• Journal of Applied Reliability
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• v.9 no.1
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• pp.59-69
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• 2009

LEDs have rapidly replaced old light devices such as incandescent or fluorescent lamps, and have been widely applied in general lighting, signals, automobile, signs and others. Since LEDs are for both indoor and outdoor use, temperature and humidity inevitably affect its reliability. We explain the result of the degradation life test on LEDs, and guide to reliability analysis procedure. Analysis on reliability measures are performed by Weibull++6 program, and a common shape parameter of Weibull distribution on the LED is suggested. Also, we make a description of reliability analysis procedures for the degradation data using collected test data from degradation tests. Reliability analysis procedures are consisted of estimating degradation models and failure time, verifying of distribution and parameters of the distribution, and estimating of reliability measures. Finally, this paper suggests reliability analysis method for light characteristics on LEDs.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.272-277
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• 2001

In order to evaluate variation of fatigue data of the LP steam turbine blade steel, it is important to estimate P - S - N curves to accurately define the probability distributions. In this study, new procedure is introduced to determine the expression of P - S - N curves. For this purpose, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue life were examined by the proposed analysis. Furthermore, parameter estimation for P - S - N curves was performed using various optimization to maximize the correlation coefficient. As a result of this, sequential linear programing method is used for estimation of P - S - N curves.

• Journal of Applied Reliability
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• v.13 no.2
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• pp.87-98
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• 2013

Accelerated degradation tests (ADTs) measuring failure-related degradation characteristic at the accelerated condition are widely used to assess the reliability of highly reliable products. Often, however, little degradation could be observed even in single-stress ADTs due to the high reliability of test unit, and as a result poor estimate of the reliability may be obtained. ADTs with multiple stress variables can be employed to overcome such difficulties. In this paper, optimal ADT plans with two stress variables are developed assuming that the degradation characteristic follows Weibull distribution by determining the stress levels, the proportion of test units allocated to each stress level such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.1
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• pp.7-14
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• 2002

In power system study, relibility assessment has been an important topic during past several decards because sudden power interruption can bring about enormous economic loss. although the size of a substation is smaller than that of generation system or transmission system, switching actions after fault(s) make reliability assessment of substation rather complex situations such as switching actions easily and permit various probability distributions in describing substation elements. Despite this ability of Monte Carlo simulation, one-parameter exponential distribution is still popular in this reliability assessment. This paper examines the characteristics of several two-parameter probability distributions, and offers new parameter decision rule based on average and variance of the target to be modelled. In case study, this paper shows the profits by using Weibull distribution which is one of two-parameter probabilistic distributions instead of exponential one.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.411-421
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• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• Journal of the Korea Concrete Institute
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• v.16 no.5 s.83
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• pp.581-589
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• 2004

This paper compares the fatigue behaviors of concretes subjected to flexural and split-tensional loadings, and proposes the fatigue reliability models based on experimental results and reliability analysis. The fatigue tests were performed for the specimens of $150 mm{\times}75 mm$ split tensional cylinders and $150 mm{\times}150 mm{\times}550 mm$ flexural beams under constant loadings at three levels (70, 80 and $90\%$) with 0.1 stress ratio, 20 Hz loading speed and sine wave. The reliability analysis on fatigue data was based on Weibull distribution of two-parameters. From fatigue test results, two criteria were proposed to reject the experimental fatigue data because of statistical variation of concrete fatigue data. Two parameters ($\alpha$and u) of Weibull distribution were obtained using graphical method, moment method and maximum likelihood method. The probability density function(P.D.F) and cumulative distribution function(C.D.F) of the Weibull distribution for fatigue life of pavement concrete were derived for various stress levels using parameters, $\alpha$ and u. The goodness-of-fit test by Kolmogorov-Smirnov test was acceptable at $5\%$ level of significance. Based on reliability analysis, a fatigue model for pavement concrete was proposed and compared from existing models.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.3
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• pp.137-143
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• 2021

In this study, the fracture strength of Flexible Secondary Barrier (FSB) composites was standardized by conducting a distribution analysis of the fracture probability, considering that the fracture strength of FSB composites such as glass fiber reinforced composites is relatively large. As the mechanical performance of FSB composites varies with the fiber direction, 20 replicate uniaxial tensile tests were performed for different temperatures ranging from the ambient to cryogenic conditions, considering the actual operating environment of liquefied natural gas. For the probability statistical analysis, the Weibull distribution analysis derived from the weakest link theory was used, considering the large variance in the fracture strength and brittle fracture behavior. The results of the Weibull distribution analysis were used to calculate the standard fracture strength of the FSB composites for different fiber directions. The findings can help ensure the reliability of the FSB mechanical properties in different fiber directions in the design of the secondary barrier and structural analyses.

• Journal of Forest and Environmental Science
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• v.36 no.1
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• 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.

• Journal of Korean Society on Water Environment
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• v.31 no.2
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• pp.142-150
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• 2015

The relationship between the number of benthic macroinvertebrate species and the accumulated survey area were investigated in a clean stream and an impaired stream of Korea. Five models to characterize species-area functions were compared, and the Weibull model fitted species-area data well. The other models (Arrhenius, Romell-Gleason, Kylin, Lognormal model) had small or notable bias. The maximum number of species and half-saturation area derived from the Weibull model may be used as the indicators of the carrying capacity and the habitat complexity respectively.