• Communications for Statistical Applications and Methods
• /
• v.24 no.4
• /
• pp.325-337
• /
• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2005.05b
• /
• pp.114-118
• /
• 2005

In this study, the DC dielectric breakdown of epoxy composites used for molding material was experimented and then its data were simulated by Weibull distribution equation. From the analysis of Weibull distribution, it was confirmed that as the allowed breakdown probability was given by 0.1[%], the applied field value needed to be under 21.5[kV/mm].

• Journal of Biomedical Engineering Research
• /
• v.37 no.1
• /
• pp.21-30
• /
• 2016

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.12 no.4
• /
• pp.790-805
• /
• 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.

• Journal of Korean Society for Quality Management
• /
• v.35 no.4
• /
• pp.159-165
• /
• 2007

Using statistical methods a change-point analysis of oil supply disruption is conducted. The statistical distribution of oil supply disruption is a weibull distribution. The detection of the change-point is applied to Bayesian method and weibull parameters are estimated through Markov chain monte carlo and parameter approach. The statistical approaches to the estimation for the change-point and weibull parameters is implemented with the sets of simulated and real data with small sizes of samples.

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

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

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.9 s.180
• /
• pp.2353-2360
• /
• 2000

Statistical fatigue properties of metallic materials are increasingly required for reliability design purpose. In this study, static and fatigue tests were conducted and the normal, log-normal, two -parameter Weibull distributions at the 5% significance level are compared using the Kolmogorov-Smirnov goodness-of-fit test. Parameter estimation were compared with experimental results using the maximum likelihood method and least square method. It is found that two-parameter Weibull distribution and maximum likelihood method provide a good fit for static and fatigue life data. Therefore, it is applicable to the static and fatigue life analysis of the spheroidal graphite cast iron. The P-S-N curves were evaluated using log-normal distribution, which showed fatigue life behavior very well.

• Journal of Korean Institute of Industrial Engineers
• /
• v.42 no.4
• /
• pp.256-262
• /
• 2016

The Weibull is widely used in reliability analysis, and several studies have attempted to improve estimation of the distribution's parameters. least squares estimation (LSE) or Maximum likelihood estimation (MLE) are often used to estimate distribution parameters. However, it has been proven that Bayesian methods are more suitable for small sample sizes than LSE and MLE. In this work, the Weibull parameter estimation accuracy of LSE, MLE, and Bayesian method are compared for sample sets with 3 to 30 data points. The Bayesian method was most accurate for sample sizes under 25, and the accuracy of the Bayesian method was similar to LSE and MLE as the sample size increased.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.42 no.3
• /
• pp.45-55
• /
• 2000

This study was carried out to derive optimal design low flows bythe Weibull-3 and Wakeby distributions for the partial consecutive duration series at seven watersheds along Han. nagdong, Geum Yeongsan and Seomjin river systems. L-coefficient of variation L-skewness and L-kurtosis were calculated by the L-moment ratio respectively. Parameters were estimated by the method of L-Moments with consecutive duration. Design low flows obtained by method of L-Moments using with consecutive duration, Design low flows obtained by method of L-Moments using different methods for plotting positions formulas in the Weibull-3 and Wakeby distributions were compared by the Root Mean Square Errors(RMSE). It has shown that design low flows derived by the method of L-moments using Weivull plotting position formula in Wakeby distribution were much closer to those of the observed data in comparison with those obtained by the methods of L-moments with the different formulas for plotting positions in Weibull-3 distribution from the viewpoint of Root Mean Square Errors.