• 대한기계학회논문집A
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• 제33권4호
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• pp.346-352
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• 2009

In the present study, the Weibull statistical analysis using the Monte-Carlo simulation has been performed to investigate the micro-Vickers hardness measurement reliability considering the variability. Experimental indentation test were performed with a micro-Vickers hardness tester for as-received and quenching and tempering specimens in SCM440 steels. The distribution of micro-Vickers hardness is found to be 2-parameter Weibull distribution function. The mean values and coefficients of variation (COV) for both data set are compared with results based on Weibull statistical analysis. Finally, Monte-Carlo simulation was performed in order to evaluate the effect of sample size on the micro-Vickers hardness measurement reliability. For the parent distribution with shape parameter 30.0 and scale parameter 200.0 (COV=0.040), the number of sample data required to obtain the true Weibull parameters was founded by 20. For the parent distribution with shape parameter 10.0 and scale parameter 200.0 (COV=0.1240), the number of sample data required to obtain the true Weibull parameters was founded by 30.

• 한국해양공학회지
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• 제10권2호
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• pp.61-68
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• 1996

Weibull distribution function is applied very successfully to the strength of brittle materials such as ceramics and the weakest link model is applied to explain the ovents. This paper deals with the effect of specimen size on the strength of ceramics. The values of tensile strength were calculated by the Monte-Calro simuation. The tensile strength obtained was plotted on Weibull probabillity papers and represented by the 3-parameter Weibull distribution. The strength distribution function was compared with the theoretical weibull distribution. As a result, it was found that the Weibull shape parameter was changed due to the size and there was a possibility of a false indication as if the weakest link model holds good. We should be very careful when we apply the Weibull statistics to estimate the strength of products.

• 한국농공학회:학술대회논문집
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• 한국농공학회 1998년도 학술발표회 발표논문집
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• pp.331-337
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• 1998

This study was carried out to derive optimal design floods by Weibull-3 distribution with the annual maximum series at seven watersheds along Man, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was acknowledged by the tests of Independence, Homogeneity, detection of Outliers. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in Weibull-3 distribution were compared by the rotative mean error and relative absolute error. It has shown that design floods derived by the method of L-moments using Weibull plotting position formula in Weibull-3 distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions in view of relative mean and relative absolute error.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2016년도 학술발표회
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• 한국산림과학회지
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• 제61권1호
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• pp.1-7
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• 1983

Weibull 분포함수(分布函數)에 의하여 임분(林分)의 직경(直徑) 분포(分布)를 추정(推定)할 수 있는 방법(方法) 중(中) 직경분포(直徑分布)의 실측치(實測値)로 직접(直接) 계산(計算)하는 방법(方法)에 대하여는 제(第) I 보(報)에서 발표(發表)하였다. 본(本) 연구(硏究)에서는 임의추출(任意抽出)한 표본목(標本木)의 평균직경(平均直徑)과 단면적평균직경(斷面績平均直徑)만을 구한 다음 Gamma함수(函數)를 사용(使用)한 Weibull 분포함수(分布函數)에 의하여 임분(林分)의 직경분포(直徑分布)를 추정(推定)하였다. 그 결과(結果) 실제(實際) 임분(林分)의 직경분포(直徑分布)와 매우 적합(適合)하였다. 그러므로 이 방법(方法)을 응용(應用)하면 임분(林分)의 직경분포(直徑分布)의 추정(推定)은 물론 장래(將來)의 임분구조(林分構造)의 해석(解析)과 예측(豫測)도 쉽게할 수 있다.

• Wind and Structures
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• 제31권4호
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• pp.311-319
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• 2020

India is a developing nation and heavily spends on the development of wind power plants to meet the national energy demand. The objective of this paper is to investigate wind power potential of Ennore site using wind data collected over a period of two years by three parameter Weibull distribution. The Weibull parameters are estimated using maximum likelihood, least square method and moment method and the accuracy is determined using R² and root mean square error values. The site specific capacity factor is calculated by the mathematical model developed by three parameter Weibull distribution at different hub heights above the ground level. At last, the wind energy economic analysis is carried out using capacity factor at 30 m, 40 m and 50 m height for different wind turbine models. The analysis showed that the site has potential to install utility wind turbines to generate energy at the lowest cost per kilowatt-hour at height of 50 m. This research provides information of wind characteristics of potential sites and helps in selecting suitable wind turbine.

• Nuclear Engineering and Technology
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• 제55권5호
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• pp.1924-1934
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• 2023

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F_en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

• 한국수자원학회논문집
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• 제46권6호
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• pp.643-653
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• 2013

적절한 확률분포형을 결정하고 그에 따른 확률수문량을 산정하는 것은 빈도해석에서 가장 중요한 절차이며, 이를 수행하기 위해서는 경험적 확률분포에서 얻어지는 자료와 가정한 확률분포에서 얻어지는 자료의 일치 정도를 판별하는 적합도 검정을 거쳐야 한다. 지금까지 일반적으로 적용된 적합도 검정 방법은 분포형의 전체적인 적합정도를 판별하여 최근의 기상이변으로 인한 극치 사상에 대하여는 충분히 고려하지 못하고 있다. 따라서 본 연구에서는 분포형의 극치 사상에 가중치를 주는 modified Anderson-Darling(AD) 검정 방법을 3변수 Weibull 분포형에 적용하여 검정통계량 한계값과 기각력을 살펴보았으며 이를 실제자료에 적용한 결과, modified AD 검정 방법이 다른 기존의 적합도 검정보다 더 우수한 기각력을 가지고 있음을 확인하였다. 이는 앞으로 3변수 Weibull 분포형을 이용한 극치 수문량 선정에 있어 modified AD 방법이 하나의 기준으로 작용할 수 있을 것이라 판단된다.

• Wind and Structures
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• 제31권5호
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• pp.419-430
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• 2020

Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.