Endüstri Mühendisliği Yüksek Lisans Tezleri / Industrial Engineering Master Theses

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Browsing Endüstri Mühendisliği Yüksek Lisans Tezleri / Industrial Engineering Master Theses by Subject "Alpha cuts"

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    Master Thesis
    Genelleştirilmiş Yansıtan Bariyerli Ödüllü Yenileme Sürecinin Asimptotik Yöntemlerle İncelenmesi
    (TOBB Ekonomi ve Teknoloji Üniversitesi Fen Bilimleri Enstitüsü, 2011) Gever, Başak; Khaniyev, Tahir; Türkşen, İ. Burhan
    In this study, a generalized renewal reward process with reflecting barrier is considered and probability characteristics of the process is investigated by analytic and asymptotic methods in both crisp logic and fuzzy logic. In the first part of the study, the process is constructed mathematically and its finite dimensional distributions are examined. Then, the three important boundary functionals are defined and the first four moments of these boundary functionals are calculated. Later, under some conditions the ergodicity of the process is proved and the exact expression of ergodic distribution of the process is obtained. Moreover, the weak convergence theorem for the ergodic distribution of the process is proved and the explicit form of the limit distribution of the process is found. Besides, it is shown that the obtained limit distribution is a residual waiting time distribution. At the end of the first part, the exact form of the moments of the ergodic distribution is obtained. In some important cases (in the cases of Exponential, Erlang and Rayleigh distributions), the asymptotic expansions of the first four moments with the explicit coefficients are written. In the second part of the study, when the random variables expressed demands, having Exponential, Gama, Erlang and Weibull distributions with a fuzzy parameter, the ergodic distribution of the process is examined. After that, the fuzzy characteristics of the ergodic distribution are investigated and the explicit forms of these characteristics are obtained.