• Journal of Applied Reliability
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• v.1 no.1
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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.

• 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.

• Journal of the Korean Solar Energy Society
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• v.33 no.1
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• pp.32-39
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• 2013

Effects of Weibull shape parameter, k, on capacity factors of wind turbines were investigated. Wind distributions with mean wind speeds of 5 m/s, 6 m/s, 7 m/s and 8 m/s were simulated and used to estimate the annual energy productions and capacity factors of a 2MW wind turbine for various Weibull shape parameters. It was found from the study that the capacity factors of wind turbines are much affected by Weibull shape parameters. When the annual mean wind speed at the hub height of a wind turbine was about 7 m/s, and the air density was assumed to be 1.225 $kg/m^3$, the maximum capacity factor of a 2 MW wind turbine having a rated wind speed of 13 m/s was found to occur with the shape parameter of 2. It was also found that as the mean wind speed increased, the Weibull k parameter which yielded the maximum capacity factor increased. The simulated results were also validated by predictions of capacity factors of wind turbines using wind data measured in complex terrain.

• Journal of Power System Engineering
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• v.14 no.4
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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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.36 no.1
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• pp.20-36
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• 2024

In this study, probabilistic models for the wave- and lifting forces were derived directly from long-term in-situ wave data embedding the Korean marine environment characteristics varying from sea to sea based on the Three-Parameter Weibull distribution. Korean marine environment characteristics varying from sea to sea carved out their presence on the probability coefficients of probabilistic models for wave- and lifting forces. Energetic wave conditions along the southern coast of Korea distinguish themselves from the others with a relatively large scale coefficient, small location coefficient, and shape coefficient around 1.3. On the other hand, mild marine environment along the western coast has a small variability, leading to small scale-coefficient, large location coefficient and shape coefficient around 2.0. In the sea off Mokpo, near the boundary between the South- and West Seas, marine environment was characterized by small scale-coefficient, large location coefficient, and shape coefficient around 1.2, implying that marine environments characteristics of the South-and West Sea coexist in the sea off Mokpo.

• Journal of the Korean Ceramic Society
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• v.34 no.9
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• pp.927-934
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• 1997

Static and cyclic fatigue tests were carried out for alumina specimen to study the statistical analyses (normal, lognormal and Weibull distribution) of fatigue lifetime data and nominal initial crack length data. Fatigue lifetime data followed Weibull distribution better than normal or lognormal distribution, for the shape parameter of the notched specimen was larger than that of the unnotched specimen. The nominal initial crack length data obtained from fatigue lifetime followed the lognormal and Weibull distribution better than normal distribution, for the coefficient of variation of the unnotched specimen was larger than that of the notched specimen, and shape parameter of unnotched specimen was smaller than that of the notched specimen.

• Advances in Energy Research
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• v.8 no.2
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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.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.6
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• pp.993-999
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• 2004

The estimation of fatigue life at the design stage of membrane type LNG tank is very important in order to arrive at feasible and cost effective solutions considering the total lifetime of the tank. In this study, the practical procedure of fatigue life prediction by use of cumulative damage factors based on Miner-Palmgren hypothesis and probability density function has been shown with the corner region of Gaz Transport Membrane type LNG tank being used as an example. In particular the parameters of Weibull distribution that determine the stress spectrum are discussed. The main results obtained from this study are as follows: 1. The recommended value for the shape parameter of Weibull distribution for the LNG tank is 1.1 in case of using the direct calculation method proposed in this study. 2. The calculated fatigue life is influenced by the shape parameter of Weibull distribution and stress block. The safe fatigue design can be achieved by using higher value of shape parameter and the stress blocks divided into more stress blocks.

• Journal of the Korean Statistical Society
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• v.8 no.2
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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.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.415-433
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• 1999

This paper considers the design of step-stress accelerated life tests for the Weibull distribution with a nonconstant shape parameter under Type I censoring. It is assumed that scale and shape parameters are log-linear functions of (possibly transformed) stress and that a cumulative exposure model holds for the effect of changing stress. The asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress is used as an optimality criterion. The optimum three step-stress plans are presented for selected values of design parameters and the effects of errors in pre- estimates of the design parameters are investigated.