• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.9 s.180
• /
• pp.2353-2360
• /
• 2000

Statistical fatigue properties of metallic materials are increasingly required for reliability design purpose. In this study, static and fatigue tests were conducted and the normal, log-normal, two -parameter Weibull distributions at the 5% significance level are compared using the Kolmogorov-Smirnov goodness-of-fit test. Parameter estimation were compared with experimental results using the maximum likelihood method and least square method. It is found that two-parameter Weibull distribution and maximum likelihood method provide a good fit for static and fatigue life data. Therefore, it is applicable to the static and fatigue life analysis of the spheroidal graphite cast iron. The P-S-N curves were evaluated using log-normal distribution, which showed fatigue life behavior very well.

• Communications for Statistical Applications and Methods
• /
• v.24 no.6
• /
• pp.641-649
• /
• 2017

Multivariate confidence regions were defined using a chi-square distribution function under a normal assumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be obtained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.

• The Korean Journal of Applied Statistics
• /
• v.24 no.2
• /
• pp.269-278
• /
• 2011

There are many researches that have considered the distribution functions and appropriate covariates corresponding to the scores in order to improve the accuracy of a diagnostic test, including the ROC curve that is represented with the relations of the sensitivity and the specificity. The ROC analysis was used by the regression model including some covariates under the assumptions that its distribution function is known or estimable. In this work, we consider a general situation that both the distribution function and the elects of covariates are unknown. For the ROC analysis, the mixtures of normal distributions are used to estimate the distribution function fitted to the credit evaluation data that is consisted of the score random variable and two sub-populations of parameters. The AUC measure is explored to compare with the nonparametric and empirical ROC curve. We conclude that the method using normal mixtures is fitted to the classical one better than other methods.

• Journal of Korean Society for Quality Management
• /
• v.44 no.1
• /
• pp.167-180
• /
• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.11 s.254
• /
• pp.1417-1424
• /
• 2006

In order to evaluate variation of fatigue life of mechanical components including engineering plastics, it is important to estimate probabilistic strain-life curves to accurately define the variation of fatigue characteristics. This paper intends to provide new assessment of P-$\varepsilon$-N (probabilistic strain-life curves) for considering the variation of fatigue characteristics in polyacetal. The fatigue strain controlled tests were conducted under constant 50% humidity and room temperature condition by a universal testing machine at strain ratio, R=0. A practical procedure is introduced to evaluate probabilistic strain-life curves. Three probabilistic distributions were used for generating P-$\varepsilon$-N curves such as normal, 2-parameter and 3-parameter Weibull. In this study, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue characteristic were examined using chi-square and Kolmogorov-Smirnov test. The more appropriate P-$\varepsilon$-N curves for these materials are generated by the proposed method considering 3-parameter Weibull distribution.

• Journal of Korean Society for Atmospheric Environment
• /
• v.2 no.3
• /
• pp.34-44
• /
• 1986

Particle size distribution of airborne suspended particulate concentrations according to particle size in the events of yellow sand phenomena, have been measured and analyzed by using Andersen air sampler for four years, January 1982 through December 1985. The conclusions are as follows: 1. Yellow sand phenomena, generally, occur between March and May. 2. The frequent occurrences of yellow sand were observed during March and April and airborne suspended particulate concentrations in the cases of yellow sand appeared to be 2 $\sim$ 3.4 times higher than those of normal conditions. 3. Geometric mean particle diameter and its geometric mean standard deviation by logarithmic normal distribution sheet, were quite close to each other and log-distribution curves showed similar shapes. 4. Analysis by particle size distribution curve showed bi-modal distribution. 5. Concentrations of coarse particles in normal conditions were 1.2 $\sim$ 2 times higher than those of fine particles and, similarly, coarse particle concentrations in yellow sand cases were 1.3 $\sim$ 2.5 times higher than those of fine particles. 6. Concentrations of coarse particles in yellow sand cases were 2 $\sim$ 3.6 times higher than those in normal conditions and those of fine particles were 1.7 $\sim$ 3.5 times higher.

• Journal of Korea Water Resources Association
• /
• v.48 no.10
• /
• pp.807-816
• /
• 2015

In general, the water stage-discharge relationship curve is established based on the assumptions of linearity and homoscedasticity. However, the relationship between the water stage and discharge is affected from geomorphological factors, which violates the basic assumptions of the water stage-discharge relationship curve. In order to reduce the error due to the violations, the curve is divided into several sections based on the manager's judgement considering change of cross-sectional shape. In this research, the objective-splitting criteria of the curve is proposed based on the measured data without the subjective decision. First, it is assumed that the coefficient of variation follows the normal distribution. Then, if the newly calculated coefficient of variation is outside of the 95% confidential interval, the curve is divided. Namely, the groups is divided by the characteristics of the coefficient of variation and the reasonable criteria is provided for establishing a multi-segmented rating curve. To validate the proposed method, it was applied to the data generated by three artificial power functions. In addition, to confirm the applicability of the proposed method, it is applied to the water stage and discharge data of the Muju water stage gauging station and Sangegyo water stage gauging station. As a result, it is found that the automatically divided rating curve improves the accuracy and extrapolation accuracy of the rating curve. Finally, through the residual analysis using Shapiro-Wilk normality test, it is confirmed that the residual of water stage-discharge relationship curve tends to follow the normal distribution.

• Nuclear Engineering and Technology
• /
• v.49 no.2
• /
• pp.373-379
• /
• 2017

Seismic probabilistic safety assessments are used to help understand the impact potential seismic events can have on the operation of a nuclear power plant. An important component to seismic probabilistic safety assessment is the seismic hazard curve which shows the frequency of seismic events. However, these hazard curves are estimated assuming a normal distribution of the seismic events. This may not be a strong assumption given the number of recorded events at each source-to-site distance. The use of a normal distribution makes the calculations significantly easier but may underestimate or overestimate the more rare events, which is of concern to nuclear power plants. This paper shows a preliminary exploration into the effect of using a distribution that perhaps more represents the distribution of events, such as the t-distribution to describe data. The integration of a probability distribution with potentially larger tails basically pushes the hazard curves outward, suggesting a different range of frequencies for use in seismic probabilistic safety assessments. Therefore the use of a more realistic distribution results in an increase in the frequency calculations suggesting rare events are less rare than thought in terms of seismic probabilistic safety assessment. However, the opposite was observed with the ground motion prediction equation considered.

• Geotechnical Engineering
• /
• v.1 no.2
• /
• pp.41-54
• /
• 1985

Generally, ground settlements and lateral displacements are accompanied by underground excavation associated with open-cut or tunnling. These ground movements cause a harmful influence upon nearby super.structures and sub-structures. Occasionally, the ground movements may pose serious problems as the function of the nearby structures may be disrupted. Therefore, prior to the subway construction in an urban area, it is necessary to identify the causes of ground settlements and estimating the extent St the magnitude of ground movements since any potential damage to the nearby structures such as gas lines, water mains, high buildings and cultural assets must be assessed. The research was performed mainly on ground movements such as surface settlements, lateral displacements, subsurface settlements and crown settlements to predict the maximum settlement and settlement zone, and to identify the causes of ground settlements in NATM sections of Busan subway. As a result, it was found that lateral distribution of settlements could be approximated reasonably by a Gaussian normal probability curve and longitudinal distribution of settlements by a cumulative Gaussian probability curve, and that the early closure of temporary invert was very important to minimize ground settlements.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.1
• /
• pp.1-9
• /
• 1991

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charlier expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modeling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we further developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A. and Booth-Baleriaux method. It is verified that the M.O.C.A. method is faster and more accure than any other method.