• International Journal of Reliability and Applications
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• v.13 no.2
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• pp.71-80
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• 2012

This paper introduces a new approach for evaluating reliability of a complex system in terms of distributional parameters where analytical determination of reliability is intractable. The concept of discrete approximation, reported in the literature so far, fails to meet the latter requirement in terms of distributional parameters. The current work aims at offering a bound based approach where reliability planners not only get a clear idea about the extent of error but also can manipulate in terms of distributional parameters. This reliability approximation has been under taken under the Weibull frame work which is the most widely used model for reliability analysis. Numerical study has been carried out to examine the strength of our proposed reliability approximation via closeness between the two reliability bounds. This approach will be very useful during the early stages of product design as the distributional parameters can be adjusted.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.367-379
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• 1998

This paper considers two modes of partially accelerated life tests for items having Weibull lifetime distributions. In a use-to-acclerated mode each item is first run at use condition and, if it does not fail for a specified time, then it is run at accelerated condition until a predetermined censoring time. In an accelerated-to-use mode each one is first run at accelerated condition and, if it does not fail for a specified time, then it is run at use condition. Maximum likelihood estimators of the parameters of the lifetime distribution at use condition, and the 'acceleration factor' are obtained. The stress change time for each mode is determined to minimize the asymptotic variance of the acceleration factor, and the two modes are compared. For selected values of the design parameters the optimum plans are obtained, and the effects of the incorrect pre-estimates of the design parameters are investigated. Minimizing the generalized asymptotic variance of the estimators of the model parameters is also considered as an optimality criterion.

• Journal of the Korean Solar Energy Society
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• v.32 no.2
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• pp.95-104
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• 2012

This study purposed to predict wind energy for small size wind power generators at 50m above the ground in each area using mean wind speed data for 10 minutes collected from 2001 to 2011 by meteorological data in large cities having over 60% of 15 story (50m) or higher apartments including Seoul, Daejeon, Gwangju and Daegu representing the inland region, and Busan, Incheon and Ulsan representing the coastal region. In the results of analysis, we confirmed close agree ment between observatory weather data and probability density distribution obtained using Weibull's parameters, and this suggests that Weibull's parameter is applicable to the estimation of wind energy. Hourly output energy using the mean wind speed for 10 minutes and output energy obtained from Weibull's parameter showed an error less than 5%, and thus it was found that wind energy can be evaluated using Weibull's modulus.

• Journal of The Korean Society of Grassland and Forage Science
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• v.11 no.4
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• pp.209-214
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• 1991

The germination of seeds is developmentally complex process requiring water uptake, which is regulated by both genotypic and environmental factors. The present study was undertaken to determine the difference in germination characteristics, and to compare the ability of the logistic and Weibull functions to describe the cumulative germination curve when two levels of osmotic potential(0, -5 bar) were put to seeds of alfalfa, tall fescue, orchardgrass, and Kentucky bluegrass. The effects of grass type, osmotic potential, and their interaction on the total germination and coefficient of germination velocity were significant(P<0.01). The Weibull equation for predicting percent cumulative germination curve of alfalfa had significantly lower residuals than the logistic equation regardless of osmotic potential(P<0.01), indicating that the Weibull equation was more efficient than the logistic equation to fit the data of the percent cumulative germination of alfalfa. The rate parameter from the logistic equation was decreased under water stress, whereas the scale and shape parameters were increased. There were significant differences in days to 20% germination estimated from the logistic and Weibull equations.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.271-290
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• 2017

We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton's families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren's oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.523-544
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• 2018

Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399-1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.217-220
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• 2003

In the case of the remediation studies, push pull test is a more time and cost effective mettled than multi-well tracer test. It also gives Just as much or more information than the traditionally used methods. But the data analysis for the hydraulic parameters, there have been some defections such as underestimation of dispersivity, requirement for effective porosity, and calculation of recovery of center of mass to estimate linear velocity. In this research, Weibull distribution function is proposed to estimate the center of mass of breakthrough curve for Push pull test. The hydraulic parameter estimation using Weibull function showed more exact values of center of mass than those of exponential regression for field test data.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• 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.