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Article Citation - WoS: 8Citation - Scopus: 10Computing Reliability Indices of a Wind Power System Via Markov Chain Modelling of Wind Speed(Sage Publications Ltd, 2024) Eryilmaz, Serkan; Bulanik, Irem; Devrim, YilserStatistical modelling of wind speed is of great importance in the evaluation of wind farm performance and power production. Various models have been proposed in the literature depending on the corresponding time scale. For hourly observed wind speed data, the dependence among successive wind speed values is inevitable. Such a dependence has been well modelled by Markov chains. In this paper, the use of Markov chains for modelling wind speed data is discussed in the context of the previously proposed likelihood ratio test. The main steps for Markov chain based modelling methodology of wind speed are presented and the limiting distribution of the Markov chain is utilized to compute wind speed probabilities. The computational formulas for reliability indices of a wind farm consisting of a specified number of wind turbines are presented through the limiting distribution of a Markov chain. A case study that is based on real data set is also presented.Article Citation - WoS: 4Citation - Scopus: 4Development and Psychometric Analysis of a Pediatric Oncology Nurses' Educational Needs Scale(Wiley, 2023) Kudubes, Asli Akdeniz; Semerci, Remziye; Ozbay, Sevil Cinar; Ay, Ayse; Boztepe, HandanBackground/objectivesIt is important to determine the educational needs of pediatric oncology nurses in order to maximize and implement nursing care interventions. Therefore, this study aims to develop a valid and reliable measurement tool to determine pediatric oncology nurses' educational needs and examine its psychometric properties. Design/methodsThis methodological study was conducted with 215 pediatric oncology nurses in Turkey between December 2021 and July 2022. Data were collected with the "Nurse Information Form" and "Pediatric Oncology Nurses' Educational Needs Scale." IBM SPSS 21.0 and IBM AMOS 25.0 software programs were used for data analysis, and descriptive statistics were used to analyze numeric variables. Exploration and confirmatory factor analyses were performed to determine the scale's factorial structure. ResultsThe factorial analysis was used to test the structural validity of the scale. A five-factor structure consisting of 42 items was developed. The Cronbach's alpha coefficient for "Illness" was .978, "Chemotherapy and Side Effect" was .978, "Another Therapy and Side Effect" was .974, "Palliative Care" was .967, "Supportive Care" was .985, and the total score was .990. Fit indices resulting from the study were chi(2)/SD: 3.961, root mean square error of approximation (RMSEA): 0.072, goodness-of-fit index (GFI): 0.95, comparative-of-fit index (CFI): 0.96, and normed fit index (NFI): 0.95. ConclusionThe Pediatric Oncology Nurses' Educational Needs Scale is a valid and reliable scale for pediatric oncology nurses to determine their educational needs.Article Citation - WoS: 26Citation - Scopus: 28Mean residual life of coherent systems consisting of multiple types of dependent components(Wiley, 2018) Eryilmaz, Serkan; Coolen, Frank P. A.; Coolen-Maturi, TahaniMean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components' lifetimes are also defined and studied.Article Citation - WoS: 12Citation - Scopus: 14The Markov Discrete Time Δ-Shock Reliability Model and a Waiting Time Problem(Wiley, 2022) Chadjiconstantinidis, Stathis; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability theory and applied probability. In this model, the system fails due to the arrivals of two consecutive shocks which are too close to each other. That is, the system breaks down when the time between two successive shocks falls below a fixed threshold delta. In the literature, the delta-shock model has been mostly studied by assuming that the time between shocks have continuous distribution. In the present paper, the discrete time version of the model is considered. In particular, a proper waiting time random variable is defined based on a sequence of two-state Markov dependent binary trials and the problem of finding the distribution of the system's lifetime is linked with the distribution of the waiting time random variable, and we study the joint as well as the marginal distributions of the lifetime, the number of shocks and the number of failures associated with these binary trials.Article Citation - WoS: 7Citation - Scopus: 9Reliability-Based Evaluation of Hybrid Wind-Solar Energy System(Sage Publications Ltd, 2021) Devrim, Yilser; Eryilmaz, SerkanIn this article, a hybrid system that consists of a specified number of wind turbines and solar modules is considered. In particular, the system is modeled using weightedk-out-of-nsystem which is also known as a threshold system in reliability literature. The system under concern consists ofn1identical wind turbines