• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.42 no.4
• /
• pp.194-202
• /
• 2019

Reliability analysis of the components frequently starts with the data that manufacturer provides. If enough failure data are collected from the field operations, the reliability should be recomputed and updated on the basis of the field failure data. However, when the failure time record for a component contains only a few observations, all statistical methodologies are limited. In this case, where the failure records for multiple number of identical components are available, a valid alternative is combining all the data from each component into one data set with enough sample size and utilizing the useful information in the censored data. The ROK Navy has been operating multiple Patrol Killer Guided missiles (PKGs) for several years. The Korea Multi-Function Control Console (KMFCC) is one of key components in PKG combat system. The maintenance record for the KMFCC contains less than ten failure observations and a censored datum. This paper proposes a Bayesian approach with a Dirichlet mixture model to estimate failure time density for KMFCC. Trends test for each component record indicated that null hypothesis, that failure occurrence is renewal process, is not rejected. Since the KMFCCs have been functioning under different operating environment, the failure time distribution may be a composition of a number of unknown distributions, i.e. a mixture distribution, rather than a single distribution. The Dirichlet mixture model was coded as probabilistic programming in Python using PyMC3. Then Markov Chain Monte Carlo (MCMC) sampling technique employed in PyMC3 probabilistically estimated the parameters' posterior distribution through the Dirichlet mixture model. The simulation results revealed that the mixture models provide superior fits to the combined data set over single models.

• Journal of Korea Water Resources Association
• /
• v.52 no.11
• /
• pp.895-904
• /
• 2019

It has been well recognized that extreme rainfall process often features a nonstationary behavior, which may not be effectively modeled within a stationary frequency modeling framework. Moreover, extreme rainfall events are often described by a two (or more)-component mixture distribution which can be attributed to the distinct rainfall patterns associated with summer monsoons and tropical cyclones. In this perspective, this study explores a Mixture Distribution based Nonstationary Frequency (MDNF) model in a changing rainfall patterns within a Bayesian framework. Subsequently, the MDNF model can effectively account for the time-varying moments (e.g. location parameter) of the Gumbel distribution in a two (or more)-component mixture distribution. The performance of the MDNF model was evaluated by various statistical measures, compared with frequency model based on both stationary and nonstationary mixture distributions. A comparison of the results highlighted that the MDNF model substantially improved the overall performance, confirming the assumption that the extreme rainfall patterns might have a distinct nonstationarity.

• Journal of Industrial Technology
• /
• v.11
• /
• pp.3-16
• /
• 1991

The lattice-fluid theory are adopted for modeling the phese equilibria in supercritical fluids, In order to investigate effects of the nonrandom distribution of holes in mixtures on the phase equilibria, the equation of state and the chemical potential of the binary miture are formulated with taking into account nonrandomness of holes distributions in the fluid mixture. The relations of phase equilibria formulated in this work are tested through predictions of solubility of heavy solids in supercritical fluids and predictions of high pressure phase equilibria of binary mixtures. Results obtained exhibit that the lattice fluid model with assumptions of nonrandomness of hole distributions is successful in quantatively mideling the phase equilibria of mixtures of molecules of dissimilar sizes, specifically solids-supercritical fluid mixtures.

• Structural Engineering and Mechanics
• /
• v.88 no.4
• /
• pp.335-354
• /
• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• Proceedings of the KSME Conference
• /
• 2001.06d
• /
• pp.989-994
• /
• 2001

Numerical simulations of high temperature catalytic combustion have been performed for the application to a gas turbine combustor. Dependences of inlet temperature and pressure on the distributions of temperature and species concentrations were investigated using plug flow model with detailed homogeneous and heterogeneous chemistries of methane-air mixtures. Honeycomb typecombustor deposited with Pt catalyst of 100mm in length and 26mm in diameter is used. The results show that rapid increase of temperature profile occurs earlier with the increase of inlet temperature and the decrease of inlet pressure. The condition which catalytic combustion is stabilized exists at certain range of inlet temperature and pressure. The state of catalytic combustion is also confirmed by the distributions of species concentration.

• Steel and Composite Structures
• /
• v.13 no.6
• /
• pp.521-537
• /
• 2012

In this study, an experimental study is performed to understand the effect of spalling on the structural behavior of fire damaged steel reinforced high strength concrete (SRHSC) columns, and the test results of temperature distributions and the displacements at elevated temperature are analyzed. Toward this goal, three long columns are tested to investigate the effect of various test parameters on structural behavior during the fire, and twelve short columns are tested to investigate residual strength and stiffness after the fire. The test parameters are mixture ratios of polypropylene fiber (0 and 0.1 vol.%), magnitudes of applied loads (concentric loads and eccentric loads), and the time period of exposure to fire (0, 30, 60 and 90 minutes). The experimental results show that there is significant effect of loading on the structural behaviors of columns under fire. The loaded concrete columns result more explosive spalling than the unloaded columns under fire. In particular, eccentrically loaded columns are severely spalled. The temperature distributions of the concrete are not affected by the loading state if there is no spalling. However, the loading state affects the temperature distributions when there is spalling occurred. In addition, it is found that polypropylene fiber prevents spalling of both loaded and unloaded columns under fire. From these experimental findings, an equation of predicting residual load capacity of the fire damaged column is proposed.

• The Korean Journal of Applied Statistics
• /
• v.25 no.6
• /
• pp.1037-1047
• /
• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• Structural Engineering and Mechanics
• /
• v.64 no.3
• /
• pp.361-379
• /
• 2017

In this article, the vibration behavior of double-bonded sandwich microplates with homogeneous core and nanocomposite facesheets reinforced by carbon nanotube and boron nitride nanotube under multi physical fields such as 2D magnetic and electric fields is investigated. Symmetric and un-symmetric distributions of nanotubes are considered for facesheets of sandwich microplates such as uniform distribution and various functionally graded distributions. The double-bonded sandwich microplates rest on visco-Pasternak foundation. Material properties of sandwich microplates are obtained by the extended rule of mixture. The sinusoidal shear deformation theory (SSDT) is employed to describe displacement fields of sandwich microplates. Also, the dimensionless natural frequency is obtained by classical plate theory (CPT) and compared with the obtained results by SSDT. It can be seen that the obtained dimensionless natural frequencies by CPT are higher than SSDT. In order to study the material length scale parameters, modified strain gradient theory at micro scale is utilized and then, the equations of motion are derived using Hamilton's principle. The effects of different parameters such as foundation parameters including Winkler, shear layer and damping coefficients, various distributions and volume fraction of nanotubes, core to facesheet thickness ratio, aspect and side ratios on the dimensionless natural frequencies are discussed in details. The results of present work can be used to optimum design and control of similar systems such as micro-electro-mechanical and nano-electro-mechanical devices.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.2
• /
• pp.129-142
• /
• 2014

We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.

• The Korean Journal of Applied Statistics
• /
• v.24 no.1
• /
• pp.185-191
• /
• 2011

In the credit evaluation study with the assumption of mixture distributions, the ROC curve is a useful method to explore the discriminatory power of default and non-default borrowers. The AROC curve is an adjusted ROC curve that can be identified with the corresponding score and is mathematically analyzed in this work. We obtain patterns of this curve by applying normal distributions. Moreover, the relationship between the AROC curve and many classification accuracy statistics are explored to find the optimal threshold. In the case of equivalent variances of two distributions, we obtain that the local minimum of the AROC curve is estimated at the optimal threshold to maximize certain classification accuracies.