THE APPLICATION OF BERNOULLI TRIALSTO THE THEORY OF APPROXIMATION Ayse Bugatekin, Gokhan Gokdere Thermal Science, 2024 In recent years, q-Bernstein polynomials and ?-Bernstein polynomials have emerged as prominent topics in approximation theory. Numerous studies have examined the convergence criteria of these polynomials, highlighting their importance and usefulness. The main idea underlying the article is that the kernels of these polynomials depend on the probabilities of the variable parameter binomial distribution. Taking advantage of this property, we developed a simplified form of these polynomials regarding binomial dependence. This facilitated the calculation of moments for a binomial variable with variable parameters. This method both simplifies the computational processes and allows us to better understand the convergence properties of these polynomials. By examining these reduced forms, important information has been obtained regarding the structure of the underlying distribution. The findings underscore the versatility and power of q-Bernstein and ?-Bernstein polynomials in approximation theory and provide a deeper understanding of their mathematical foundations and potential applications.
Some important details on technical system: Matrix representation, odds ratio, embedding subsystems Mehmet Gurcan, Ayse Bugatekin, Yunus Gural Thermal Science, 2019 The system signature calculated independently from the distribution of the lifetime of the units in the analysis of technical systems enables us to have important information about the reliability of the system. System signature is a probability vector obtained from possible sequences of units according to the moments of deterioration. The reliability of the system can be easily obtained if the distribution of the lifetime of the units is known and if the distributions can be listed as open among themselves. However, when the distributions cannot be listed as open among themselves, it is a very important finding that the system reliability is calculated with the help of system signature by generating the order statistics. It is also possible to calculate the odds ratios of the units when the lifetime of the units is certain. In this study, odds ratio could be calculated by calculating the probability of fail the system of each unit by considering the possible situations of the system, as in the system signature, regardless of the distribution of lifetime of the units. In addition, the technical system is represented by a matrix by establishing a relation between the system fail probabilities of the units obtained in the study and the system signature. However, examples of some technical systems given in the study.
Combined technical system Ayse Bugatekin, Mehmet Gurcan, Yunus Gural Thermal Science, 2019 Technical systems are important systems frequently used by applied sciences. Proper operation of technical systems is very important. Therefore, the statistically calculated reliability of a technical system is an important indicator for the system. Technical systems occur in different structures depending on the connection types of the components that constitute the system. The connection diagrams of components can be encountered in a highly complex situation. In such cases, the reliability of the system is difficult to calculate. There is no single method in the literature to calculate the reliability of a technical system. The methods in the literature differ according to the connection types of the systems. In this study, a method and a MATLAB program have been proposed for calculating the reliability of k-out-of-n F systems and consecutive k-out-of-n F systems. The proposed method can also be used for different connections.
Numerical investigation of reliability of pump systems from thermal power plants Ayse Bugatekin Thermal Science, 2018 This article deals with numerical investigation of reliability of pump systems from thermal power plants. The reliability is examined by using intensity function for a system composed of n-linearly ordered pumps. The time between failures of pumps is taken as experimental. Firstly, appropriate model for the data is determined. Estimates of parameters are obtained with maximum likelihood method and intensity function models are written. Finally, reliability of consecutive 3-out-of-5:F systems are calculated for certain time periods by using the obtained intensity functions.
Moments of sample extremes of order statistics from discrete uniform distribution and numerical results Sinan Calik, Ayse Bugatekin Thermal Science, 2018 In this study, the mth raw moments of sample extremes of order statistics from discrete uniform distribution are obtained. The results of sample extremes of order statistics of random variable for the independent and identically discrete uniform distribution are given. Numerical values are shown in table form
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