• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.211-223
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• 1997

We introduce the linear estimators based on order statistics in the three-parameter Weibull distribution and compare the small sample performances of proposed linear estimators in the three- parameter Weibull distribution with an unidentified outlier.

• 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.

• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.859-870
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• 2009

We obtain a skewed double Weibull distribution by a double Weibull distribution, and evaluate its coefficient of skewness. And we obtain the approximate maximum likelihood estimator(AML) and moment estimator of skew parameter in the skewed double Weibull distribution, and hence compare simulated mean squared errors(MSE) of those estimators. We compare simulated MSE of two proposed reliability estimators in two independent skewed double Weibull distributions each with different skew parameters. Finally we introduce a skewed double Weibull distribution generated by a uniform kernel.

• 동력기계공학회지
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• 제14권4호
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• pp.56-62
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• 2010

This paper is concerned with the stochastic nature of elevated temperature tensile strength and creep rupture time in 18Cr-8Ni stainless steels. The Weibull statistical analysis using the NRIM data sheet has been performed to investigate the effects of variability of the elevated temperature tensile strength and creep rupture time on the testing temperature. From those investigations, the distributions of temperature tensile strength and creep rupture time were well followed in 2-parameter Weibull. The shape parameter and scale parameter for the Weibull distribution of tensile strength were decreased with increasing the testing temperature. For the creep rupture time, generally, the shape parameter were decreased with increasing the testing temperature.

• 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.

• 대한기계학회논문집
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• 제12권4호
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• pp.790-805
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• 1988

본 연구에서는 유리섬유 강화 에폭시 복합재료의 파괴 강도와 피로 수명을 정 규분포, 로그 정규 분포와 2모수 및 3모수 Weibull 분포 함수의 기대값으로 살펴 보았 다. 2연속 응력 피로 실험 [작은 응력에서 큰 응력으로의 실험(low-high test), 큰 응력에서 작은 응력으로의 실험(high-low test)]의 결과도 분포 함수들을 사용하여 분 석하였다. 비통계학적 누적 손상 법칙들(non-statistical cumulative damage rules) 을 2연속 응력 피로 수명 분산 예측에 이용하기 위해서 동등 순위 가정(equal rank assumption)을 확장하여 수정하였다. 수정한 누적 손상 모형은 Miner의 법칙, Brou- tman과 Sahu의 손상모형 및 Hashin과 Rotem의 모형 등이다.

• Journal of the Korean Statistical Society
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• 제8권2호
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• pp.99-105
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• 1979

In Thoman and Bain and Schafer and Sheffield, procedures for testing the equality of the scale parameters of two Weibull populations with a common shape parameter and procedures for selecting the Weibull population with the largest scale parameter are given. We give, in this paper, a modified procedure for the above testing and selection problems, which is more powerful than those previoulsy given.

• Advances in Energy Research
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• 제8권2호
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• pp.95-110
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• 2022

Wind energy can be utilized for the generation of electricity, due to significant wind potential at different parts of the world, some countries have already been generating of electricity through wind. Pakistan is still well behind and has not yet made any appreciable effort for the same. The objective of this work was to add some new strategies to calculate Weibull parameters and assess wind energy potential. A new approach calculates Weibull parameters; we also developed an alternate formula to calculate shape parameters instead of the gamma function. We obtained k (shape parameter) and c (scale parameter) for two-parameter Weibull distribution using five statistical methods for five different cities in Pakistan. Maximum likelihood method, Modified Maximum likelihood Method, Method of Moment, Energy Pattern Method, Empirical Method, and have been to calculate and differentiate the values of (shape parameter) k and (scale parameter) c. The performance of these five methods is estimated using the Goodness-of-Fit Test, including root mean square error, mean absolute bias error, mean absolute percentage error, and chi-square error. The daily 10-minute average values of wind speed data (obtained from energydata.info) of different cities of Pakistan for the year 2016 are used to estimate the Weibull parameters. The study finds that Hyderabad city has the largest wind potential than Karachi, Quetta, Lahore, and Peshawar. Hyderabad and Karachi are two possible sites where wind turbines can produce reasonable electricity.

• 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.

• 한국신뢰성학회지:신뢰성응용연구
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• 제1권1호
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• pp.17-33
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• 2001

The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.