The failure rate in reliability: Approximations and bounds.
Cocozza-Thivent, Christiane, Kalashnikov, Vladimir (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Cocozza-Thivent, Christiane, Kalashnikov, Vladimir (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Christiane Cocozza-Thivent, Michel Roussignol (2010)
ESAIM: Probability and Statistics
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We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.
Sumita, Ushio, Huang, Jia-Ping (2009)
International Journal of Mathematics and Mathematical Sciences
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Daley, D.J., Rolski, T., Vesilo, R. (2007)
Journal of Applied Mathematics and Decision Sciences
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Maria Jankiewicz (1978)
Applicationes Mathematicae
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Michael I. Taksar (1987)
Séminaire de probabilités de Strasbourg
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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....
D'Amico, Guglielmo, Janssen, Jacques, Manca, Raimondo (2009)
Journal of Applied Mathematics and Decision Sciences
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Masao Nagasawa (1972)
Séminaire de probabilités de Strasbourg
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Ball, Frank G., Milne, Robin K., Yeo, Geoffrey F. (2007)
Journal of Applied Mathematics and Decision Sciences
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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.
W. P. Cherry, R. L. Disney (1983)
Applicationes Mathematicae
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