Weibull Distribution Method Research Articles

Application of statistical modeling of image spatial structures to automated visual inspection of product quality

Automated visual inspection (AVI) attracts increasing interest in product quality control both academic and industrial communities, particularly on mass production processes, because product qualities of most types can be characterized with their corresponding surface visual attributes. However, many product images in AVI systems are comprised of stochastically accumulative fragmentations (particles) of local homogeneity, without distinctive foregrounds and backgrounds, which brings great challenges in computer analysis, e.g., rice images, fabric images, and consequently, in the intelligent identification of the product qualities. A method of Weibull distribution (WD)-based statistical modeling of image spatial structures (ISSs) to inspect automatically the product quality is presented. The ISS, obtained with multi-scale and omnidirectional Gaussian derivative filters (OGDFs), was demonstrated to be subject to a representative WD model of integral form based on the theory of sequential fragmentation in advance. The WD-model parameters (WD-MPs) of the ISS, with essential human perceptual significance, were extracted as the visual features for product quality identification. The classification performance of the proposed product quality inspection method, namely, the proposed WD-MP features integrated with an introduced spline regression (SR) classifier in this study, was verified on two case studies in the field of the AVI of product quality, namely, automated rice quality classification, and intelligent fabric quality assessment in the corresponding assembly lines of industrial scale. Experimental results indicate that the proposed WD-MP features can effectively characterize the statistical distribution profiles of ISS of complex grain images, piled with a large number of stochastically accumulative fragmentations. The proposed method provides an effective tool for grain image modeling and analysis and consequently lays a foundation for the intelligent perception of product qualities on assembly lines.

Wind Potential Assessment for the Utilization from Wind Energy in the Household Level: A Case Study of Nakhonratchasima Thailand

Wind energy is an important alternative energy resource because of it clean, does not cause pollution and it can be used as replacement of a fossil fuel energy. Utilization of the wind energy, the wind speed data has to be analyzed to make sure before use it. In this article is to present the wind speed data analysis by using Weibull distribution method. Wind speed data from the meteorological station at Pakchong district, Nakhonratchasima province, Thailand was used as the case study. The results show that this area has wind speed about 2.5 to 3.5 m/s. The average wind power density was 17.513 W/m2 and the total wind energy was 153.9819 kW·hr/m2 per year. This wind potential of this area can be used for water pumping and electricity generating for use in a household.

The Study of Electroluminescence and Reliability of Polyimide Films in High DC Fields

Electroluminescence (EL) intensity of the polyimide (PI) films was tested under dc high electric field by home-made experimental device. The results showed that the EL intensity of PI films increased along with the electric field. EL intensity is approximately to background intensity when the electric-field intensity was less than 2.00 MV/cm. EL intensity increases along with increasing the electric field when electric-field intensity greater than 2.00 MV/cm. When electric-field at 2.80 MV/cm, EL intensity increasing strongly suggests that the excitation process related to hot electrons accelerated by the field approaching a critical threshold. Meanwhile, this work elaborates a method to deal with identical samples get different experimental data by using Weibull distribution method, and the concept of the reliability was presented. The nine groups of EL experimental data were analyzed, and the result showed that the lifetime of mid-value (t = 164.9 min). Mid-value of the breakdown field is E = 2.76 MV/cm.DOI: http://dx.doi.org/10.5755/j01.ms.21.4.9694

Performance Analysis of Methods for Estimating Weibull Parameters for Wind Speed Distribution in the District of Maroua

In this study, five numerical Weibull distribution methods, namely, the maximum likelihood method, the modified maximum likelihood method (MLM), the energy pattern factor method (EPF), the graphical method (GM), and the empirical method (EM) were explored using hourly synoptic data collected from 1985 to 2013 in the district of Maroua in Cameroon. The performance analysis revealed that the MLM was the most accurate model followed by the EPF and the GM. Furthermore, the comparison between the wind speed standard deviation predicted by the proposed models and the measured data showed that the MLM has a smaller relative error of -3.33% on average compared to -11.67% on average for the EPF and -8.86% on average for the GM. As a result, the MLM was precisely recommended to estimate the scale and shape parameters for an accurate and efficient wind energy potential evaluation. Keywords : Empirical method; energy pattern factor method; graphical method; maximum likelihood method; modified maximum likelihood method; wind speed.

