Semi-Markov processes for reliability studies
Christiane Cocozza-Thivent, Michel Roussignol (1997)
ESAIM: Probability and Statistics
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Christiane Cocozza-Thivent, Michel Roussignol (1997)
ESAIM: Probability and Statistics
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Maria Jankiewicz (1978)
Applicationes Mathematicae
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R. L. Disney, D. C. McNickle (1985)
Applicationes Mathematicae
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Giovanni Masala, Giuseppina Cannas, Marco Micocci (2014)
Biometrical Letters
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In this paper we apply a parametric semi-Markov process to model the dynamic evolution of HIV-1 infected patients. The seriousness of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introduce the main features of nonhomogeneous semi-Markov models. After determining the transition probabilities and the waiting time distributions in each state of the disease, we solve the evolution equations of the process in order to estimate the interval transition probabilities....
Brahim Ouhbi, Ali Boudi, Mohamed Tkiouat (2007)
RAIRO - Operations Research
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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.
Rajmund Drenyovszki, Lóránt Kovács, Kálmán Tornai, András Oláh, István Pintér (2017)
Kybernetika
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In our paper we investigate the applicability of independent and identically distributed random sequences, first order Markov and higher order Markov chains as well as semi-Markov processes for bottom-up electricity load modeling. We use appliance time series from publicly available data sets containing fine grained power measurements. The comparison of models are based on metrics which are supposed to be important in power systems like Load Factor, Loss of Load Probability. Furthermore,...
K. Arndt, P. Franken (1979)
Applicationes Mathematicae
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Guglielmo D'Amico (2014)
Applications of Mathematics
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Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation...
D'Amico, Guglielmo, Janssen, Jacques, Manca, Raimondo (2009)
Journal of Applied Mathematics and Decision Sciences
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Anna Jaśkiewicz (2009)
Applicationes Mathematicae
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We establish the average cost optimality equation and show the existence of an (ε-)optimal stationary policy for semi-Markov control processes without compactness and continuity assumptions. The only condition we impose on the model is the V-geometric ergodicity of the embedded Markov chain governed by a stationary policy.
W. P. Cherry, R. L. Disney (1983)
Applicationes Mathematicae
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Sumita, Ushio, Huang, Jia-Ping (2009)
International Journal of Mathematics and Mathematical Sciences
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