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Öğe Alt ve üst rekor değerler için bir karma model(Ege Üniversitesi, Fen Bilimleri Enstitüsü, 2015) Kozan, Agah; Tanıl, HalilBu çalışmada, birbirinden bağımsız ve aynı sürekli dağılıma sahip rasgele değişkenler dizisi üzerinde tanımlı olan alt ve üst rekor modelleri birleştirilmiş ve elde edilen bu yeni modeldeki rasgele değişkenlere "Karma-Rekor Değerler" adı verilmiştir. Karma-rekorlar ile güncel rekorlar (current records) arasındaki ilişki üzerinde durularak, bu modelin literatürdeki yeri saptanmıştır. Ayrıca, karma-rekor sayısı ve karma-rekor zamanlarına ilişkin dağılımlar ortaya konmuştur. Son olarak, karma-rekorların küçükten büyüğe sıralanması ile ortaya çıkan ve "Sıralı-Karma-Rekorlar" adı verilen modele ilişkin ortak olasılık yoğunluk fonksiyonu elde edilmiştir.Öğe Bir sistemin ürettiği en düşük M skor ve azalan genelleştirilmiş sıra istatistikleri(Ege Üniversitesi, 2010) Kozan, Agah; Tanıl, HalilBu çalışmada, bir sistemin ürettiği, bağımsız ve aynı sürekli F dağılımına sahip skorlar dikkate alındığında, ℓ’nci yenilenme sonrası en düşük m skor listesine dayalı sıra istatistikleri tanımlanmış ve bu sıra istatistiklerinin marjinal ve ortak olasılık yoğunluk fonksiyonları elde edilmiştir. Ayrıca, bu listeye dayalı sıra istatistikleri ile azalan genelleştirilmiş sıra istatistikleri arasındaki ilişki ortaya konmuştur. Son olarak, tanımlanan sıra istatistiklerinin dağılım fonksiyonu, tekli ve çarpım momentleri, karakteristik fonksiyonları elde edilmiş ve birtakım yeni indirgeme bağıntılarına ulaşılmıştır.Öğe Bir sistemin ürettiği en düşük M skor ve azalan genelleştirilmiş sıra istatistikleri(Ege Üniversitesi, 2010) Kozan, Agah; Tanıl, HalilAzalan (dual) genelleştirilmiş sıra istatistikleri, En düşük m skor, En yüksek m skor, Azalan rekorlar, Azalan k - rekorlar, Meijer'in G fonksiyonu, indirgeme bağıntıları.;Bu çalışmada, bir sistemin ürettiği, bağımsız ve aynı sürekli F dağılımına sahip skorlar dikkate alındığında, ?{nci yenilenme sonrası en düşük m skor listesine dayalı sıra istatistikleri tanımlanmış ve bu sıra istatistiklerinin marjinal ve ortak olasılık yoğunluk fonksiyonları elde edilmiştir. Ayrıca, bu listeye dayalı sıra istatistikleri ile azalan genelleştirilmiş sıra istatistikleri arasındaki ilişki ortaya konmuştur. Son olarak, tanımlanan sıra istatistiklerinin dağılım fonksiyonu, tekli ve çarpım momentleri, karakteristik fonksiyonları elde edilmiş ve birtakım yeni indirgeme bağıntılarına ulaşılmıştır.;Lower generalized order statistics, Bottom m scores, Top m scores, Lower record values, Lower k - th record values, Meijer's G function, Recurrence relations.Öğe Dual Response Surface Optimization Based on Skill Scores(Univ Kebangsaan Malaysia, Fac Science & Technology, 2024) Kozan, Agah; Zeybek, Melis; Kozan, ElifThe popular formulations of dual -response optimization are constructed on minimizing a function of bias and system variability. This study provides an opportunity to evaluate the dual response surface ( DRS ) problem from a different perspective by adapting two new terms such that internal and external quality forecasts. The background of the proposed approach focuses on the relationship between internal and external quality forecasts and discusses the DRS problem in regards of skill scores by defining a model quality criterion. Skill is the relative accuracy of the forecast and defines a correspondence between forecast of interest and reference forecasts. The reference forecast does not require any knowledge or modelling; thus, it is an unskilled forecast. In this context, skill score is a measure of this relative improvement and widely used in evaluating the performance of operational and experimental forecasts. An alternative version of mean square error ( MSE ) which is reconstructed by skill scores and model quality criterion is proposed as an objective function for the DRS problem. Integrating the relationship between internal and external quality forecasts into such a response function can improve the effectiveness and cooperation of the applied technique. The proposed approach has a flexible structure and provides decision makers alternative solutions for different values of the model quality criterion. The proposed procedure is discussed by conducted a simulation study and demonstrated in an engineering process.