• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.643-652
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• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of Korean Society of Forest Science
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• v.98 no.5
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• pp.576-583
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• 2009

Based on the stem analysis and biomass measurement of 36 trees and 1,576 branches in Pinus sylvestris var. mongolica (Mongolian pine) plantations of Northeast China, this study was conducted to develop estimation model equation for leaf biomass of a single tree and branch, to examine the vertical distribution of leaf biomass in the crown, and to evaluate the proportional ratios of biomass by tree parts, stem, branch, and leaf. The results indicated that DBH and crown length were quite appropriate to estimate leaf biomass. The biomass of single branch was highly correlated with branch collar diameter and relative height of branch in the crown, but not much with stand density, site quality, and tree height. Weibull distribution function would have been appropriate to express vertical distribution of leaf biomass. The shape parameters from 29 sample trees out of 36 were less than 3.6, indicating that vertical distribution of leaf biomass in the crown was displayed by bell-shaped curve, a little inclined toward positive side. Apparent correlationship was obtained between leaf biomass and branch biomass having resulted in linear function equation. The stem biomass occupied around 80% and branch and leaf made up about 20% of total biomass in a single tree. As the level of tree class was increased from class I to class V, the proportion of the stem biomass to total biomass was gradually increased, but that of branch and leaf became decreased.

• Journal of the Society of Naval Architects of Korea
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• v.56 no.3
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• pp.231-241
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• 2019

In this study, a simplified analysis method was developed to evaluate the fatigue damage of an ice-going ship under broken ice condition. The global ice load, which is essentially calculated at the design stage of the Arctic vessel, and the hull form information were used to estimate the local ice load acting on the outer-shell of the ship. The local ice load was applied to the finite element analysis model, and the Weibull parameters for the target fatigue point were derived. Finally, fatigue damage was evaluated by applying the S-N curve and the Palmgren-Miner rule. For the verification of the proposed method, numerical analyses using direct approach were performed for the same conditions. A numerical model that implements the interaction between ice and structure was introduced to verify the local ice load and the stress calculated from the proposed method. Finally, the fatigue analyses of the Baltic Sea for actual ice conditions were performed, and the results of the proposed method, the method using numerical analysis, and the LR method were compared.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.445-461
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• 2019

It is possible that data are not always fitted with sufficient precision by the existing distributions; therefore this article presents a methodology that enables the use of families of asymmetric distributions as alternative probabilistic models for survival analysis, with censorship on the right, different from those usually studied (the Exponential, Gamma, Weibull, and Lognormal distributions). We use a more flexible parametric model in terms of density behavior, assuming that data can be fit by a distribution of stable distribution families considered unconventional in the analyses of survival data that are appropriate when extreme values occur, with small probabilities that should not be ignored. In the methodology, the determination of the analytical expression of the risk function h(t) of the $L{\acute{e}}vy$ distribution is included, as it is not usually reported in the literature. A simulation was conducted to evaluate the performance of the candidate distribution when modeling survival times, including the estimation of parameters via the maximum likelihood method, survival function ${\hat{S}}$(t) and Kaplan-Meier estimator. The obtained estimates did not exhibit significant changes for different sample sizes and censorship fractions in the sample. To illustrate the usefulness of the proposed methodology, an application with real data, regarding the survival times of patients with colon cancer, was considered.

• Journal of Korea Water Resources Association
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• v.40 no.1 s.174
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• pp.39-50
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• 2007

This paper presents applications of the log-linear ROCOF(rate-of-occurrence-of-failure) and the Weibull ROCOF to model the failure rate of individual cast iron pipes in a water distribution system and provides a method of estimating the economically optimal replacement time of the pipes using the 'modified time-scale'. The performance of the two ROCOFs is examined using the maximized log-likelihood estimates of the ROCOFs for the two types of failure data: 'failure-time data' and 'failure-number data'. The optimal replacement time equations for the two models are developed by applying the 'modified time-scale' to ensure the numerical convergence of the estimated values of the model parameters. The methodology is applied to the case study water distribution cast iron pipes and it is found that the log-linear ROCOF has better modeling capability than the Weibull ROCOF when the 'failure-time data' is used. Furthermore, the 'failure-time data' is determined to be more appropriate for both ROCOFs compared to the 'failure-number data' in terms of the ROCOF modeling performances for the water mains under study, implying that recording each failure time results in better modeling of the failure rate than recording failure numbers in some time intervals.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.5
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• pp.513-521
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• 2012

