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Article Citation - WoS: 1Citation - Scopus: 2On the Lifetime of a Random Binary Sequence(Elsevier Science Bv, 2011) Eryilmaz, SerkanConsider 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.Article Citation - WoS: 11Citation - Scopus: 12Discrete Time Shock Models Involving Runs(Elsevier Science Bv, 2015) Eryilmaz, SerkanIn this paper, three different discrete time shock models are studied. In the first model, the failure occurs when the additively accumulated damage exceeds a certain level while in the second model the system fails upon the local damage caused by the consecutively occurring shocks. The third model is a mixed model and combines the first and second models. The survival functions of the systems under these models are obtained when the occurrences of the shocks are independent, and when they are Markov dependent over the periods. (C) 2015 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 6On the Mean and Extreme Distances Between Failures in Markovian Binary Sequences(Elsevier Science Bv, 2011) Eryilmaz, Serkan; Yalcin, FeminThis paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented. (C) 2011 Elsevier B.V. All rights reserved.
