• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.

• Journal of KSNVE
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• v.8 no.4
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• pp.715-722
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• 1998

An investigation into the stochastic bifurcation and response statistics of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to genrage a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinanary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.399-406
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• 1998

An investigation into the stochastic bifurcation and response statistits of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

• Journal of Korean Society of Transportation
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• v.20 no.5
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• pp.67-79
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• 2002

In this paper, observed trajectories of a vehicle platoon are viewed as one realization of a finite sequence of random trajectories. In this point of view, we develop novel and mathematically rigorous concept of traffic flow variables such as local traffic density, instantaneous traffic flow, and velocity field and investigate their nature on a general probability space of a sequence of random trajectories which represent vehicle trajectories. We present a simple model of random trajectories as an illustrative example and, derive the values of traffic flow variables based on the new definitions in this model. In particular, we construct the model for the sequence of random vehicle trajectories with a system of stochastic differential equations. Each equation of the system nay represent microscopic random maneuvering behavior of each vehicle with properly designed drift coefficient functions and diffusion coefficient functions. The system of stochastic differential equations nay generate a well-defined probability space of a sequence of random vehicle trajectories. We derive the partial differential equation for the expected cumulative plot with appropriate initial conditions. By solving the equation with numerical methods, we obtain the values of expected cumulative plot, local traffic density, and instantaneous traffic flow. In addition, we derive the partial differential equation for the expected travel time to a certain location with appropriate initial and/or boundary conditions, which is solvable numerically. We apply this model to a case of single vehicle trajectory.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1089-1091
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• 1996

This paper presents a design method of Kalman Filter on continuous nonlinear stochastic system via BPF(Block Pulse Function). When we design Kalman Filter on nonlinear stochastic system, we must linearize this systems. In this paper, we uses the adaptive approach scheme and BPF for linearizing of nonlinear system and solving the Riccati differential equation which is usually guite difficult. This method proposed in this paper is simple and have computational advantages. Furthermore this method is very applicable to analysis and design of Kalman Filter on nonlinear stochastic systems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1292-1297
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• 2000

For dynamic system under the external irregular disturbance, a performance of the controller designed by using of the 'Heo-stochastic control methodology' is investigated by simulations and experiments. MIMO Flexible cantilever beam, sticked with piezoceramics used as a sensor and actuator, under the irregular disturbance at bottom is modelled in physical domain. Dynamic moment equation about the system is derived through both the Ito's stochastic differential equation and Fokker-Planck-Kolmogoroff equation and also system's characteristics in stochastic domain is analyzed. In this study, the controller suppresses the amplitude of the system's moment response to the external disturbance. MIMO PI controller('Heo-stochastic MIMO PI controller') is designed in the stochastic domain and the response characteristics are investigated in the time domain

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.440-444
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• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.1-9
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• 2012

Decisions on reliability screening rules and burn-in policies are determined based on the estimated reliability. The variability in a semiconductor manufacturing process does not only causes quality problems but it also makes reliability estimation more complicated. This study investigates the nonuniformity characteristics of integrated circuit reliability according to defect density distribution within a wafer and between wafers then develops optimal burn-in policy based on the estimated reliability. New reliability estimation model based on yield information is developed using a spatial stochastic process. Spatial defect density variation is reflected in the reliability estimation, and the defect densities of each die location are considered as input variables of the burn-in optimization. Reliability screening and optimal burn-in policy subject to the burn-in cost minimization is examined, and numerical experiments are conducted.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.215-224
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• 2017

The moment closure method is an approximation method to compute the moments for stochastic models of chemical reaction systems. In this paper, we develop an analytic estimation of errors generated from the approximation of an infinite system of differential equations into a finite system truncated by the moment closure method. As an example, we apply the result to an essential bimolecular reaction system, the dimerization model.

• International Journal of Control, Automation, and Systems
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• v.5 no.4
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• pp.355-363
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• 2007

The paper deals with the Kalman stochastic filtering problem for linear continuous-time systems with both instantaneous and time-delayed measurements. Different from the standard linear system, the system state is corrupted by multiplicative white noise, and the instantaneous measurement and the delayed measurement are also corrupted by multiplicative white noise. A new approach to the problem is presented by using projection formulation and reorganized innovation analysis. More importantly, the proposed approach in the paper can be applied to solve many complicated problems such as stochastic $H_{\infty}$ estimation, $H_{\infty}$ control stochastic system with preview and so on.