• Kyungpook Mathematical Journal
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• v.21 no.2
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• pp.251-262
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• 1981

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.83-86
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• 1980

• Kyungpook Mathematical Journal
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• v.14 no.2
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• pp.185-194
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• 1974

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2084-2093
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• 2022

Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is approximated with the sum of lognormal random variables after minimal cutsets are obtained, and rare-event approximation is applied. As handling complicated analytic expressions for the sum of lognormal random variables is challenging, several approximation methods, especially Monte Carlo simulation, are widely used in practice for uncertainty analysis. In this study, a theoretical approach for analyzing the sum of lognormal random variables using an efficient numerical integration method is proposed for uncertainty analysis in probability safety assessments. The change of variables from correlated random variables with a complicated region of integration to independent random variables with a unit hypercube region of integration is applied to obtain an efficient numerical integration. The theoretical advantages of the proposed method over other approximation methods are shown through a benchmark problem. The proposed method provides an accurate and efficient approach to calculate the uncertainty of the top event in probabilistic safety assessment when the uncertainties of basic events are described with lognormal random variables.

• Advances in Computational Design
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• v.4 no.1
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• pp.15-32
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• 2019

One of the efficient and useful tools to achieve the optimal design of structures is employing the sensitivity analysis in the finite element model. In the numerical optimization process, often the semi-analytical method is used for estimation of derivatives of the objective function with respect to design variables. Numerical methods for calculation of sensitivities are susceptible to the step size in design parameters perturbation and this is one of the great disadvantages of these methods. This article uses complex variables method to calculate the sensitivity analysis and combine it with discrete sensitivity analysis. Finally, it provides a new method to obtain the sensitivity analysis for linear structures. The use of complex variables method for sensitivity analysis has several advantages compared to other numerical methods. Implementing the finite element to calculate first derivatives of sensitivity using this method has no complexity and only requires the change in finite element meshing in the imaginary axis. This means that the real value of coordinates does not change. Second, this method has the lower dependency on the step size. In this research, the process of sensitivity analysis calculation using a finite element model based on complex variables is explained for linear problems, and some examples that have known analytical solution are solved. Results obtained by using the presented method in comparison with exact solution and also finite difference method indicate the excellent efficiency of the proposed method, and it can predict the sustainable and accurate results with the several different step sizes, despite low dependence on step size.

• East Asian mathematical journal
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• v.33 no.3
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.937-945
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• 2017

The purpose of using a control chart is to detect any change that occurs in the process. When control charts are used to monitor processes, we want to identify this changes as quickly as possible. Many problems in quality control involve a vector of observations of several characteristics rather than a single characteristic. Multivariate CUSUM or EWMA charts have been developed to address the problem of monitoring covariance matrix or the joint monitoring of mean vector and covariance matrix. However, control charts tend to work poorly when we use the highly correlatted variables. In order to overcome it, Hawkins (1991) proposed the use of regression adjustment variables. In this paper, to monitor covariance matrix, we investigate the performance of MEWMA-type control charts with and without the use of regression adjusted variables.

• International Journal of Aeronautical and Space Sciences
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• v.5 no.2
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• pp.1-8
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• 2004

Real-Time Kinematic GPS positioning is widely used for many applications.Resolving ambiguities is the key to precise positioning. Integer ambiguity resolution isthe process of resolving the unknown cycle ambiguities of double difference carrierphase data as integers. Two important issues of resolving are efficiency andreliability. In the conventional search techniques, we generally used chi-squarerandom variables for decision variables. Mathematically, a chi-square random variableis the sum of mutually independent, squared zero-mean unit-variance normal(Gaussian) random variables. With this base knowledge, we can separate decisionvariables to several normal random variables. We showed it with related equationsand conceptual diagrams. With this separation, we can improve the computationalefficiency of the process without losing the needed performance. If we averageseparated normal random variables sequentially, averaged values are also normalrandom variables. So we can use them as decision variables, which prevent from asudden increase of some decision variable. With the method using averaged decisionvalues, we can get the solution more quicklv and more reliably.To verify the performance of our proposed algorithm, we conducted simulations.We used some visual diagrams that are useful for intuitional approach. We analyzedthe performance of the proposed algorithm and compared it to the conventionalmethods.

• Journal of the Ergonomics Society of Korea
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• v.19 no.3
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• pp.23-37
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• 2000

Usability is one of the most important factors that affect customers' decision to purchase a product. Several studies have been conducted to model the relationship between the product design variables and the product usability. Since there could be hundreds of design variables to be considered in the model, a variable screening method is required. Traditional variable screening methods are based on expert opinions (Expert screening) in most Kansei engineering studies. Suggested in this study are statistical methods for screening important design variables by using the principal component regression(PCR), cluster analysis, and partial least squares(PLS) method. Product variables with high effect (PCR screening and PLS screening) or representative variables (Cluster screening) can be used to model the usability. Proposed variable screening methods are used to model the usability for 36 audio/visual products. The three analysis methods (PCR, Cluster, and PLS) show better model performance than the Expert screening in terms of $R^2$, the number of variables in the model, and PRESS. It is expected that these methods can be used for screening the product design variables efficiently.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.12
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• pp.635-645
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• 2020

This research was conducted to achieve several objectives and focus research was based on financial behavior theory and prospect theory as grounded theory e.g., investigate the financial decision-making behavior between financial and real assets investment, and confirm the relationship existing between herding behavior and overconfidence factors to the level of loss and regret aversion, and financial literacy into real assets investment decisions. The study used 220 real estate auction respondents as investor samples at the State Assets and Auction Service Office Makassar, South Sulawesi, Indonesia. Data was collected through the use of a questionnaire consisting of 23 questions to measure the variables. Moreover, the research data passed through several feasibility tests like the inner and outer modeling by Partial Least Square - Structural equation model (PLS-SEM) while the hypotheses formulated were also tested to determine the magnitude of the variable relationship. Through the use of the direct and intervening test, loss and regret aversion variables have a positive and significant effect while financial literacy variables have no significant effect. There is a slight difference in the decision-making process for real assets and financial assets investors. Investment decision making behavior in the financial assets sector requires less complicated decisions compared to the decisions related to real assets investments.