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Article Citation - WoS: 8Citation - Scopus: 9The Number of Failed Components Upon System Failure When the Lifetimes Are Discretely Distributed(Elsevier Sci Ltd, 2022) Eryilmaz, Serkan; Yalcin, FeminThe number of failed components at the time when the system fails is an important quantity which can be effectively used in the determination of the optimal number of spares. This paper is concerned with the distribution and expected value of this quantity when the lifetimes of a given coherent system are discretely distributed. In particular, the distribution of the corresponding random quantity is derived for all coherent systems of order three and four. The mean number of the failed components upon system failure is exactly derived for a linear consecutive-2-out-of-n:F structure. The mean of the quantity under concern is also computed for series and parallel systems consisting of disjoint modules. The latter computation provides an efficient way to obtain the corresponding mean for a larger system via the modules which have smaller number of components.Article Citation - WoS: 16Citation - Scopus: 18Start-Up Demonstration Test Based on Total Successes and Total Failures With Dependent Start-Ups(Ieee-inst Electrical Electronics Engineers inc, 2012) Yalcin, Femin; Eryilmaz, SerkanStart-up demonstration testing is an effective method for illustrating the reliability of a unit before purchasing it. The test consists of starting-up the unit, and observing the outcomes, either success or failure. According to the total successes total failures (TSTF) test procedure, a unit under test is accepted when a specified number of successes is observed before a specified number of failures; otherwise, the unit is rejected. We study the TSTF procedure for dependent start-ups where the outcome of the present start-up depends on the total number of successful start-ups so far. The main characteristics of the TSTF test are obtained under this previous-sum dependent model, and numerical illustrations are presented.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.Article Citation - WoS: 13Citation - Scopus: 12q-geometric and q-binomial Distributions of Order k(Elsevier Science Bv, 2014) Yalcin, Femin; Eryilmaz, SerkanIn this paper, we generalize geometric and binomial distributions of order k to q-geometric and q-binomial distributions of order k using Bernoulli trials with a geometrically varying success probability. In particular, we derive expressions for the probability mass functions of these distributions. For q = 1, these distributions reduce to geometric and binomial distributions of order k which have been extensively studied in the literature. (C) 2014 Elsevier B.V. All rights reserved.
