Displaying similar documents to “Single-use reliability computation of a semi-Markovian system”

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....

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

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.

Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

Jeffrey J. Hunter (2016)

Special Matrices

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This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the...

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 ∈ } . 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.

Reduction of absorbing Markov chain

Mariusz Górajski (2009)

Annales UMCS, Mathematica

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In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on...