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Article Citation - WoS: 18Citation - Scopus: 21Failure Rates of Consecutive k-out-of-n< Systems(Springer Heidelberg, 2012) Eryilmaz, Serkan; Navarro, JorgeLinear and circular consecutive k-out-of-n systems are very popular models in reliability theory, survival analysis, and biological disciplines and other related lifetime sciences. In these theories, the failure rate function is a key notion for measuring the ageing process. In this paper we obtain some mixture representations for consecutive systems and we apply a mixture-based failure rate analysis for both linear and circular consecutive systems. In particular, we analyze the limiting behavior of the system failure rate when the time increases and we obtain some ordering properties. We first consider the popular case of systems with components having independent and identically distributed lifetimes. In practice, these assumptions may fail. So we also study the case of independent non-identically distributed component lifetimes. This case has special interest when a cold-standby redundancy is used for some components. In this sense, we analyze where to place the best components in the systems. Even more, we also study systems with dependent components by assuming that their lifetimes are exchangeable. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 13The Concept of Weak Exchangeability and Its Applications(Springer Heidelberg, 2017) Eryilmaz, SerkanA finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.Letter Theoretical Modelling of Magnetron Sputtering of Boron Nitride Coating(Springer Heidelberg, 2023) Rake, Nakka; Kaftanoglu, Bilgin; Hacaloglu, Tugce; Aydogan, AsudeThe fundamentals of the magnetron sputtering (MS) technique are simple. However, the complex interplay of various physical and chemical sub-processes lies in its simplicity. The direct simulation Monte Carlo (DSMC) method is used to model the MS of the Boron Nitride (BN) coating. The Lorentz force, which is created by an electric field, magnetic field and particle collision, is utilised to model the BN coating. Three distinct bias voltages are used to generate three different BN-coating models under the same conditions. The modelling of BN coatings reveals that the deposition rate decreases as the substrate voltage increases.Article Citation - WoS: 17Citation - Scopus: 16A Study on Reliability of Coherent Systems Equipped With a Cold Standby Component(Springer Heidelberg, 2014) Eryilmaz, SerkanIn this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property.Article Citation - WoS: 7Citation - Scopus: 8Generalized Waiting Time Distributions Associated With Runs(Springer Heidelberg, 2016) Eryilmaz, SerkanLet be a {X-t, t >= 1} sequence of random variables with two possible values as either "1" (success) or "0" (failure). Define an independent sequence of random variables {D-i, i >= 1}. The random variable is associated with the success when it occupies the ith place in a run of successes. We define the weight of a success run as the sum of the D values corresponding to the successes in the run. Define the following two random variables: is the number of trials until the weight of a single success run exceeds or equals k, and is the number of trials until the weight of each of r success runs equals or exceeds k in {X-t, t >= 1}. Distributional properties of the waiting time random variables and are studied and illustrative examples are presented.Article Norming Subspaces Isomorphic to l1(Springer Heidelberg, 2015) Ostrovska, SofiyaNorming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l(1) provided that the following two conditions are satisfied: (1) X* contains a subspace isomorphic to l(1); and (2) X* contains a separable norming subspace.Article Citation - WoS: 5Citation - Scopus: 5Some Reliability Measures and Maintenance Policies for a Coherent System Composed of Different Types of Components(Springer Heidelberg, 2023) Kelkinnama, Maryam; Eryilmaz, SerkanConsider an n-components coherent system monitored at one or two inspection times, and some information about the system and its components is obtained. Under these conditions, some variants of mean residual lifetimes can be defined. Also, the dual concept of the residual lifetime, i.e., inactivity time is defined for a failed system under different conditions. This article is concerned with the study of mean residual lives and mean inactivity times for a coherent system made of multiple types of dependent components. The dependency structure is modeled by a survival copula. The notion of survival signature is employed to represent the system's reliability function and subsequently its mean residual lives and mean inactivity times under different events at the monitoring time. These dynamic measures are used frequently to study the reliability characteristics of a system. Also, they provide helpful tools for designing the optimal maintenance policies to preserving the system from sudden and costly failures. Here, we extend some maintenance strategies for a coherent system consists of multiple dependent components. Some illustrative examples are provided.Article Citation - WoS: 3Citation - Scopus: 6A Discrete Optimality System for an Optimal Harvesting Problem(Springer Heidelberg, 2017) Bakan, Hacer Oz; Yilmaz, Fikriye; Weber, Gerhard-WilhelmIn this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge-Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.Article Citation - WoS: 15Citation - Scopus: 18The Sharpness of Convergence Results for q-bernstein Polynomials in The Case q > 1(Springer Heidelberg, 2008) Ostrovska, SofiyaDue to the fact that in the case q > 1 the q-Bernstein polynomials are no longer positive linear operators on C[0, 1], the study of their convergence properties turns out to be essentially more difficult than that for q 1. In this paper, new saturation theorems related to the convergence of q-Bernstein polynomials in the case q > 1 are proved.Article Citation - WoS: 14Citation - Scopus: 14A Regime Switching Model for Temperature Modeling and Applications To Weather Derivatives Pricing(Springer Heidelberg, 2020) Turkvatan, Aysun; Omay, Tolga; Hayfavi, Azize; Omay, Tolga; Omay, Tolga; Economics; EconomicsIn this study, we propose a regime-switching model for temperature dynamics, where the parameters depend on a Markov chain. We improve upon the traditional models by modeling jumps in temperature dynamics via the chain itself. Moreover, we compare the performance of the proposed model with the existing models. The results indicate that the proposed model outperforms in the short time forecast horizon while the forecast performance of the proposed model is in line with the existing models for the long time horizon. It is shown that the proposed model is a relatively better representation of temperature dynamics compared to the existing models. Furthermore, we derive prices of weather derivatives written on several temperature indices.
