Parameter Weibull Distribution Research Articles

Reliability prediction and evaluation model of smart electricity meter based on edge computing

In order to solve the problems of poor measurement stability and failure time of smart electricity meter in the process of life reliability analysis, this paper based on the least square method of regression analysis to estimate the parameters of Weibull distribution and accelerated life test model. The reliability index of smart electricity meter predicted by the new Weibull parameter estimation method is similar to that predicted by the point estimation method, but the reliability error of smart electricity meter predicted by the component stress method is large, indicating that there is an error between the actual operation of smart electricity meter and the predicted results in the design stage. The method proposed in this paper predicts the reliability of smart electricity meters under actual operation conditions, and predicts the correction factors of smart electricity meters' failure rate. The correction factors of various models are summarized to improve the reliability of smart electricity meters. In addition, the failure time before the smart meter is deduced and the failure rate of smart meter is more accurate.

Mechanical and Functional Property Investigation of 2-Layered Pervious Concrete

Background: Pervious concrete pavements are considered one of the well accepted stormwater management strategies as per environmental protection agencies. The interconnected pore structure in the pervious concrete allows the stormwater to percolate and thus reduce the runoff. Methods: The laboratory and field investigations on the pervious concrete pavements have shown that the abrasion and clogging are major distresses that reduce the functional performance of these sustainable pavements. The open graded structure of the pervious concrete undergoes ravelling due to vehicular movement and they may also allow the suspended particles in stormwater runoff to get clogged inside the pore structure. In this study, 2-layered pervious concrete was designed to balance the trade-offs between strength and durability. The porosity and density of 2-layered pervious concrete were found to be in the domain of conventional pervious concrete. Result: The failure pattern in compression indicated that the failure of the specimen was concentrated on the bottom layer compared to the top layer. Further, the compressive strength was found to be in the range of 11.90 to 20.0 MPa. The pore distribution at the interface of the top and bottom aggregate was found to follow 3-parameter Weibull distribution, where the scale parameter increased as the aggregate size increased. The abrasion resistance was found to be lower compared to conventional pervious concrete. Conclusion: Overall, it was found that 2-layered pervious concrete can be one of the alternatives to implement pervious concrete pavements addressing the demerits of conventional pervious concrete.

Parameter estimation of Weibull distribution on type III censored survival data by maximum likelihood estimator method: Case study of lung cancer patient data at Dr. Kariadi Hospital Semarang

Research on survival data is quite important. Many modeling problems can be made related to survival data. One of the survival data methods is the Type III Censored method, which is a type of censoring that is limited by time, with individuals entering the study at different times during a certain period of time. In this study, the research focus is to obtain point estimates of the Weibull distribution parameters using the Maximum Likelihood Estimator method. The method is used to examine the survival data of Weibull distribution censored type III on secondary data of patients with lung cancer at Dr. Kariadi Hospital Semarang. Based on the results of the analysis, the Weibull distribution with a point estimator for the scale parameter is α̂ = 94.875997 and the shape parameter is β̂ = 1.638958.

Estimation of parameters and quantiles of the Weibull distribution

We propose three new estimators of the Weibull distribution parameters which lead to three new plug-in estimators of quantiles. One of them is a modification of the maximum likelihood estimator and two of them are based on nonparametric estimators of the Gini coefficient. We also make some review of estimators of the Weibull distribution parameters and quantiles. We compare the small sample performance (in terms of bias and mean squared error) of the known and new estimators and extreme quantiles. Based on simulations, we obtain, among others, that the proposed modification of the maximum likelihood estimator of the shape parameter has a smaller bias and mean squared error than the maximum likelihood estimator, and is better or as good as known estimators when the sample size is not very small. Moreover, one of the proposed estimator, based on the nonparametric estimator of the Gini coefficient, leads to good extreme quantiles estimates (better than the maximum likelihood estimator) in the case of small sample sizes.

