• 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 the Korean Statistical Society
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• v.12 no.2
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• pp.69-80
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• 1983

The purpose of this paper is to obtain representation of the mathematical special functions and the numerical values of the mean square errors for the quasi-ranges in random small smaples ($n \leq 30$) from the Weibull distribution with a shape and a scale parameters, and to estimate the scale parameter by use of unbiased estimator based on the quasi-range. It will be shown that the jackknife estimator of the range is worse than the range of random samples from the given distribution in the sense of the mean square error.

• Journal of the Korean Data and Information Science Society
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• v.5 no.2
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• pp.19-27
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• 1994

It is known that the maximum likelihood method does not provide explicit estimator for the scale parameter of the Weibull distribution based on Type-II censored samples. In this paper we provide an approximate maximum likelihood estimator (AMLE) of the scale parameter of the Weibull distribution with Type-II censoring. We obtain the asymptotic variance and simulate the values of the bias and the variance of this estimator based on 3000 Monte Carlo runs for n = 10(10)30 and r,s = 0(1)4. We also simulate the absolute biases of the MLE and the proposed AMLE for complete samples. It is found that the absolute bias of the AMLE is smaller than the absolute bias of the MLE.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.64-69
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• 2004

The characteristics of the probability distribution for mechanical properties, e.g. tensile strength, reduction of area, and elongation, for STS304 stainless steel in elevated temperature are investigated. Tensile test is performed by constant crosshead speed controls with 1mm/min. The probability distribution function of measured mechanical properties seems to follow $\alpha$ 3-parameter Weibull, and shows a slight dependence on the temperature. When the temperature is raised, the shape parameter a is increased, but both the scale parameter $\beta$ and location parameter v are decreased.

• Journal of Korean Society of Forest Science
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• v.90 no.2
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• pp.176-183
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• 2001

Loblolly pine (Pinus taeda L.) is the most economically important timber producing species in the southern United States. Much attention has been given to predicting diameter distributions for the solution of multiple-product yield estimates. The three-parameter Weibull diameter distribution yield prediction systems were developed for loblolly pine plantations. A parameter recovery procedure for the Weibull distribution function based on four percentile equations was applied to develop diameter distribution yield prediction models. Four percentiles (0th, 25th, 50th, 95th) of the cumulative diameter distribution were predicted as a function of quadratic mean diameter. Individual tree height prediction equations were developed for the calculation of yields by diameter class. By using individual tree content prediction equations, expected yield by diameter class can be computed. To reduce rounding-off errors, the Weibull cumulative upper bound limit difference procedure applied in this study shows slightly better results compared with upper and lower bound procedure applied in the past studies. To evaluate this system, the predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level to check if any significant differences existed. Statistically, no significant differences were detected based on the data from 516 evaluation data sets. This diameter distribution yield prediction system will be useful in loblolly pine stand structure modeling, in updating forest inventories, and in evaluating investment opportunities.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.4
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• pp.375-381
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• 2011

The primary aim of this study is to investigate the probabilistic characteristics of the fatigue parameters that describe the fatigue crack growth behavior in magnesium alloy. Statistical fatigue crack propagation experiments have been performed on rolled AZ31 magnesium alloy CT specimens with different specimen thickness, load ratio, and maximum load at ambient temperature in a laboratory. Using the statistical fatigue data obtained from these experiments, the goodness-of-fit of the probability distribution of the fatigue behavior parameters is evaluated in this study by performing statistical analyses. The crack growth rate coefficient is a fatigue parameter having a very large COV(Coefficient of Variation), but the variation of a crack growth rate exponent is not substantial. It is considered that a crack growth rate exponent can be a material constant. It is also found that the best fit probability distribution of the parameters such as the crack growth rate coefficient and crack growth rate exponent for a magnesium alloy is a three-parameter Weibull distribution, and two-parameter Weibull distribution is a good distribution only for the crack growth rate coefficient.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.6
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• pp.90-96
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• 1998

Helical gear system is widely used to transmit heavy duty power with harmonies and silences between parallel shafts. This paper predicts a life with Weibull distribution and estimates a reliability based on recycle principle of helical gear systems. 2-parameter Weibull distribution is generally adopted to estimate the mechanical life and the reliability of most gear systems, because this Weibull distribution is proper to explain a characteristics or a life of parts of gear systems with linearity of probability density data on weibull data sheet. For a high reliability, this paper estimates a number of overhaul times and a number of needed substitutes (exchange attachment,1 or parts) with following renewal theory, One is make an exchange of whole module include failure attachments/parts and second estimating method is only exchange of a failure attachments / parts.

• Wind and Structures
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• v.21 no.2
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• pp.203-221
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• 2015

Wind speed is the most important parameter in the design and study of wind energy conversion systems. The weibull distribution is commonly used for wind energy analysis as it can represent the wind variations with an acceptable level of accuracy. In this study, the wind data for 11 cities in Iran have been analysed over a period of one year. The Goodness of fit test is used for testing data fit to weibull distribution. The results show that this data fit to weibull function very well. The scale and shape factors are two parameters of the weibull distribution that depend on the area under study. The kinds of numerical methods commonly used for estimating weibull parameters are reviewed. Their performance for the cities under study was compared according to root mean square and wind energy errors. The result of the study reveals the empirical, modified maximum likelihood estimate of wind speed with minimum error. Also, that the moment and modified maximum likelihood are the best methods for estimating the energy production of wind turbines.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1281-1289
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• 2011

This paper deals with several statistical distribution functions for the analysis of fatigue life data of composite laminates for small wind-turbine blades. A series of tensile tests was performed on triaxial glass/epoxy laminates for loading directions of $0^{\circ}$, $45^{\circ}$, and $90^{\circ}$. Then, fatigue tests were carried out to determine the fatigue life at the aforementioned loading directions and the fatigue stresses at four levels. Two-parameter Weibull, three-parameter Weibull, normal, and log-normal distributions were used to fit the fatigue life data of the triaxial composite laminates. The three-parameter Weibull distribution most accurately described the fatigue life data measured experimentally for all the cases considered. Furthermore, the variation of fatigue life was simultaneously affected by the loading direction and fatigue stress level.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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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.