• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.107-114
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• 2013

Modelling of failures is an important element of reliability modelling. Empirical modelling approach suitable for complex item is explored in this paper. First step of the empirical modelling approach is to plot hazard function, density function, Weibull probability plot as well as cumulative intensity function to see which model fits best for the given data. Next step of the empirical modelling approach is select appropriate model for the data and fit the parametric model accordingly and estimate the parameters.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.125-134
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• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.3
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• pp.147-160
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• 2020

A stochastic probabilistic model for harbor structures such as rubble-mound breakwater has been formulated by using the generalized Wiener process considering the nonlinearity of damage drift and its nonlinear uncertainty, by which the damage path with real-time can be tracked, the residual useful lifetime at some age can also be analyzed properly. The formulated stochastic model can easily calculate the probability of failure with the passage of time through the probability density function of cumulative damage. In particular, the probability density functions of residual useful lifetime of the existing harbor structures can be derived, which can take into account the current age, its present damage state and the future damage process to be occurred. By using the maximum likelihood method and the least square method together, the involved parameters in the stochastic model can be estimated. In the calibration of the stochastic model presented in this paper, the present results are very well similar with the results of MCS about tracking of the damage paths as well as evaluating of the density functions of the cumulative damage and the residual useful lifetime. MTTF and MRL are also evaluated exactly. Meanwhile, the stochastic probabilistic model has been applied to the rubble-mound breakwater. The related parameters can be estimated by using the experimental data of the cumulative damages of armor units measured as a function of time. The theoretical results about the probability density function of cumulative damage and the probability of failure are very well agreed with MCS results such that the density functions of the cumulative damage tend to move to rightward and the amounts of its uncertainty are increased as the elapsed time goes on. Thus, the probabilities of failure with the elapsed time are also increased sharply. Finally, the behaviors of residual useful lifetime have been investigated with the elapsed age. It is concluded for rubble-mound breakwaters that the probability density functions of residual useful lifetime tends to have a longer tail in the right side rather than the left side because of the gradual increases of cumulative damage of armor units. Therefore, its MRLs are sharply decreased after some age. In this paper, the special attentions are paid to the relationship of MTTF and MRL and the elapsed age of the existing structure. In spite of that the sum of the elapsed age and MRL must be equal to MTTF deterministically, the large difference has been shown as the elapsed age is increased which is due to the uncertainty of cumulative damage to be occurred in the future.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.8
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• pp.1-6
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• 2011

In this paper, another analytical approach for dual-hop amplify-and-forward(AF) relay systems is proposed over Rayleigh fading channels. Previous approaches derived the moment generating function(MGF) by using the cumulative distribution function(CDF) or probability density function(PDF) of the received signal-to-noise ratio(SNR) for source-relay-destination(S-R-D) link. Then, the average symbol error rate is expressed based on derived MGFs. In this paper, another new approach is proposed. It means that the MGF is directly derived by utilizing PDFs of both source-relay(S-R) and relay-destination(R-D) links. Additionary, the newly derived MGF is compared and analyzed with previous ones. Furthermore, simulation results are presented to validate the accuracy of proposed analytical expression. Based on this, it is confirmed that the proposed analytical approach can be a another solution for dual-hop AF relay systems.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.243-247
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• 2014

Let {$X_n$, $n{\geq}1$} be a sequence of i.i.d. random variables with absolutely continuous cumulative distribution function(cdf) F(x) and the corresponding probability density function(pdf) f(x). In this paper, we give characterizations of Pareto and Weibull distribution by considering conditional expectations of record values.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.33-41
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• 2006

Theoretical-numerical approach of combustion instability in a specific rocket engine is conducted with parametric response functions. Fluctuating instantaneous burning rate is assumed to be functionally coupled with acoustic pressures and have a finite or time-varying amplitudes and phase lags. Only when the amplitudes and phases of combustion response function are sufficiently large and small respectively, the triggered unstable waves are amplified.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1276-1282
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• 2013

This paper proposes a stochastic modeling of plug-in electric vehicles (PEVs) distribution in power systems, and analyzes the corresponding clustering characteristic. It is essential for power utilities to estimate the PEV charging demand as the penetration level of PEV is expected to increase rapidly in the near future. Although the distribution of PEVs in power systems is the primary factor for estimating the PEV charging demand, the data currently available are statistics related to fuel-driven vehicles and to existing electric demands in power systems. In this paper, we calculate the number of households using electricity at individual ending buses of a power system based on the electric demands. Then, we estimate the number of PEVs per household using the probability density function of PEVs derived from the given statistics about fuel-driven vehicles. Finally, we present the clustering characteristic of the PEV distribution via case studies employing the test systems.

• Journal of the Society of Naval Architects of Korea
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• v.56 no.5
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• pp.383-388
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• 2019

It is essential to reduce the Infra-red signature for increasing ship's survivability in ship design stage. However the ship's IR signature is quite sensitive to the maritime and atmosphere. Therefore, it is very important to select the marine meteorological data to be applied to the signature analysis. In this study, we selected the three meteorological sample sets from the population of the Korea Meteorological Administration's marine environment data in 2017. These samples were selected through the two-dimensional stratified sampling method, taking into account the geopolitical threats of the Korean peninsula and the effective area of the buoy. These sample sets were applied to three naval ships classified by their tonnage, and then the IR signature analysis was performed to derive the Contrast Radiant Intensity (CRI) values. Based on the CRI values, the validity of each sample set was determined by comparing Cumulative Distribution Function (CDF), and Probability Density Function (PDF). Also, we checked the degree of scattering in each sample set and determined the efficiency of analysis time and cost according to marine meteorological sample sets to confirm the possibility of a probabilistic method. Through this process, we selected the standard for optimization of marine meteorological sample for ship IR signature analysis. Based on this optimization sample, by applying probabilistic method to the management of IR signature for naval ships, the robust design is possible.