Analysis of Wind Energy Prospect for Power Generation by Three Weibull Distribution Methods

Wind energy is one of the fastest growing sectors in renewable energy. These energy resources are freely available throughout the world. It is one of the zero emission energy sources. The wind energy is used mainly for two purposes namely irrigation (water pumping) and electricity generation. The prospect of wind energy can be analyzed by different methods. Weibull distribution method is one of the widely acceptable methods for estimating wind energy. In this paper, the prospect of wind energy in Bangladesh is analyzed by Weibull distribution method. The data were collected from Meteorological Department of Bangladesh located in different areas of the country. Three different Weibull distribution methods were used to find out Weibull parameters which were verified using different widely acceptable statistical tools. Relative percentage error, chi-square error, analysis of variance etc. are the efficient statistical tools to rank the method which was used in this study. The study identified the most prospects windy site by applying efficient least square method with minimum error.

Wind Characteristics of Three Meteorological Stations in China

With rapid economic development of China, demand for energy is growing rapidly. Many experts have begun to pay attention on exploiting wind energy. Wind characteristics of three meteorological stations in China were analyzed to find out if or not it is possible to build a wind farm in this paper. First of all, studies about the wind characteristics and potential wind energy were summarized. Then ways of collecting and manipulating wind data were introduced. Wind-generation potential was assessed by the method of Weibull distribution. Wind shear exponent, extreme wind speed in 50 years, and turbulence intensity were calculated. The wind characteristics were summarized and assessment of wind-generation potential was given. At last, the wind was simulated with autoregressive method by Matlab software.

A combination method for modeling wind power plants in power systems reliability evaluation

The production of wind energy often involves uncertainties due to the stochastic nature of wind speeds and the variation of the power curve. In this study, a method for modeling wind power plant in power systems reliability evaluation is proposed. This method is a combination of analytical and simulation methods. Initially, the mechanical behavior of each wind turbine generator (WTG) is modeled through sequential Monte Carlo method. Then, considering the wind speed of the area, the Markov model is used for modeling the power output of wind farm. The combination method is compared with the Auto Regressive Moving Average (ARMA) time series method and some other techniques such as Weibull and normal distribution methods in wind speed modeling. Also in this study, the effects of different parameters, such as failure, repair rate and number of output power levels of WTG on the system reliability are analyzed.

배전용 전력 케이블을 위한 비-가교 폴리올레핀 재질의 절연특성 연구

A cross linked polyethylene (XLPE) material has been widely used to develop a distribution power cable due to its excellent electrical characteristics and mechanical strength. However, several problems such as environmental disruption, electrical aging, thermosetting property, and impurities which cause degradation also arise. Therefore, a novel dielectric material should be developed to substitute for the XLPE. Several kinds of polyolefin materials to substitute for the conventional dielectric material, XLPE are developed and A cylindrical rod to cylindrical rod electrode system made with stainless steel is used to perform the experiments according to the ASTM D-149 protocol under an AC and Impulse input voltage condition. The experimental results are calculated by the Weibull distribution method and analyzed by an Finite Element Method(FEM). Finally, the dielectric characteristics of the conventional XLPE and novel polyolefin are experimented compared with each other in this study.

Performance analysis of Weibull methods for estimation of wind speed distributions in the adamaoua region of Cameroon

This paper explores the performance analysis of five Weibull distribution methods to select the more accurate estimation for the Weibull parameters using time-series of measured daily wind speed data collected in three localities in the Adamaoua region of Cameroon. The Weibull distribution with two parameters, the shape k, and the scale C, was specifically considered to be a good quality probabilistic model for wind speed distributions. The five Weibull distribution methods proved to be effective in evaluating the parameters of the Weibull distribution. This fact was supported by the values of the root mean square error, the Chi-square (χ²) and the correlation coefficient R² which showed magnitudes very close to each other. In addition, the comparison between wind speed distributions predicted by the Weibull methods and wind speed distributions measured locally, suggested that the most accurate two-parameter Weibull distribution method is the Energy Pattern Factor Method (EPF). As a result, to reduce uncertainties related to the wind energy output calculation, the EPF is recommended for estimating wind speed distributions.

