• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 춘계학술대회
• /
• pp.365-370
• /
• 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).

• 대한기계학회논문집B
• /
• 제22권5호
• /
• pp.607-617
• /
• 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.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2004년도 추계학술대회 논문집
• /
• pp.630-633
• /
• 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
• /
• 제5권1호
• /
• pp.11-18
• /
• 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.

• 한국군사과학기술학회지
• /
• 제14권5호
• /
• pp.850-858
• /
• 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.

• 한국지진공학회논문집
• /
• 제9권6호
• /
• pp.53-58
• /
• 2005

본 연구에서는 지진하중을 받는 교량의 거동을 확률밀도함수를 통하여 분석할 수 있는 기법을 개발하였다. 확률밀도함수의 전개는 추계론적 이론을 이용한 반해석적 방법을 통하여 구하였으며, 반해석적 방법은 교량운동방정식으로부터 상응하는 Fokker-Planck equation을 구한 후, path-integral solution을 유도하여 이를 수치적으로 해석함으로써 구할 수 있다. 교량거동의 확률밀도 함수전개로부터 교량거동의 확률적 특성을 파악하고 확률밀도함수의 범위로부터 교량응답거동의 포락선을 얻을 수 있으며 이를 이용하여 최대응답의 범위를 결정할 수 있다는 것을 밝혔다.

• 대한기계학회논문집
• /
• 제10권1호
• /
• pp.110-120
• /
• 1986

본 45。충돌분사에서는 충돌분류의 평균속도, 난류강도, 난류전단응력등을 측정분석하여 기 연구발표한 자료를 토대로 하여 난류의 충돌배합이 활발히 일어나는 영역(X/X$_{0}$=2,3,4)에서 충돌분류의 특성을 통계학적으로 측정연구코저 한다. 따라서 각방향으로 발생하는 난류성분을 Gauss의 확률분포식과 비교검토하고, 2차원 결합확률정도선도를 측정도시하여 2방향의 난류성분들의 결합난동형상을 온라인 컴퓨 터 시스템에 의하여 분석할 계획이다. 또한 난류성분의 고차모멘트를 측정하여 비대칭도와 편평도등도 연구 구명코저 한다.다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제19권1호
• /
• pp.23-45
• /
• 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.

• 터널과지하공간
• /
• 제8권4호
• /
• pp.351-358
• /
• 1998

현장에서 측정된 절리 trace 길이에 의거하여 영속성을 산정할 수 있는 통계적 분석법을 개발하였다. 이 방법에서는 잠재적 키블록과 불연속면의 상대적인 규모에 따라 절리 trace 기링 또는 원형절리의 직경에 대한 확률밀도분포를 이용한다. 대규모 지하공동의 설계 및 안전적 굴착에 대한 개발된 분석법의 활용성을 설명하기 위하여 규모 및 영속성이 다른 잠재적 키블록의 안정성을 고찰하였다.

• Wind and Structures
• /
• 제25권3호
• /
• pp.261-282
• /
• 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.