• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.273-278
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• 2009

The determination of the associated weights in the theory of ordered weighted averaging (OWA) operators is one of the important issue. Recently, Wang and Parkan [Information Sciences 175 (2005) 20-29] proposed a minimax disparity approach for obtaining OWA operator weights and the approach is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Liu [International Journal of Approximate Reasoning, accepted] showed that the minimum variance OWA problem of Fuller and Majlender [Fuzzy Sets and Systems 136 (2003) 203-215] and the minimax disparity OWA problem of Wang and Parkan always produce the same weight vector using the dual theory of linear programming. In this paper, we give an improved proof of the minimax disparity problem of Wang and Parkan while Liu's method is rather complicated. Our method gives the exact optimum solution of OWA operator weights for all levels of orness, $0\leq\alpha\leq1$, whose values are piecewise linear and continuous functions of $\alpha$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.12C
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• pp.1125-1132
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• 2005

Ultra-wideband (UWB) ranging poses a set of time delay estimation problems for designers. The possibility of a large error can be a challenging problem for accurate ranging and positioning. An approximate analysis of large error performance of UWB ranging in multipath and multiuser environments is posed. Both analytical and experimental approaches are taken to evaluate the large error variance in a correlation-based serial search scenario.

• Bulletin of the Society of Naval Architects of Korea
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• v.8 no.2
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• pp.25-34
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• 1971

The characters of linear response of ship among irregular waves were researched. But nonlinear characters of ship motion in irregular waves have not been considered. Then the author showed a method to linearize nonlinearity of damping coefficient of ship by making statistically equivalent linear theory and get equivalent gain K from the condition that the difference of variance between linear response and approximate response is minimum and show that the results of correlogram and spectrum, obtained from this method, for model 700 GT Ferry boat agree with the actual response. The author pays a particular attention not to the nonlinear element but to nonlinear system itself.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.65-82
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• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of Korean Society for Quality Management
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• v.30 no.4
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• pp.106-119
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• 2002

The fatigue curve with estimated parameters represents the estimate of the median or mean life at a given applied stress But, in order to assist a designer in making decisions regarding the fatigue failure mode, it is common practice to construct a design curve on the lower or safe side of data. In this study, to overcome the limitations(i.e., no runout, equal variance, and quality of the approximation, etc) of Shen, Wirsching, and Cashman's method which suggested the approximate design curve for nonlinear models using tolerance interval constructed by Owen's method, an algorithm to find design curves under the fatigue model using a parametric bootstrap method, is proposed and illustrated with multiple fatigue data sets.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.93-111
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• 2023

In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-α model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.5
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• pp.605-615
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• 1986

The phase-locked loop(PLL) is a communication receiver which operates as a coherent detector by continuously correcting the phase error. In this paper analysis for the Phase-error behavior of analog phase-locked loop (APLL) in the presence of additive white gaussian noise has been done theoretically and experimentally. A close form solution of the first-order loop is obtained and approximate solutions are derived for the second-order loops with RC, leadlag and perfect integrator filters. The perdormance of APLL's and their characteristics are also thoroughly investigated through experiments. In order to analyze the effect of the stochastic nature on nonlinear dynamics characteristics of the second order APLL, the phase error distribution and its variance have been obtained by using the Fokker-Planck equation. Theoretical results agree closely with those of experiment.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.69-84
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• 1997

We consider a linear calibration problem, $y_i = $$\alpha + \beta (x_i - x_0) + \epsilon_i$, $i=1, 2, {\cdot}{\cdot},n$ $y_f = \alpha + \beta (x_f - x_0) + \epsilon, $ where we observe $(x_i, y_i)$'s for the controlled calibration experiments and later we make inference about $x_f$ from a new observation $y_f$. The objective of the calibration design problem is to find the optimal design $x = (x_i, \cdots, x_n$ that gives the best estimates for $x_f$. We compare Kim(1989)'s Bayesian design which minimizes the expected value of the posterior variance of $x_f$ and some optimal designs from literature. Kim suggested the Bayesian optimal design based on the analysis of the characteristics of the expected loss function and numerical must be equal to the prior mean and that the sum of squares be as large as possible. The designs to be compared are (1) Buonaccorsi(1986)'s AV optimal design that minimizes the average asymptotic variance of the classical estimators, (2) D-optimal and A-optimal design for the linear regression model that optimize some functions of $M(x) = \sum x_i x_i'$, and (3) Hunter & Lamboy (1981)'s reference design from their paper. In order to compare the designs which are optimal in some sense, we consider two criteria. First, we compare them by the expected posterior variance criterion and secondly, we perform the Monte Carlo simulation to obtain the HPD intervals and compare the lengths of them. If the prior mean of $x_f$ is at the center of the finite design interval, then the Bayesian, AV optimal, D-optimal and A-optimal designs are indentical and they are equally weighted end-point design. However if the prior mean is not at the center, then they are not expected to be identical.In this case, we demonstrate that the almost Bayesian-optimal design was slightly better than the approximate AV optimal design. We also investigate the effects of the prior variance of the parameters and solution for the case when the number of experiments is odd.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1493-1510
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• 2000

Theoretical models that can be used to predict the range of main lobe widths and the probability distribution of the peak sidelobe levels of two-dimensionally sparse arrays are presented here. The arrays are considered to comprise microphones that are randomly positioned on a segmented grid of a given size. First, approximate expressions for the expected squared magnitude of the aperture smoothing function and the variance of the squared magnitude of the aperture smoothing function about this mean are formulated for the random arrays considered in the present study. By using the variance function, the mean value and the lower end of the range i.e., the first I percent of the mainlobe distribution can be predicted with reasonable accuracy. To predict the probability distribution of the peak sidelobe levels, distributions of levels are modeled by a Weibull distribution at each peak in the sidelobe region of the expected squared magnitude of the aperture smoothing function. The two parameters of the Weibull distribution are estimated from the means and variances of the levels at the corresponding locations. Next, the probability distribution of the peak sidelobe levels are assumed to be determined by a procedure in which the peak sidelobe level is determined as the maximum among a finite number of independent random sidelobe levels. It is found that the model obtained from the above approach predicts the probability density function of the peak sidelobe level distribution reasonably well for the various combinations of two different numbers of microphones and grid sizes tested in the present study. The application of these models to the design of random, sparse arrays having specified performance levels is also discussed.

• Nuclear Engineering and Technology
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• v.52 no.9
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• pp.2119-2129
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• 2020

Flow-accelerated corrosion (FAC), liquid droplet impingement erosion (LDIE), cavitation and flashing can cause continuous wall-thinning in nuclear secondary pipes. In order to prevent pipe rupture events resulting from the wall-thinning, most NPPs (nuclear power plants) implement their management programs, which include periodic thickness inspection using UT (ultrasonic test). Meanwhile, it is well known in field experiences that the thickness measurement errors (or deviations) are often comparable with the amount of thickness reduction. Because of these errors, it is difficult to estimate wall-thinning exactly whether the significant thinning has occurred in the inspected components or not. In the previous study, the authors presented an approximate estimation procedure as the first step for thickness measurement deviations at each inspected component and the statistical & quantitative characteristics of the measurement deviations using plant experience data. In this study, statistical significance was quantified for the current methods used for wall-thinning determination. Also, the authors proposed new estimation procedures for determining local wall-thinning to overcome the weakness of the current methods, in which the proposed procedure is based on analysis of variance (ANOVA) method using subgrouping of measured thinning values at all measurement grids. The new procedures were also quantified for their statistical significance. As the results, it is confirmed that the new methods have better estimation confidence than the methods having used until now.