Wind Energy Analysis, Utilizations, And Economic Viability For Different Applications In Iraq

Thirty years of wind data, for 22 stations and a experimental locations inside Iraq, were used to calculate the potential of wind energy in Iraq. A full statistical analysis has been carried out for five selected stations which involved hourly wind speed, monthly average speed, annual values of shape and scale parameters of normal and weibull distribution. Frequency distribution, speed distribution, with their individual and cumulative probability pattern, are analyzed. It can be seen that 24% of the country enjoys monthly wind speed greater than 4 m/sec. Therefore, wind energy is sufficient for water pumping or electricity supply for remote areas in Iraq. Here we examine the viability of utilizing wind energy to supplement solar energy by comparing the supply and demand for different utilizations. The economic viability of wind energy visa vis traditional energy resources is also discussed.

A Minimum Discrepancy Method for Weibull Distribution Parameter Estimation

The most applied principles for parameter estimation are maximum likelihood and least square error. This paper presents a new principle with regard to the parameter estimation of the three-parameter Weibull distribution. By transforming the cumulative distribution function, constructed is a mapping from the value of the random variable and its corresponding cumulative distribution probability to the scale parameter. The scale parameter estimated by such a mapping is the random variable value and the corresponding cumulative distribution probability dependent when the shape parameter and/ or location parameter applied in the mapping is subject to error. Given a set of random variable values or a set of sample values, a larger error in the shape/location parameter brings about larger differences between the scale parameter values obtained with the individual random variable values or sample values, respectively. Based on such a causal relationship between the discrepancy and the shape/ location parameter value applied in the mapping relation, a new parameter estimation method is proposed. For the Weibull distribution parameter estimation according to a set of sample values, the right shape parameter and location parameter are those minimizing the discrepancy between the scale parameter values obtained with the individual sample values, respectively. Case studies demonstrate that the proposed method outperforms the maximum likelihood method and the Weibull plot-based least squares method.

New closed-form efficient estimators for a bivariate Weibull distribution

This study aimed to develop new closed-form and efficient estimators for the parameters of the bivariate Weibull distribution. New estimators can be produced using closed-form -consistent estimators for all parameters, except for the association parameter for which the estimator is not in closed form. This is carried out by utilizing a theorem that produces asymptotically efficient estimators. To achieve this, -consistent estimators are introduced. Fisher observed and expected information matrices are derived and used to develop new estimators. A simulation study and real data application are included to validate the new estimators. Given that the new estimators are as asymptotically efficient as maximum likelihood estimators and are in closed form, except for the association parameter, they can be used effectively in state-space modelling or real-time processing models. This is because of the shorter computing time associated with them than with maximum likelihood estimators.

Study on Rolling Bearing Life Based on Weibull Distribution and Correlation Coefficient Optimization and Maximum Likelihood Estimation

For the reliability evaluation of rolling bearing life, this paper proposes a parameter estimation method based on the correlation coefficient optimization method and the maximum likelihood estimation method (Cor-MLE), which can obtain more accurate Weibull distribution parameter estimation. Subsequently, the feasibility of Cor-MLE method for Weibull parameter estimation was verified by Monte Carlo simulation data and rolling bearing life test data. Compared with the parameter estimation results of least square method, grey model method and correlation coefficient optimization method, it is proved that the estimation results of this method have high accuracy and can meet the life analysis of rolling bearings.

Comparative evaluation of optimal Weibull parameters for wind power predictions using numerical and metaheuristic optimization methods for different Indian terrains.

The accurate selection of the wind speed distributions is crucial for a better utilisation of wind energy. The Weibull distribution is most commonly used distribution and hence its parameters need to be optimized. In this study five numerical methods, namely, maximum likelihood method (MLM), graphical method (GM), empirical method of Justus (EMJ), modified maximum likelihood method (MMLM) and wind atlas analysis and application program (WAsP) and three metaheuristic optimization algorithms, namely, social spider optimization (SSO), particle swarm optimization (PSO) and genetic algorithm (GA) are applied for estimating Weibull distribution parameters at three different locations (onshore-Kayathar, nearshore-Jafrabad and offshore-Gulf of Khambhat (GOK) in India and also comparison of numerical and optimization methods are employed to tune the optimal parameters. The accuracy of the methods was evaluated using three different statistical analysis techniques. As per the results, GOK has the maximum wind power density of 450.2W/m2 compared to Jafrabad and Kayathar. It was observed that among the five methods used for Weibull parameters estimation, WAsP method presented a better curve fit with the histogram of the wind speed. The results shows that SSO and PSO presents a comparably better performance than GA in the term of accuracy on the basis of closeness to converged solution.

