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Subject: Matrix-exponential distribution

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Now showing 1 - 4 of 4
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    Article
    Citation - WoS: 19
    Citation - Scopus: 14
    Assessment of Shock Models for a Particular Class of Intershock Time Distributions
    (Springer, 2022) Kus, Coskun; Tuncel, Altan; Eryilmaz, Serkan
    In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems' lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.
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    Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Reliability Assessment for Censored Δ-Shock Models
    (Springer, 2022) Chadjiconstantinidis, Stathis; Eryilmaz, Serkan
    This paper is devoted to study censored delta-shock models for both cases when the intershock times have discrete and continuous distributions. In particular, the distribution and moments of the system's lifetime are studied via probability generating functions and Laplace transforms. For discrete intershock time distributions, several recursions for evaluating the probability mass function, the survival function and the moments of the system's lifetime are given. As it is shown for the discrete case, the distribution of the system's lifetime is directly linked with matrix-geometric distributions for particular classes of intershock time distributions, such as phase-type distributions. Thus, matrix-based expressions are readily obtained for the exact distribution of the system's lifetime under discrete setup. Also, discrete uniform intershock time distributions are examined. For the case of continuous intershock time distributions, it is shown that the shifted lifetime has a compound geometric distribution, and based on this, the distribution of the system's lifetime is approximated via discrete mixture distributions having a mass at delta and matrix-exponential distributions for the continuous part. Both for the discrete and the continuous case, Lundberg-type bounds and asymptotics for the survival function of system's lifetime are given. To illustrate the results, some numerical examples, both for the discrete and the continuous case, are also given.
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    Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Reliability of the Two-Unit Priority Standby System Revisited
    (Sage Publications Ltd, 2022) Eryilmaz, Serkan; Finkelstein, Maxim
    This paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system's lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential distributions.
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    Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Analysis of the Two-Unit Cold Standby Repairable System With Damage and Repair Time Dependency Via Matrix-Exponential Distributions
    (Taylor & Francis Ltd, 2021) Kus, Coskun; Eryilmaz, Serkan
    In this paper, two-unit standby repairable system is studied via matrix-exponential distributions. The system under concern consists of one active and one standby components, and fails if either a damage size upon the failure of the active component is larger than a repair limit or the repair time of the failed unit exceeds the lifetime of the active unit, whichever happens first. Under the assumption that the damage size and repair time are statistically dependent, the Laplace transform of the system's lifetime is obtained. The Laplace transform is shown to be rational under particular cases, and the reliability evaluation of the system is performed via well-known distributional properties of the matrix-exponential distributions. The problem of estimating the unknown parameters of the operation time and repair time distributions is also discussed based on system's lifetime data.