• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.265-279
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• 1999

In this study, one of the techniques on the extension of low flow series has been developed, in which the daily streamflows were simulated by the Tank model with the input of extended daily rainfall series which were stochastically generated by the Markov chain model. The annual lowest flow serried for each of the given durations were formulated form the simulated daily streamflow sequences. The frequency of the estimated annual lowest flow series was analyzed. The distribution types to be used for the frequency analysis were two-parameter and three-parameter log-normal distribution, two-parameter and three-parameter Gamma distribution, three-parameter log-Gamma distribution, Gumbel distribution, and Weibull distribution, of which parameters were estimated by the moment method and the maximum likelihood method. The goodness-of-fit test for probability distribution is evaluated by the Kolmogorov-Sminrov test. The fitted distribution function for each duration series is applied to frequency analysis for developing duration-low flow-frequency curves at Yongdam Dam station. It was shown that the purposed technique in this study is available to generate the daily streamflow series with fair accuracy and useful to determine the probabilistic low flow in the watersheds having the poor historic records of low flow series.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.165-177
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• 2019

This paper considers corrosion wastage of two ship hull structure members as a part of investigated fuel oil tanks of 25 aging bulk carriers. Taking into account that many factors which influence corrosion wastage of ship hull structures are of uncertain nature, the related corrosion rate ($c_1$) is considered here as a real-valued continuous distribution, assuming that the corrosion wastage starts after 5, 6 or 7 years. In all considered cases, by using available data and applying three basic statistical tests, it is established that between two-parameter continuous distributions, normal, Weibull and logistic distributions are best fitted distributions for the mentioned corrosion rate ($c_1$). Note that the presented statistical, numerical and graphical results concerning two mentioned ship hull structure members allow to compare and discuss the corresponding probabilistic estimates for the corrosion rate ($c_1$).

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.697-700
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• 2006

저수시 하천유량(Low Streamflow)의 추정은 하천의 수질관리, 용수공급계획, 댐 방류계획등의 수자원관리에 있어서 매우 중요한 부분이다. 이러한 중요성에 따라 Vogel과 Kroll (1989)은 저수시 하천유량을 추정하기 위한 여러 가지 확률분포함수를 제안하였다. 가장 흔히 제안되어지는 이변수 확률분포(Two-Parameter Distribution)로는 Lognormal 분포와 Weibull 분포가 있으며 이와 더불어 Three-Parameter Lognormal, Three-Parameter Weibull, Log Person Type Ⅲ 분포도 널리 사용되어진다. 그러나 이러한 여러 가지 확률 분포함수 중에서 가장 적절한 확률분포의 선택은 저수시 하천유량의 물리적인 측면과는 상관없이 주로 적합도(Gooness of Fit)에 기인된 통계치에 의해서만 결정되기도 하는데 이러한 경우 잘못된 가정을 받아들이는 확률이 높아짐에 따라 추정결과의 신뢰성(Reliability)을 감소시킬 수 있다. 이러한 문제점을 극복하기 위해서 Onoz와 Bayazit (2001)는 Recession Curve를 지수함수로 가정하고 최대 갈수 기간의 길이(Maximum Dry Period Length)의 확률에 대한 이론적인 결과치들을 사용하여 Weibull 분포의 특정한 경우에 해당되어지는 Power 분포를 유도하였으며 유도된 Power 분포의 매개변수를 추정하기 위하여 L-Moment 방법을 사용하였다. 또한 Onoz와 Bayazit (2001) 작은 유출량에서 확률분포와 잘 맞지 않는 경우 작은 유출량값에 작은 가중치를 부여하여 확률분포에 대한 영향을 줄이는 방법인 LL-Moment 방법을 제안하였다. 본 연구에서는 낙동강 유역의 1번부터 5번 소유역에 대해 SSARR 모형을 이용하여 모의한 유출량을 이용하여 Weibull 분포, L-Moment방법에 의해 추정된 매개변수를 사용한 Power 분포, LL-Moment 방법에 의해 추정된 매개변수를 사용한 Power 분포를 적용하였으며 이들 분포의 적합도를 PPCC Test를 사용하여 평가해봄으로써 낙동강 유역에서의 저수시의 유출량 추정에 대한 Power 분포의 적용성을 판단해 보았다.