Statistical Diagnosis of the Best Weibull Methods for Wind Power Assessment for Agricultural Applications

The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), standard deviation method (STDM), maximum likelihood method (MLM), power density method (PDM), modified maximum likelihood method (MMLM) and equivalent energy method (EEM) were used to estimate the Weibull parameters and six statistical tools, namely relative percentage of error, root mean square error (RMSE), mean percentage of error, mean absolute percentage of error, chi-square error and analysis of variance were used to precisely rank the methods. The statistical fittings of the measured and calculated wind speed data are assessed for justifying the performance of the methods. The capacity factor and total energy generated by a small model wind turbine is calculated by numerical integration using Trapezoidal sums and Simpson’s rules. The results show that MOM and MLM are the most efficient methods for determining the value of k and c to fit Weibull distribution curves.

An efficient reliability system for censoring the data based on the hybrid approach

In software reliability modeling, the model parameters are computed from the test data. By removing the uncertainty of the parameter the uncertainty in the total system reliability can also be underestimated. The reliability of manufactured items often involves performing a life test and examining observed times of failure. The lack of existing failure data from a single test makes modeling difficult. This is overcome by combining entropy principle and Kullback Leibler method. In this paper reliability is tested for Type II censored data by combining Kullback Leibler method and Bayesian method. This paper provides aspects of Kullback Leibler information with the introduction of Weibull distribution and Bayesian method for computing risk in Type II censoring scheme. Kullback-Leibler determines the decomposition of entropy in censoring schemes using the Weibull distribution. The method involves estimating the posterior distribution of the Kullback-Leibler information. In our paper we are computing the reliability of the system and analyses the risk involved. The relative risks due to each cause of failure are investigated. The risk of the censoring scheme is analyzed.

Wind Energy Potential in Taiwan

The purpose of this paper is to contribute the database to users of wind power in Taiwan. The study analyzes 12 stations in Taiwan. The data were collected during the period 2001-2010. The Weibull distribution method was used to analyze wind characteristics and wind energy potential in the different site and height as well. The results show that the wind speed at the height 100 m and roughness length 0.1 m in Taiwan between 1.7 m/s and 4.3 m/s, and the power density from 5 W/m2 to 75 W/m2. Taipei is the windy place, while Taichung is the less. The direction of the wind most commonly comes from north-east. The wind energy varies depend on season, strong wind in spring and winter, while weak wind in autumn and summer. The results obtained contribute to a global vision of the wind energy potential and the windy areas in Taiwan.

Reliability Studies of Tensile Strength for Parts Produced by Direct Metal Laser Sintering Using Weibull Analysis

A study was carried out to find the reliability of components manufactured by direct metal laser sintering (DMLS) for tensile strength. An orthogonal array of modified L8 experimental design using Taguchi’s experimental design techniques was developed and used. Test results were analysed using analysis of variance technique to identify the main process parameter that influences the tensile strength. It has been found that sintering speed had more influence on tensile strength as compared to other process parameters. Regression analysis shows that regression model for tensile strength is within the significance level and adequate within 90%. Detailed investigations on reliability using Weibull analysis shows that the distribution plot considered as a good Weibull design. Results show that the Weibull distribution method can be used for describing the distribution of failure times for tensile strength of DMLS components for functional applications.

Reliability Assessment for Multiple NC Machine Tools Oriented to General Repair

An approach of assessing reliability for multiple NC machine tools with general repair based on log-linear proportional intensity model(LPIM) is proposed, and an LPIM function for failure times is built. Point and confidence bounds estimates of model parameters are given by maximum likelihood method and Fisher information matrix method. Point estimates of reliability metrics are also derived with their confidence bounds offered through Delta method. Likelihood ratio tests are adopted to check the time trend and repair effect. A real example analysis demonstrates that, LPIM approach outperforms Weibull distribution method and NHPP model considering the effects of repair activities, capable to capture quantitatively repair effects on machine tools reliability, hence the instantaneous and cumulative reliability properties obtained more practical.

Random Censored Data MLE of Weibull Distribution Based on Simulink

Maximum likelihood estimation (MLE) is a commonly used method of Weibull distribution, but it needs to calculate the transcendental equations which is based on the computer programming. In this paper, we established a new MLE model of Weibull distribution in a case of random censoring. And this model was proved feasible and correct via three examples. At the same time, the model can be used for a variety of censored data and complete life data of Weibull distribution of MLE.

