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Access Right: info:eu-repo/semantics/openAccessSubject: Markov chain

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Now showing 1 - 3 of 3
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    Article
    Citation - WoS: 43
    Citation - Scopus: 50
    On the lifetime behavior of a discrete time shock model
    (Elsevier, 2013) Eryilmaz, Serkan
    In this article, we study a shock model in which the shocks occur according to a binomial process, i.e. the interarrival times between successive shocks follow a geometric distribution with mean 1/p. According to the model, the system fails when the time between two consecutive shocks is less than a prespecified level. This is the discrete time version of the so-called delta-shock model which has been previously studied for the continuous case. We obtain the probability mass function and probability generating function of the system's lifetime. We also present an extension of the results to the case where the shock occurrences are dependent in a Markovian fashion. (C) 2012 Elsevier B.V. All rights reserved.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 2
    On the Lifetime of a Random Binary Sequence
    (Elsevier Science Bv, 2011) Eryilmaz, Serkan
    Consider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task ("1") or the failure of the element ("0"). Initially, m tasks are sent to the system. At the second step, a complex of length m(1) is formed and sent to the system, where m(1) is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of "1" or "0". We obtain a recursive equation for the expected value of this waiting time random variable. (C) 2011 Elsevier B.V. All rights reserved.
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    Article
    Citation - WoS: 11
    Citation - Scopus: 13
    Compound Markov Negative Binomial Distribution
    (Elsevier, 2016) Eryilmaz, Serkan
    Let {Y-i}(i >= 1) be a sequence of {0,1} variables which forms a Markov chain with a given initial probability distribution and one-step transition probability matrix. Define N-n to be the number of trials until the nth success ("1") in {Y-i}(i >= 1). In this paper, we study the distribution of the random variable T = Sigma(Nn)(i=1) X-i, where {X-i}(i >= 1) is a sequence of independent and identically distributed random variables having a common phase-type distribution. The distribution of T is obtained by means of phase-type distributions. (C) 2015 Elsevier B.V. All rights reserved.