• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.678-685
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• 2005

Estimating parameters of the lifetime distribution is investigated when field failure data are not completely reported. To take into account the reality and the accuracy of the estimates in such a case, the failure reporting probability is incorporated in estimating parameters. Firstly, method of maximum likelihood estimate(MLE) is used to estimate parameters of the lifetime distribution when failure reporting probability is known. Secondly, Expectation and Maximization(EM) algorithm is used to estimate the failure reporting probability and parameters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both case, procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simulation results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• Journal of Korean Society of Forest Science
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• v.80 no.4
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• pp.420-426
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• 1991

This study was conducted to provide fundamental information to make rational management planning in eastern seacoast forest, mainly composed of black pine (Pinus Thunbergii), Kangweon Province. Diameter distribution was estimated by the method of Weibull distribution. The results were as fallows ; 1. Average diameter in the eastern seacoast forests of Kangweon Province was 10.3cm, and the average D. B. H, of 16 study sites ranged from 6.9 to 14.6cm. 2. Parameters of the Weibull distribution were estimated in each study sites and the estimated parameters of the all study forests were a=5, b=5.6997 and c=1.4079. 3. Tested by Kolmogorov-Smirnov method for the significant differences between actual and estimated diameter distribution, the result showed that estimated values were well fitted to the actual ones at 5% significance level.

• 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.

• 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.22 no.4
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• pp.333-348
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• 2015

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.241-250
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• 2016

In this paper, we consider statistical inferences on the estimation of the parameters of a Weibull distribution when data are randomly censored. Maximum likelihood estimators (MLEs) and approximate MLEs are derived to estimate the parameters. We consider two cases for the censoring model: the assumption that the censoring distribution does not involve any parameters of interest and a censoring distribution that follows a Weibull distribution. A simulation study is conducted to compare the performances of the estimators. The result shows that the MLEs and the approximate MLEs are similar in terms of biases and mean square errors; in addition, the assumption of the censoring model has a strong influence on the estimation of scale parameter.

• Wind and Structures
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• v.28 no.1
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• pp.63-70
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• 2019

Due to developing environmental concern use of renewable energy source is very essential. The great demand for the energy supply coupled with inadequate energy sources creates an emergency to find a new solution for the energy shortage. The appropriate wind energy distribution is the fundamental requirement for the assessment of wind energy potential available at the particular site essential for the design of wind farms. Hence the proper specification of the wind speed distribution plays a vital role. In this paper the Bimodal Weibull distribution is used to estimate the Capacity factor at the proposed site. The shape and scale parameters estimated using Maximum likelihood method is used as the initial value for extrapolation. Application of this model will give an accurate result overwhelming the concept of overestimation or underestimation of Capacity factor.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.359-370
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• 1999

We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1091-1102
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• 2003

The Weibull variate is commonly used as a lifetime distribution in reliability applications. Estimation of parameters is revisited in the two-parameter Weibull distribution. The method of product spacings, the method of quantile estimates and the method of least squares are applied to this distribution. A comparative study between a simple minded estimate, the maximum likelihood estimate, the product spacings estimate, the quantile estimate, the least squares estimate, and the adjusted least squares estimate is presented.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.39-44
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• 2002

We compare MISE of the MLE, UMVUE, invariantly optimal estimator and Jacknife estimator for the reliability function of the Weibull distribution when the sample size is small.