andn2identical solar modules, and each turbine and module can be in one of two states as working or failed. The probability that the entire hybrid system withn=n1+n2components produces power at minimum levelkis computed and evaluated. The importance of single-wind turbine and solar module is also calculated to measure which renewable energy component is more critical and important. Extensive numerical results that are based on real data set are presented to illustrate the model.Article Citation - WoS: 26Citation - Scopus: 28Reliability Assessment for Discrete Time Shock Models Via Phase-Type Distributions(Wiley, 2021) Eryilmaz, Serkan; Kan, CihangirIn this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.Article Citation - WoS: 9Citation - Scopus: 10Coherent System With Standby Components(Wiley, 2018) Eryilmaz, Serkan; Erkan, T. ErmanA coherent system that consists of n independent components and equipped with r cold standby components is considered. A generalized mixture representation for the survival function of such a system is obtained, and it is used to examine reliability properties of the system. In particular, the effect of adding r standby components to a given set of original components is measured by computing mean time to failure of the system. The limiting behavior of the failure rate of the system is also examined using the mixture representation. The results are illustrated for a bridge system. A case study that is concerned with an oil pipeline system is also presented.Article Citation - WoS: 2Citation - Scopus: 2A New Extended δ-shock Model With the Consideration of Shock Magnitude(Wiley, 2024) Lorvand, Hamed; Eryilmaz, SerkanIn this article, a new delta$$ \delta $$-shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non-critical shock occurs in a time length less than delta 1$$ {\delta}_1 $$ or a shock after a critical shock occurs in a time length less than delta 2,$$ {\delta}_2, $$ where delta 1Article Citation - WoS: 10Citation - Scopus: 10Systems Composed of Two Types of Nonidentical and Dependent Components(Wiley-blackwell, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringA coherent system of order n that consists two different types of dependent components is considered. The lifetimes of the components in each group are assumed to follow an exchangeable joint distribution, and the two random vectors, which represent the lifetimes of the components in each group are also assumed to be dependent. Under this particular form of dependence, all components are assumed to be dependent but they are categorized with respect to their reliability functions. Mixture representation is obtained for the survival function of the system's lifetime. Mixture representations are also obtained for the series and parallel systems consisting of disjoint modules such that all components of Type I are involved in one module (subsystem) and all components of Type II are placed in the other module. The theoretical results are illustrated with examples. (c) 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 388-394, 2015Article Citation - WoS: 6Citation - Scopus: 7DISTRIBUTIONS OF RANDOM VARIABLES INVOLVED IN DISCRETE CENSORED δ-SHOCK MODELS(Cambridge Univ Press, 2023) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanSuppose that a system is affected by a sequence of random shocks that occur over certain time periods. In this paper we study the discrete censored delta-shock model, delta <= 1 , for which the system fails whenever no shock occurs within a -length time period from the last shock, by supposing that the interarrival times between consecutive shocks are described by a first-order Markov chain (as well as under the binomial shock process, i.e., when the interarrival times between successive shocks have a geometric distribution). Using the Markov chain embedding technique introduced by Chadjiconstantinidis et al. (Adv. Appl. Prob. 32, 2000), we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system. The joint and marginal probability generating functions of these random variables are obtained, and several recursions and exact formulae are given for the evaluation of their probability mass functions and moments. It is shown that the system's lifetime follows a Markov geometric distribution of order (a geometric distribution of order under the binomial setup) and also that it follows a matrix-geometric distribution. Some reliability properties are also given under the binomial shock process, by showing that a shift of the system's lifetime random variable follows a compound geometric distribution. Finally, we introduce a new mixed discrete censored delta -shock model, for which the system fails when no shock occurs within a -length time period from the last shock, or the magnitude of the shock is larger than a given critical threshold . gamma > 0. Similarly, for this mixed model, we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system, under the binomial shock process.
