• Proceedings of the KSME Conference
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• 2004.04a
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• pp.365-370
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• 2004

Generally, component and FR-4 board are connected by solder joint. Because material properties of components and FR-4 board are different, component and FR-4 board show different coefficients of thermal expansion (CTE) and thus strains in component and board are different when they are heated. That is, the differences in CTE of component and FR-4 board cause the dissimilarity in shear strain and solder joint' failure. The first order Taylor series expansion of the limit state function incorporating with Tresca failure criterion is used in order to estimate the failure probability of solder joints under heated condition. Using shear stresses and shear strains appeared on the solder joint, we estimate the failure probability of solder joints with the Tresca failure criterion. The effects of random variables such as CTE, distance of the solder joint from the neutral point(DNP), temperature variation and height of solder on the failure probability of the solder joint are systematically studied by using the failure probability model with first order reliability method(FORM).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.5
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• pp.607-617
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• 1998

Comparisons of joint probability density distribution obtained from the raw data of measured droplet sizes and velocities in a transient diesel fuel spray with computed joint probability density function were made. Simultaneous droplet sizes and velocities were obtained using PDPA. Mathematical probability density functions which can fit the experimental distributions were extracted using the principle of maximum likelihood. Through the statistical process of functions, mean droplet diameters, non-dimensional mass, momentum and kinetic energy were estimated and compared with the experimental ones. A joint log-hyperbolic density function presents quite well the experimental joint density distribution which were extracted from experimental data.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.630-633
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• 2004

Generally, component and FR-4 board are connected by solder joint. Because material properties of components and FR-4 board are different, component and FR-4 board show different coefficients of thermal expansion (CTE) and thus strains in component and board are different when they are heated. That is, the differences in CTE of component and FR-4 board cause the dissimilarity in shear strain and BGA solder joint s failure. The first order Taylor series expansion of the limit state function incorporating with thermal fatigue models is used in order to estimate the failure probability of solder joints under heated condition. A model based on plastic-strain rate such as the Coffin-Manson Fatigue Model is utilized in this study. The effects of random variables such as frequency, maximum temperature, and temperature variations on the failure probability of the BGA solder joint are systematically investigated by using a failure probability model with the first order reliability method(FORM).

• International Journal of Concrete Structures and Materials
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• v.5 no.1
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• pp.11-18
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• 2011

Carbonation in RC (reinforced concrete) structure is considered as one of the most critical deteriorations in urban cities. Although RC column has one mix condition, carbonation depth is measured spatially differently due to its various environmental and internal conditions such as sound, cracked, and joint concrete. In this paper, field investigation was performed for 27 RC columns subjected to carbonation for eighteen years. Through this investigation, carbonation distribution in sound, cracked, and joint concrete were derived with crack mappings. Considering each related area and calculated PDF (probability of durability failure) of sound, cracked, and joint concrete through Monte Carlo Simulation (MCS), repairing timings for RC columns are derived based on several IPDF (intended probability of durability failure) of 1, 3, and 5%. The technique of equivalent probability including carbonation behaviors which are obtained from different conditions can provide the reasonable repairing strategy and the priority order for repairing in a given traffic service area.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.5
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• pp.850-858
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• 2011

The risk analysis plays an important role in weapon system acquisition project due to uncertainties in the acquisition process. But in domestic, studies on risk analysis are insufficient and risk cost is not included in acquisition budget in policy. Therefore, in this study, we suggest a method that measures risk or success probability of project using the stochastic model. In particular, in order to calculate the success probability, we apply the joint probability distribution model of cost and schedule that are critical factors influencing the project risk. And also we verify the applicability of this model in Korean defence industry environment through case studies.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.53-58
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• 2005

Semi-analytical methodology to examine the dynamic responses of a bridge is developed via the joint probability density function. The evolution of joint probability density function is evaluated by the semi-analytical procedure developed. The joint probability function of the bridge responses can be obtained by solving the path-integral solution of the Fokker-Planet equation corresponding to the stochastic differential equations of the system. The response characteristics are observed from the joint probability density function and the boundary of the envelope of the probability density function can provide the maxima ol the bridge responses.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.110-120
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• 1986

45.deg. corss jet flow, at the mixing of two jet flows, was experimentally studied. For this study, only the statistical turbulent characteristics and high order moments will be analysed by on-line computer system (hot-wire anemometer system, dynamic analyser and computer system, plotting and printing system). Since mean velocity distributions, intensities of turbulence, Reynolds stresses, correlation coefficients, and other general results were already studied and presented. One dimensional probability density distributions of u', v', and w' were analysed comparing with Gaussian curve, which showed skew and flat tendency according to the Y and Z directions. For the analysis of the joint flow of turublent components, the joint probability density distributions were examined. The fagures were drawn so as to be read joint probabilities, joint probability densities, fluctuating velocities u', v', and w'. For further detailed examination of the variations of skewness and flatness phenomena, iso-joint probability density contours obtained from the profiles of the joint probability density distributions were studied. According to the displacement of positions from the center of the mixing flow and the directions, the flatness and skewness factors were increased.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• Tunnel and Underground Space
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• v.8 no.4
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• pp.351-358
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• 1998

A statistical method for assessing the joint persistence based on the in-situ measurement of joint trace length has been derived. This method utilizes the probability density distribution of either the joint trace length or the diameter of hypothetically circular joint diameter depending on the relative size of joint surface to that of the potential keyblock. The stability of potential keyblock with different sizes and joint persistences has been also calculated to illustrate the applicability of the developed method to the design and the safe excavation of large scale underground openings.

• Wind and Structures
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• v.25 no.3
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• pp.261-282
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• 2017

The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.