• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.790-805
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• 1988

Static strength and fatigue life scattering of glass fiber reinforced epoxy composite materials has been studied. Normal, lognormal, two-parameter and three-parameter Weibull distribution functions are used for strength and one-stress fatigue life distribution. The value of mean fatigue life is analysed using mean fatigue life, mean log fatigue life and expected value of 2 and 3-parameter Weibull distribution functions. Modification on non-statistical cumulative damage models is made in order to interpret the result of two-stress level fatigue life scattering. The comparison results show that 3-parameter Weibull distribution has better predictions in static strength and one-stress level fatigue life distributions. However, no advantage of 3-parameter Weibll distribution is found over 2-parameter Weibull distribution in two-stress level fatigue life predictions. It is found that two-stress level fatigue life prediction by the expanded equal rank assumption is close to the experimental data.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.349-361
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• 2009

In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.4
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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.

• Wind and Structures
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• v.31 no.5
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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.

• Journal of the Korea Institute of Military Science and Technology
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• v.24 no.4
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• pp.401-407
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• 2021

To confirm the change of muzzle velocity and the most suitable probability distribution model of the 155 mm K9 howitzer barrel with chrome plating and changed rifling. Using a statistical program, the muzzle velocity were plotted on a normal distribution, a 2-parameter and 3-parameter Weibull distribution on a probability paper. Also, statistical parameters were estimated and muzzle velocity fitness test and probability of K676 charge were plotted. In both the chrome-plated with standard rifling and changed rifling for K9 barrel, the 2-parameter and 3-parameter Weibull distribution were skewed to the left compared to the normal distribution. It was confirmed that the muzzle velocity of the K9 barrel with chromium-plated is suitable for the normal distribution and 3-parameter Weibull distribution model.

• Journal of Ocean Engineering and Technology
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• v.10 no.2
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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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.11a
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• pp.106-108
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• 1997

In this paper, the breakdown strength of Pure HDPE(High density polyethylene) films and aged HDPE films were evaluated using 2-parameter Weibull distribution function. The result show that both were fitted 2-parameter Weibull distribution. This method could be used to be the diagnostic tool to evalute the insulation performance and endurance under the multiple stresses.

• Wind and Structures
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• v.31 no.4
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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.

• Journal of Biosystems Engineering
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• v.11 no.1
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• pp.76-85
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• 1986

This study was intended to examine the failure characteristics and breakdowns of the head-fed type combines generally used on farms. The failure distribution was assumed to follow Weibull distribution function and the Weibull parameters of the major parts, units and combine as whole were estimated by using the data collected in a survey. A computer program for the estimation of the Weibull parameter was developed. Monte Carlo method was used in predicting the time between failures. The results of study may be summarized as follows: 1. The number of failures per combine was 4.83 times per year and 0.3 times per hectare of combines of different ages. 2. According to the Kolmogorov-Smirnov test method, it was proved that the Weibull distribution function is well fitted to the characteristics of the failure and breakdowns of combines. 3. Weibull parameters of failure distribution of the combine as a whole were estimated to give the shape parameter ${\beta}$=1.3089 and the scale parameter ${\alpha}$=105.2409. The combining area with 80% reliability was 1.1 ha, and the probability of operating the combine without any failure for a year, was $2.76{\times}10^{-4}$. 4. The mean time between failures (MTBF) of the combines was predicted to be 3.2 ha of operation, which corresponds to 32 hours of operation.