Öğe Exceedance statistics based on bottom-k-lists(Springer, 2024) Kozan, Agah; Uyar, Burak; Tanil, HalilSimilar to usual lower records, Bottom-k-lists (Kozan and Tanil, & Idot;statistik J Turk Stat Assoc 13:73-79, 2013) have a wide range of practical applications in meteorology, hydrology, sports, etc. Also, exceedance statistics can be viewed as a close relative to tolerance limits-an important field of statistical science. In this study, an idea of combining these two important subjects together is studied and an exceedance statistic is defined based on bottom-k-lists in an independent and identically distributed (iid) continuous random sequence. Probability mass function (pmf) of a selected exceedance statistic is obtained. Also, an illustrative application of the exceedance statistic is given.Öğe INTERVAL ROBUST DESIGN ON QUALITY IMPROVEMENT FOR N ON-NORMAL AND CONTAMINATED RESPONSES(University Cincinnati Industrial Engineering, 2024) Baydar, Atakan; Zeybek, Melis; Kozan, Elif; Kozan, AgahThe basis of robust parameter design is the creation of a design that can resist the negative effects caused by uncontrollable or difficult-to-control external and environmental factors, which affect the product parameters in achieving product design during product realization activities. Robustness is the ability of a product or process to be least affected by variabilities caused by external factors. The success of the response surface methodology generally depends on a model chosen to fit the data distribution. Making incorrect assumptions regarding data distribution when creating response surface models can affect the effectiveness of the quality improvement strategy used. Non-normal or contaminated data is a common phenomenon in quality improvement applications. Although non-normal data is common in robust parameter applications, it is often the case that users ignore the underlying distribution shape of the data at the modeling stage and use normal theory techniques naively. This study proposes a dual response surface approach based on robust confidence intervals for cases where the experimental data do not meet normality assumptions or have contaminated data distribution. A new dual response surface methodology is proposed based on modeling the MAD - t confidence interval, S-n - t confidence interval, and Q(n) - t confidence interval formulations with the response surface methodology. All the proposed methods make the process median unbiased for the mean using the skewness of the experimental data. Two well-known experimental design studies are used to demonstrate the procedure and its advantages.Öğe İstatistik Bölümü Bilgisayar Laboratuvarı altyapı projesi(Ege Üniversitesi, 2015) Mert, Ali; Köksoy, Onur; Kozan, Agah[Abstract Not Available]Öğe A modified Spearman's rho parameter-free test statistic for early detection of newly emerging phenomena(Taylor & Francis Inc, 2019) Tanil, Halil; Kozan, AgahThis paper presents a new and powerful parameter-free test statistic for early detection of newly emerging phenomena, especially for small sample sizes. the exact distribution of the proposed test statistic is obtained. First four cumulants of it and its critical values at some selected levels of significances are calculated and summarized. A comparative simulation study is performed with some well-known rank-based tests to see its power performance.Öğe A modified Spearman's rho parameter-free test statistic for early detection of newly emerging phenomena(Taylor & Francis Inc, 2022) Tanil, Halil; Kozan, AgahThis paper presents a new and powerful parameter-free test statistic for early detection of newly emerging phenomena, especially for small sample sizes. The exact distribution of the proposed test statistic is obtained. First four cumulants of it and its critical values at some selected levels of significances are calculated and summarized. A comparative simulation study is performed with some well-known rank-based tests to see its power performance.Öğe A nonparametric partially sequential test for early detection of newly emerging phenomena(Taylor & Francis Ltd, 2022) Tanil, Halil; Kozan, AgahAn event encountered for the first time can become a common phenomenon in a population through transmission over time. This study focuses on nonparametric partially sequential test statistics in order to early detect such events. For this purpose, firstly, the partially sequential test statistic given in Mukherjee [1] is considered. Then, with a modification of this statistic, a new nonparametric partially sequential test statistic that works at almost the desired alpha level of significance is revealed. Also, based on Monte-Carlo simulations, the proposed test statistic is shown to be more powerful than Mukherjee's statistic. Lastly, two illustrative numerical examples are also given.Öğe On Distributional Properties of Record Ranges and Record Range Times(2017) Kozan, Agah; Tanıl, Halil…
