Failures for Semi-Markov Processes and Estimation. Stat. Probab. Lett. 59 (2001) 245–255. CrossRef
Ouhbi, B. and Limnios, N., Non-parametric Reliability Estimation of Semi-Markov Processes. J. Stat. Plan. Inference 109 (2003) 155–165. CrossRef
Pyke, R. and Schaufele, R., The existence and uniqueness of stationary measures for Markov renewal processes. Ann. Math. Stat. 37 (1966) 1439–1462. CrossRef
Pyke, R., Markov renewal processes: definitions and preliminary properties. Ann. Math. Stat. 32 (1961) 1231–1241. CrossRef
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.
Scenski, A., Cumulative operational time analysis of finite semi-Markov reliability models. Reliab. Eng. Syst. Saf. 44 (1994) 17–25.
S. Ross, Applied probability models with optimization applications. Dover New York (1992).
Rubino, G. and Sericola, B., Interval availability analysis using operational periods. Perform. Eval. 14 (1992) 257–272. CrossRef
J. Janssen and N. Limnios Eds., Semi-Markov models and Applications. Kluwer Academic, Dordrecht (1999).