Design wave height selection in intermediate-depth waters

Two methods are compared for selection of design wave height for maritime structures in intermediate-depth water. One is the Composite Weibull distribution (CWD) method by Battjes and Groenendijk (2000) and another is the breaker index method by Goda (1974). The former is found inappropriate for practical use because of its inherent tendency of underestimating maximum wave height in intermediate-depth waters. Underestimation is caused by its artificial setting of the Weibull shape parameter at k2=3.6. A sample calculation for the offshore significant waves with H1/3=8.3m and T1/3=Tm−1,0=12.5m is presented to compare H0.1% by the CWD method and H1/250 by the breaker index method to demonstrate their differences. The present paper discourages use of the CWD method in design works in intermediate-depth waters, and recommends the breaker index method instead.

Statistical analysis of compressive strength for the reliability of parts produced by direct metal laser sintering (DMLS)

A study was carried out to find the reliability of components manufactured by direct metal laser sintering (DMLS) for compressive strength. An orthogonal array of modified L8 experimental design using Taguchi’s experimental design techniques was developed and used. Test results were analysed using analysis of variance (ANOVA) technique to identify the main process parameter that influences the compressive strength. It has been found that infiltration had more influence on compressive strength as compared to other process parameters. Regression analysis shows that regression model for compressive strength is within the significance level and adequate within 90%. Detailed investigations on reliability using Weibull analysis shows that the distribution plot and were considered as a good design for Weibull analysis. The Weibull distribution method can be used for describing the distribution of times to compressive strength of rapid prototyped components using DMLS for functional applications.

Effects of Laser Shock Processing on Fatigue Lives of Heat-Resistant Steel and Estimation of Fatigue Safe Lives

Fatigue tensile treatment was performed on 00Cr12 heat-resistant steel specimens which had been treated by laser shock processing (LSP). The unilateral tolerance factor statistical analysis method and the two-dimensional Weibull distribution method were used to predict the values of fatigue safe lives of the specimens respectively. The results indicate that the fatigue lives of 00Cr12 specimens were enhanced greatly after LSP, and improved by 62% compared with the specimens which were not treated by LSP. The unilateral tolerance factor method obtained an exact estimation value of the fatigue safe life; while the two-dimensional Weibull distribution method can get a range of values of fatigue safe lives, the fatigue safe lives of the specimens which after LSP were a range from 116570 to 150230, the average value was 132330. The two-dimensional Weibull distribution method has more engineering applicability and can be used to estimate the fatigue safe lives with fewer experiments.

The reinforcing mechanism of carbon fiber in composite adhesive for bonding carbon/carbon composites

A carbon fiber reinforced adhesive was developed for bonding carbon/carbon composites. The Weibull distribution method was used to analyze the bonding strength data, and the results showed that when the volume fraction of carbon fiber was 6 vol.%, the Weibull modulus was 42.9393 and the bonding strength of the adhesive was 11.3763 MPa. A model was proposed to explain the reinforcement of carbon fiber, and it was found that the strength of adhesive was a cubic function of the volume fraction of carbon fiber, and the function model was consistent with the Weibull data. We investigated that the carbon fiber could bridge adhesive matrix as a bridging effect for releasing the residual stress and inhibiting the extension of micro-crack.

Experimental Approach and Evaluation on Dynamic Reliability of PBGA Assembly

The aim of this paper is to provide a systematic method to perform experimental test and theoretical evaluation on fatigue characteristics of plastic-ball-grid-array (PBGA) assembly under random vibration. A specified PBGA assembly which contains different structural and material parameters was manufactured. The fatigue characteristics of PBGA assembly under random vibration were tested. Manson-Coffin empirically derived formula and rain-flow algorithm were used to achieve the fatigue life of solder joints. In the meantime, the failure curve (reliability-cycle number curve) can be obtained by using Weibull distribution method when PBGA assembly is on different working situation. Finally, life prediction of corner solder balls was deduced based on three-band technology and cumulative damage index. Test results lay a basis for high-reliability design of PBGA assembly for engineering application.