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

Brahim Ouhbi; Ali Boudi; Mohamed Tkiouat

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Displaying similar documents to “The expected cumulative operational time for finite semi-Markov systems and estimation”

Semi-Markov switches

R. L. Disney, D. C. McNickle (1985)

Applicationes Mathematicae

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Bottom-up modeling of domestic appliances with Markov chains and semi-Markov processes

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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,...

Single-use reliability computation of a semi-Markovian system

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...

Survival probabilities for HIV infected patients through semi-Markov processes

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....

Extended piecewise Markov processes in continuous time

Maria Jankiewicz (1978)

Applicationes Mathematicae

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Semi-Markov processes for reliability studies

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.

On the number of word occurrences in a semi-Markov sequence of letters

Margarita Karaliopoulou (2009)

ESAIM: Probability and Statistics

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Let a finite alphabet . We consider a sequence of letters from generated by a discrete time semi-Markov process ${Z_{γ}; γ \in} .$ We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.