• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.5
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• pp.577-588
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• 2011

This paper provides a novel extended Moving Least Squares(MLS) difference method for the potential problem with weak and strong discontinuities. The conventional MLS difference method is enhanced with jump functions such as step function, wedge function and scissors function to model discontinuities in the solution and the derivative fields. When discretizing the governing equations, additional unknowns are not yielded because the jump functions are decided from the known interface condition. The Poisson type PDE's are discretized by the difference equations constructed on nodes. The system of equations built up by assembling the difference equations are directly solved, which is very efficient. Numerical examples show the excellence of the proposed numerical method. The method is expected to be applied to various discontinuity related problems such as crack problem, moving boundary problem and interaction problems.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.277-286
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• 1998

This paper investigates the problem of determining optimal replacement policies for equipment subject to failures with cyclic rates. In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonhomogeneous process with/without a cyclic component in the failure rate function. The analytical results for various situations are presented along with numerical examples using simulated data.

• Journal of the Korean Society of Visualization
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• v.9 no.4
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• pp.22-27
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• 2011

In this study, we present methods of coupling a commercial code, ANSYS CFX, and the user Fortran codes for solving an unsteady electro-osmotic flow around a pair of electrodes, receiving DC, attached to the top and the bottom walls of a two-dimensional cavity. We developed a module of Fortran programs for solving the ion-transport equations as well as the Poisson equations for the potential to be used in coupling with the CFX. We present how the developed codes are applied to solving the transient DC electro-osmotic flow problem within a simple cavity. We also address various problems encountered during the development process and explain why such problems are raised.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.881-889
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• 2005

In this study, we consider characteristics of waiting times in single-server 3-node tandem queues with a Poisson arrival process, finite buffers and deterministic or non-overlapping service times at each queue. There are three buffers: one at the first node is infinite and the others are finite. The explicit expressions of waiting times in all areas of the systems, which are driven as functions of finite buffer capacities, show that the sojourn time does not depend on the finite buffer capacities and also allow one to compute and compare characteristics of waiting times at all areas of the system under two blocking policies: communication and manufacturing blocking. As an application of these results, moreover, an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on waiting times is considered. Some numerical examples are also provided.

• Journal of Korean Society for Quality Management
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• v.26 no.4
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• pp.111-123
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• 1998

We consider the problem of modeling count data where the observation period is determined by the life time of the system under study. We assume random effects or a frailty model to allow for a possible association between the death times and the counts. We assume that, given a random effect or a frailty, the death times follow a Weibull distribution with a hazard rate. For the counts, given a frailty, a Poisson process is assumed with the intensity depending on time. A gamma distribution is assumed for the frailty model. Maximum likelihood estimators of the model parameters are obtained. A model for the time to death and the number of failures system received is constructed and consequences of the model are examined.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.533-540
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• 2000

The problem of information related to I poission experiments, each having a distinct failure rate $\theta$i I=1,2,…,I, is considered. Instead of using a standard exchangeable prior for $\theta$=($\theta$1,$\theta$2,…,$\theta$I), we consider a partition of the experiments and take the $\theta$i's belonging to the same partition subgroup to be exchangeable and the $\theta$i's belonging to distinct subgroups to be independent. And we perform Gibbs sampling approach for Bayesian inference on $\theta$ conditional on a partition. Numerical study using real data is provided.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.967-973
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• 1995

A neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector to estimate the mass of an object Since there is uncertainty about the location of the axis of the beam relative to the object, we could have aiming errors which may lead to incorrect information about the object. Under the two assumptions that neutral particle scattering distribution and aiming errors have a circular normal distribution respectively, we have derived an exact probability distribution of neutral particles. It becomes a Poison-power function distribution., We proved monotone likelihood ratio property of tlis distribution. This property can be used to find a criteria for the hypothesis testing problem.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.701-721
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• 2007

Recently, a new singular function(NSF) method was posed to get accurate numerical solution on quasi-uniform grids for two-dimensional Poisson and interface problems with domain singularities by the first author and his coworkers. Using the singular function representation of the solution, dual singular functions, and an extraction formula for stress intensity factors, the method poses a weak problem whose solution is in $H^2({\Omega})$ or $H^2({\Omega}_i)$. In this paper, we show that the singular functions, which are not in $H^2({\Omega})$, also satisfy the integration by parts and note that this fact suggests the possibility of different choice of the weak formulations. We show that the original choice of weak formulation of NSF method is critical.

• Journal of Applied Reliability
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• v.4 no.2
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• pp.91-104
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• 2004

In this paper we consider the concurrent spare part(CSP) requirements problem of new equipment system. When a part fails, the part is replaced and the repair of failed part is impossible and cannibalization is allowed. We assume that the failure of a part knows a Poisson process. The operational availability concept in CSP is defined, and derive a formula to calculate the operational availability using expected machine operating time during CSP period. A mathematical model is derived for making an CSP requirement determination subject to the constraint of satisfying any given operational availability limitation and an heuristic solution search procedure is derived. An illustrative example is shown to explain the solution procedure.