• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.500-506
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• 2017

In 2014, ISO 55000s has been enacted and the power plant asset management is becoming a hot issue for all over the world. The asset management system is being developed as a combination of CBM(Condition Based Maintenance) and RCM(Reliability Centered Maintenance). Therefore, the research on the calculation of the failure rate which is the most basic index of RCM is actively carried out. The failure rate calculation has been going on for a long time, and the most widely used probability distribution is the Weibull distribution. In the Weibull distribution, the failure rate function is determined in three types according to the value of the shape parameter. However, the Weibull distribution has a limitation that it is difficult to apply it when the trend of failure rate changes-such as bathtub curves. In this paper, the failure rate is calculated using the mixture Weibull distribution which can appropriately express the change of the shape of the failure rate. Based on these results, we propose the necessity and validity of applying mixture Weibull distribution.

• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.57
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• pp.113-122
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• 2000

A mixture of two distributions, each belonging to the same known Weibull distributions, is proposed and a simple graphical method for estimating the parameters of the Weibull distribution is applied. It appears from the results of this study that the mixed Weibull distribution is an appropriate expression for describing industrial property mortality characteristics.

• Journal of Forest and Environmental Science
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• v.34 no.6
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• pp.451-456
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• 2018

The use of single component distribution to describe the irregular stand structure of degraded forest often lead to bias. Such biasness can be overcome by the application of finite mixture distribution. Therefore, in this study, finite mixture distribution was used to characterise the irregular stand structure of the Gmelina arborea plantation in Omo forest reserve. Thirty plots, ten each from the three stands established in 1984, 1990 and 2005 were used. The data were pooled per stand and fitted. Four finite mixture distributions including normal mixture, lognormal mixture, gamma mixture and Weibull mixture were considered. The method of maximum likelihood was used to fit the finite mixture distributions to the data. Model assessment was based on negative loglikelihood value ($-{\Lambda}{\Lambda}$), Akaike information criterion (AIC), Bayesian information criterion (BIC) and root mean square error (RMSE). The results showed that the mixture distributions provide accurate and precise characterisation of the irregular diameter distribution of the degraded Gmelina arborea stands. The $-{\Lambda}{\Lambda}$, AIC, BIC and RMSE values ranged from -715.233 to -348.375, 703.926 to 1433.588, 718.598 to 1451.334 and 3.003 to 7.492, respectively. Their performances were relatively the same. This approach can be used to describe other irregular forest stand structures, especially the multi-species forest.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.107-114
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• 2013

Modelling of failures is an important element of reliability modelling. Empirical modelling approach suitable for complex item is explored in this paper. First step of the empirical modelling approach is to plot hazard function, density function, Weibull probability plot as well as cumulative intensity function to see which model fits best for the given data. Next step of the empirical modelling approach is select appropriate model for the data and fit the parametric model accordingly and estimate the parameters.

• Journal of the Korean Solar Energy Society
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• v.33 no.2
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• pp.18-27
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• 2013

This paper presents a method for assessing the wind energy potential at complex terrain using probability distribution. And the proper probability models of the parameters estimating the wind energy are presented. Finally a mixture-Weibull determined by numerical methods procedure are proposed to assess the probability distribution of the energy potential at a site. The developed method is applied to the Kwanjungchun Bridge and compared with wind records which the neighboring weather station.

• Smart Structures and Systems
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• v.17 no.6
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• pp.1087-1105
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• 2016

Traffic load and volume is one of the most important physical quantities for bridge safety evaluation and maintenance strategies formulation. This paper aims to conduct the statistical analysis of traffic volume information and the multimodal modeling of gross vehicle weight (GVW) based on the monitoring data obtained from the weigh-in-motion (WIM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. A genetic algorithm (GA)-based mixture parameter estimation approach is developed for derivation of the unknown mixture parameters in mixed distribution models. The statistical analysis of one-year WIM data is firstly performed according to the vehicle type, single axle weight, and GVW. The probability density function (PDF) and cumulative distribution function (CDF) of the GVW data of selected vehicle types are then formulated by use of three kinds of finite mixed distributions (normal, lognormal and Weibull). The mixture parameters are determined by use of the proposed GA-based method. The results indicate that the stochastic properties of the GVW data acquired from the field-instrumented WIM sensors are effectively characterized by the method of finite mixture distributions in conjunction with the proposed GA-based mixture parameter identification algorithm. Moreover, it is revealed that the Weibull mixture distribution is relatively superior in modeling of the WIM data on the basis of the calculated Akaike's information criterion (AIC) values.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2010.03b
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• pp.32-32
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• 2010

A epoxy/multilayered silicate nanocomposite was prepared by a new AC electric application method and micro silica particle was poured into the nanocomposite in order to prepare epoxy/micro-and-nano- mixed composites (EMNC). Electric insulation breakdown strength was measured in a sphere-sphere electrode system designed for the prevention of edge breakdown and the data were estimated by Weibull plot. As the exfoliated silicate nano-plates were homogeniously dispersed in the micro silica particles, the insulation property was higherd.

• Smart Structures and Systems
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• v.21 no.5
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• pp.591-600
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• 2018

The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

• Journal of Electrical Engineering and Technology
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• v.13 no.4
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• pp.1663-1672
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• 2018

In recent times, gas insulated medium voltage (MV) circuit breakers (CB) form a vital component in power system network, considering its advantages such as reduced size and safety margins. Gas insulation characteristics of circuit breakers are generally measured by lightning impulse (LI) test according to IEC standard 60060-1 as a factory routine test. Considering the environmental issues of $SF_6$ gas, many research works are being carried out towards the mixture of $SF_6$ gases for high voltage insulation applications. However, few reports are only available regarding the LI withstand and streamer propagation characteristics (at both positive and negative polarity of waveform) of $SF_6/N_2$ gas mixture insulated medium voltage circuit breakers. In this paper, positive and negative polarity LI tests are carried out on 22 kV medium voltage circuit breaker filled with $SF_6/N_2$ gas mixture at different gas pressures (1-5 bar) and at different gas mixture ratios. Important LI parameters such as breakdown voltage, streamer velocity, time to breakdown and acceleration voltage are evaluated with IEC standard LI ($1.2/50{\mu}s$) waveform. Weibull distribution analysis of LI breakdown voltage data is carried out and 50% probability breakdown voltage, scale parameter and shape parameter are evaluated. Results illustrate that the $25%SF_6+75%N_2$ gas filled insulation considerably enhances the LI withstand and breakdown strength of MV circuit breakers. LI breakdown voltage of circuit breaker under negative polarity shows higher value when compared with positive polarity. Results show that maintaining the gas pressure at 0.3 MPa (3 bar) with 10% $SF_6$ gas mixed with 90% $N_2$ will give optimum lighting impulse withstand performance of 22 kV MV circuit breaker.