• Journal of Power System Engineering
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• v.18 no.1
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• pp.91-98
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• 2014

In this investigation, the effect of crack orientation on spatial randomness of fatigue crack growth rate (FCGR) in friction stir welded (FSWed) 7075-T651 aluminum alloy joints has been statistically analyzed by Weibull distribution. The fatigue crack growth tests are conducted under three different constant stress intensity factor range (SIFR) control at room temperature with R = 0.1 and frequency 10Hz on compact tension (CT) specimen machined at base metal (BM) and weld metal (WM). The experimental fatigue crack growth rate data were obtained for two types of specimens having LT and TL orientations. LT specimens both base metal and weld metal showed higher fatigue crack growth rate as compared to TL specimens. In the lower SIFR region, FCGR were found to be almost 3 times higher in higher SIFR region. The shape parameter of Weibull both LT and TL orientation for FCGR was increased with increasing SIFR, the scale parameter was also increased with increasing SIFR. The smallest value of the shape parameter was shown in weld metal specimens having LT orientation at lower SIFR region.

• Aerospace Engineering and Technology
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• v.6 no.1
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• pp.1-6
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• 2007

The present study provides the compressive design allowable of a unidirectional glass/epoxy composite laminate processed by wet lay-up at room temperature. The compressive strength values measured from 39 specimens have been assumed to follow the two-parameter Weibull distribution. Following the statistical guidelines provided by MIL-HDBK-17F, the B-basis and A-basis values of the aforementioned laminate are found to be 82.6% and 65.9%, of the mean compressive strength, respectively. The B-basis value is then discounted further at 50% for the in-situ application on the main wing spar caps of an experimental canard aircraft.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.647-663
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• 2017

Weibull distribution is a popular distribution for modeling lifetimes because it reflects the characteristics of failure adequately and it models either increasing or decreasing failure rates simply. It is a standard method of the lifetimes test to wait until all samples failed; however, censoring can occur due to some realistic limitations. In this paper, we propose a generalized likelihood ratio (GLR) chart to monitor changes in the scale parameter for type I right-censored Weibull lifetime data. We also compare the performance of the proposed GLR chart with two CUSUM charts proposed earlier using average run length (ARL). Simulation results show that the Weibull GLR chart is effective to detect a wide range of shift sizes when the shape parameter and sample size are large and the censoring rate is not too high.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.311-314
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• 2003

Concrete structures such as bridge, pavement, airfield, and offshore structure are normally subjected to repeated load. This paper proposes a failure probability models of concrete subjected to split tension repeated-loads, based on experimental results. The fatigue tests were performed at the stress ratio of 0.1, the loading shape of sine, the frequency of 20Hz, and the stress levels of 90, 80 and 70%. The fatigue test specimen was 150mm in diameter and 75mm in thickness. The fatigue analysis did not include which exceeded 0.9 of statistical coefficient of determination values or did not failure at 2$\times$$10^6$ cycles. The graphical method, the moment method, and maximum likelihood estimation method were used to obtain Weibull distribution parameters. The goodness-of-fit test by Kolmogorov-Smirnov test was acceptable 5% level of significance. As a result, the proposed failure probability model based on the two-parameter($\alpha and \mu$) Weibull distribution was good enough to estimate accurately the fatigue life subjected to tension mode.

• Water for future
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• v.29 no.1
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• pp.129-139
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• 1996

It is very important to select appropriate distributions for hydrological data in planning and designing hydraulic structures. Also, it is necessary to check whether the selected distribution reproduces the statistical characteristics of the real data. In this study, the parameters of the two- and three-parameter gamma, two- and three-parameter lognormal, Gumbel, two- and three-parameter log-Gumbel, GEV, log-Pearsonn type III, two- and three-parameter Weibull, four- and five-parameter Wakeby distributions were estimated for the rainfall data of 22 sites in Korea with 7 different durations based on the methods of moments, probability weighted moments, and maximum likelihood. And the validity conditions were checked for the estimated parameters. The separation effect for each distribution was examined throught 10,000 simulations using the estimated parameters. As results, the separation effect was the smallest: log-Pearson type III for moment method, log-Pearson type III and GEV for probability weighted moment method, and GEV for maximum likelihood method. However, it is large for the two-parameter distributions.

• Journal of Power System Engineering
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• v.21 no.3
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• pp.37-44
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• 2017

In this study, failure analysis of the angular pin for molding machines to aluminum component molding was carried out. SM45C steel was used for the angular pin, it was surface hardened by the induction surface hardening heat treatment. The cross section of damaged angular pin was observed, and micro Vickers hardness value from the fractured part was measured. Brittle fracture was occurred from the fracture surface of angular pin, therefore, impact toughness value was evaluated by V-notch Charpy impact test. It was confirmed that the impact absorption energy was high when was tempered at a high temperature for a long time, and the toughness was slightly increased. Also, 2-parameter Weibull statistical analysis was investigated in order to evaluate the reliability of the measured micro Vickers hardness values and absorbed energy. The micro Vickers hardness and absorbed energy well followed a two-parameter Weibull probability distribution, respectively. The reverse design against angular pin was proposed as possible by using test results.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.