The aim of this study was to determine the brittle fracture behavior of reactor pressure vessel steel by considering the temperature dependence of a damage model. A multi-island genetic algorithm was linked to a Weibull stress model, which is the model typically used for brittle fracture evaluation, to improve the calibration procedure. The improved calibration procedure and fracture toughness test data for SA508 carbon steel at the temperatures $-60^{\circ}C$, $-80^{\circ}C$, and $-100^{\circ}C$ were used to decide the damage parameters required for the brittle fracture evaluation. The model was found to show temperature dependence, similar to the case of NUREG/CR-6930. Finally, on the basis of the quantification of the difference between 2- and 3-parameter Weibull stress models, an engineering equation that can help obtain more realistic fracture behavior by using the simpler 2-parameter Weibull stress model was proposed.

• Korean Journal of Agricultural and Forest Meteorology
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• v.12 no.2
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• pp.83-94
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• 2010

The objective of this study was to determine the best probability distributions of annual, seasonal and monthly precipitation in Korea. Data observed at 32 stations in Korea were analyzed using the L-moment ratio diagram and the average weighted distance (AWD) to identify the best probability distributions of each precipitation. The probability distribution was best represented by 3-parameter Weibull distribution (W3) for the annual precipitation, 3-parameter lognormal distribution (LN3) for spring and autumn seasons, and generalized extreme value distribution (GEV) for summer and winter seasons. The best probability distribution models for monthly precipitation were LN3 for January, W3 for February and July, 2-parameter Weibull distribution (W2) for March, generalized Pareto distribution (GPA) for April, September, October and November, GEV for May and June, and log-Pearson type III (LP3) for August and December. However, from the goodness-of-fit test for the best probability distributions of the best fit, GPA for April, September, October and November, and LN3 for January showed considerably high reject rates due to computational errors in estimation of the probability distribution parameters and relatively higher AWD values. Meanwhile, analyses using data from 55 stations including additional 23 stations indicated insignificant differences to those using original data. Further studies using more long-term data are needed to identify more optimal probability distributions for each precipitation.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.234-243
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• 1992

Fatigue crack initiation life has a wide scatter and this makes the fatigue design of structural members difficult. In order to make the fatigue life distribution clear, it is required to prepare a large number of specimens and repeat the fatigue tests under the same loading condition. Such fatigue tests usually take much time and cost. In this study, a fatigue testing method using a multi-notched test specimen for the purpose of estimating the distribution function of fatigue crack initiation life by small number of fatigue tests is used. The purpose of this study is to verify the above fatigue testing method of a multi-notched specimen by using Bayesian reliability analysis, Least square method and Skewness method for the determination of unknown Weibull parameters. The multi-notched specimen is a specimen in which several tens of statistically identical notches are prepared.

• Smart Structures and Systems
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• v.21 no.5
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• pp.591-600
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• 2018

The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.16 no.3
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• pp.130-141
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• 2004

For a coastal or harbor structure design, one of the most important environmental factors is the appropriate design wave condition. Especially, the information of deepwater wave height distribution is essential for reliability design. In this paper, a set of deep water wave data obtained from KORDI(2003) were analyzed for extreme wave heights. These wave data at 67 stations off the Korean coast from 1979 to 1998 were arranged in the 16 directions. The probability distributions considered in this research were the Weibull, the Gumbel, the Log-pearson Type-III, and Lognormal distribution. For each of these distributions, three parameter estimation methods, i.e. the method of moments, maximum likelihood and probability weighted moments, were applied. Chi-square and Kolmogorov-Smirnov goodness-of-fit tests were performed, and the assumed distribution was accepted at the confidence level 95%. Gumbel distribution which best fits to the 67 station was selected as the most probable parent distribution, and optimally estimated parameters and 50 year design wave heights were presented.