• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.185-191
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• 2013

Kiefer (1961) studied asymptotic behavior of empirical distribution using the law of the iterated logarithm. Robertson and Wright (1974a) discussed whether this type of result would hold for a maximum likelihood estimator of a stochastically ordered distribution function; however, we show that this cannot be achieved. We provide only a partial answer to this problem. The result is applicable to both estimation and testing problems under the restriction of stochastic ordering.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.232-237
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• 2001

The evaluation of specimen thickness effect of fatigue crack growth life by the simulation of probabilistic fatigue crack growth is presented. In this paper, the material resistance to fatigue crack growth is treated as a spatial stochastic process, which varies randomly on the crack surface. Using the previous experimental data, the non-Gaussian(eventually Weibull, in this report) random fields simulation method is applied. This method is useful to estimate the probability distribution of fatigue crack growth life and the variability due to specimen thickness by simulating material resistance to fatigue crack growth along a crack path.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.199-202
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• 2001

This article deals with stochastic reliability systems that include a repair facility and unreliable machines: the main facility of working and an auxiliary facility of "super-reserve" machines. The number of super-reserve machines are random number with a arbitrarily distribution and working machines break down exponentially. Defective machines line up for repair, whose durations are arbitrarily distributed. Refurbished machines return to the main facility. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance until all of super-reserve machines are exhausted. Then, the busy period is regenerated. The whole system also falls into the category of closed queues, with more options than those of basic models. The techniques include two-variate Markov and semi-regenerative processes, and a duality principle, to find the probability distribution of the number of intact machines. Explicit formulas obtained demonstrate a relatively effortless use of functionals of the main stochastic characteristics (such as expenses due to repair, maintenance, waiting, and rewards for higher reliability) and optimization of their objective function. Applications include computer networking, human resources, and manufacturing processes.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

• Magazine of the Korean Society of Agricultural Engineers
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• v.35 no.3
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• pp.91-99
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• 1993

The loads and resistances are random in nature. It Is thus necessary to consider these variabilities for more reasonable and reliable structural analysis. The purpose of the present study is to develop a stochastic finite element program which can analyze plane structures. The model requires only the means, standard deviations and distribution types of the load and resistance varualbes. This model can determine from the analysis the means and standard deviations of nodal displacement for all nodal points. The implemention results show good agreement at 10% significant level with the simulation results, if material properties and load conditions fallow the normal distribution.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.439-454
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• 2013

This study presents a Bayesian multiple change-point detection approach to segment and classify the observations that no longer come from an initial population after a certain time. Inferences are based on the multiple change-points in a sequence of random variables where the probability distribution changes. Bayesian multiple change-point estimation is classifies each observation into a segment. We use a truncated Poisson distribution for the number of change-points and conjugate prior for the exponential family distributions. The Bayesian method can lead the unsupervised classification of discrete, continuous variables and multivariate vectors based on latent class models; therefore, the solution for change-points corresponds to the stochastic partitions of observed data. We demonstrate segmentation with real data.

• Proceedings of the KIEE Conference
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• 2004.11b
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• pp.69-71
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• 2004

This paper presents a method to predict failure probability related to aging. To calculate failure probability, the Weibull distribution is used due to age-related reliability. The Weibull distribution has shape and scale parameters. Each estimated parameter is obtained from Data Analytic Method (Type II Censoring) which is relatively simpler and faster than the traditional calculation ways for estimating parameters. Also, this paper shows the calculation procedures of a probabilistic failure prediction through a stochastic data analysis. Consequently, the proposed methods would be likely to permit that the new deregulated environment forces utilities to reduce overall costs while maintaining an age-related reliability index.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• Journal of Korean Society for Quality Management
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• v.35 no.4
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• pp.61-66
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• 2007

The performance of a building material degrades as time goes by and the failure of the material is often defined as the point at which the performance of the material reaches a pre-specified degraded level. Based on a stochastic deterioration model, a performance based service life prediction method for building materials and components is developed. As a stochastic degradation model, a gamma process is considered and lifetime distribution and service life of a material are predicted using the degradation model. A numerical example is provided to illustrate the use of the proposed service life prediction method.