• Korean Journal of Computational Design and Engineering
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• v.15 no.3
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• pp.178-188
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• 2010

This paper addresses the problem of determining if two surfaces intersect tangentially or transversally in a mathematically consistent manner and approximating an intersection curve. When floating point arithmetic is used in the computation, due to the limited precision, it often happens that the decision for tangential and transversal intersection is not clear cut. To handle this problem, in this paper, interval arithmetic is proposed to use, which provides a mathematically consistent way for such decision. After the decision, the intersection is traced using the validated ODE solver, which runs in interval arithmetic. Then an iterative method is used for computing the accurate intersection point at a given arc-length of the intersection curve. The computed intersection points are then approximated by using a B-spline curve, which is provided as one instance of intersection curve for further geometric processing. Examples are provided to demonstrate the proposed method.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.181-187
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• 2004

One of objectives in epidemiologic studies is to detect the amount of change caused by a specific risk factor. Risk ratio is one of the most useful measurements in epidemiology. When we perform the inference for this measurement with rare events, the standard approach based on the normal approximation may fail, in particular when there are no disease cases observed. In this paper, we discuss and evaluate several existing methods for constructing a confidence interval of risk ratio through simulation when the disease of interest is a rare event. The results in this paper provide guidance with how to construct interval estimates for risk difference and risk ratio when there are no disease cases observed.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.435-446
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• 2012

Epidemiologic studies frequently try to estimate the impact of a specific risk factor. The risk difference and the risk ratio are generally useful measurements for this purpose. When using such measurements for rare events, the standard approaches based on the normal approximation may fail, in particular when no events are observed. In this paper, we discuss and evaluate several existing methods to construct confidence intervals around risk differences and risk ratios using Monte-Carlo simulations when the disease of interest is rare. The results in this paper provide guidance how to construct interval estimates of the risk differences and the risk ratios when no events are detected.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.359-364
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• 2002

In case of pn control chart often used in mass production system of plant industry and so on, we could evaluate it's performance by the approximation to normal distribution. It has many differences according to sample sizes and defective fraction, and have disadvantage that needs much samples to use the normal distribution approximation. Existent control charts can not detect the cause of process something wrong because it is taking the sampling intervals of fixed length about all times from the process. Therefore, to overcome this shortcoming we use VSI(variable sampling intervals) techniques in this paper. This technique takes a long sampling interval to have the next sampling point if the sample point is in stable state, and if the sample point is near control lines, it takes short sampling interval because the probability to escape control limit is high. To analyze performance of pn control charts that have existent fixed sampling intervals(FSI) and that use VSI technique, we compare ATS of two charts, and analyze the performance of each control chart by the sample sizes, process fraction defective and control limits that Ryan and Schwertman had proposed.

• The KIPS Transactions:PartD
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• v.15D no.4
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• pp.475-484
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• 2008

Nowadays, lots of data mining applications based on continuous and online real time are increasing by the rapid growth of the data processing technique. In order to do association rule mining in that application, we have to use new techniques to find the frequent itemsets. Most of the existing techniques to find the frequent itemsets should scan the total database repeatedly. But in the application based on the continuous and online real time, it is impossible to scan the total database repeatedly. We have to find the frequent itemsets with only one scan of the data interval for that kind of application. So in this paper we propose an approximation technique which finds the maximum size of the frequent itemsets and items included in the maximum size of the frequent itemsets for the processing of association rule mining.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.613-629
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• 2007

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

• IE interfaces
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• v.22 no.3
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• pp.214-222
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• 2009

In the early design stage, system reliability must be estimated from life testing data at the component level. Previously, a point estimate of system reliability was obtained from the unbiased estimate of the component reliability after assuming that the number of failed components for a given time followed a binomial distribution. For deriving the confidence interval of system reliability, either the lognormal distribution or the normal approximation of the binomial distribution was assumed for the estimator of system reliability. In this paper, a new estimator is used for the component level reliability, which is biased but has a smaller mean square error than the previous one. We propose to use the beta distribution rather than the lognormal or approximated normal distribution for developing the confidence interval of the system reliability. A numerical example based on Monte Carlo simulation illustrates advantages of the proposed approach over the previous approach.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.4
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• pp.510-519
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• 2015

Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.2
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• pp.56-64
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• 1998

Multi-layered perceptrons that are a nonlinear neural network model, have been widely used for various applications mainly thanks to good function approximation capability for nonlinear fuctions. However, for digital hardware implementation of the multi-layere perceptrons, the quantization scheme using "look-up tables (LUTs)" is commonly employed to handle nonlinear signmoid activation functions in the neworks, and thus requires large amount of storage to prevent unacceptable quantization errors. This paper is concerned with a new effective methodology for digital hardware implementation of multi-layered perceptrons, and proposes a "piecewise affine approximation" method in which input domain is divided into (small number of) sub-intervals and nonlinear sigmoid function is linearly approximated within each sub-interval. Using the proposed method, we develop an expression and an error backpropagation type learning algorithm for a multi-layered perceptron, and compare the performance with the quantization method through Monte Carlo simulations on XOR problems. Simulation results show that, in terms of learning convergece, the proposed method with a small number of sub-intervals significantly outperforms the quantization method with a very large storage requirement. We expect from these results that the proposed method can be utilized in digital system implementation to significantly reduce the storage requirement, quantization error, and learning time of the quantization method.quantization method.