Fatigue lives of self compacting concrete containing recycled concrete aggregates and blended cements

AbstractAn effort has been made to enhance the flexural fatigue lives of self compacting concrete (SCC) in which half of the natural aggregates (NA) were substituted with recycled concrete aggregates (RCA) by means of blended cements. Blended SCC mixes containing either silica fume (SF) or metakaolin (MK) along with cement, and fly ash (FA) was also adopted. Fatigue lives have been evaluated as mean value, design value life and theoretical value. The Weibull distribution parameters were utilized for the valuation of mean and design values of fatigue lives for different considered mixes. It has been observed that adding RCA in SCC causes degradation in the fatigue lives, which can be enhanced by adopting the blended mixture comprising of SF or MK, cement and FA. Both SF and MK established a promising result in improving fatigue lives. Still, the blend of MK in SCC contributed most effectively in enhancing the fatigue life of SCC comprising RCA.

Bayesian analysis of designed reliability improvement experiments with application to adaptive termination

AbstractIn reliability improvement experiments, engineers are very interested in which factors affect the reliability of products. Furthermore, they hope to terminate experiment early without affecting the identified results. In this article, we assume the shape and scale parameters of Weibull distributions vary with experimental factors, and construct a Bayesian framework to identify important factors. We model the relationships between the parameters of Weibull distributions and experimental factors, and determine important factors based on Bayesian credibility intervals. Because the proposed method can analyze lifetime data with heavy censoring, we adaptive terminate experiment through estimating and comparing model coefficients under different experiment times. The results show that experiment time is shortened while the important factors are not changed.

Creep damage coupling model of concrete based on the statistical damage theory

The creep behavior is one of the key issues in the design and construction of hydraulic concrete structures. However, it is an enormous challenge to accurately predict the development of creep deformation in concrete structures. Since the creep deformation behavior of concrete under long-term load action originates from the interaction between creep and damage, a new creep damage coupling model was developed by introducing the damage variable into the creep constitutive equation. This model utilized the statistical damage theory framework and assumed that the damage variable follows the random distribution described by the Weibull function. Then Weibull distribution parameters F0 and m were derived to determine the evolution equation of the damage variable D. Considering stress under complex stress conditions may change, the stress-strain correlation of concrete under complex stress conditions was deduced using the elastic creep theory. Moreover, the results of uniaxial compressive concrete creep tests with the corresponding numerical simulations under different levels of sustained loads, and the accuracy and applicability of the creep damage coupling model were verified. Consequently, the nonlinear creep properties of hydraulic concrete were analyzed by combining it with acoustic emission techniques.

Distribution of individual wave overtopping volumes at rubble mound seawalls

For a safe design of a rubble mound seawall, overtopping characteristics such as the mean overtopping discharge (q) and the maximum individual overtopping volume (Vmax) should be limited. Unlike q, the estimation of Vmax is more complex and requires a wave-by-wave analysis of overtopping as well as a statistical analysis. The present study contributes to the knowledge of the distribution of individual overtopping volumes and the estimation of Vmax at rubble mound seawalls. A total of 135, small-scale 2D physical model tests were conducted across a practical range of crest freeboards and considered the slopes of 1:1.5 and 1:2. The well-known 2-parameter Weibull and Exponential distributions were first fitted to the experimental data to estimate the Vmax. Different approaches to sample the observed distribution of wave-by-wave overtopping volumes were evaluated including a threshold method using the top 10%, 30%, and 50% of individual overtopping volumes, and a method that applies a greater weighting to the larger events. For both Weibull and Exponential distributions, the weighted method was found to be the best one providing a 23% and 17% decrease in scatter index (SI) values compared to the best of existing methods. To facilitate the estimation of Vmax for design purposes, a simple empirical formula was developed as a function of the dimensionless mean overtopping discharge (q*) and the number of overtopping waves (Now). This formula with SI = 37% outperformed the distribution-based methods as well as the best of existing formulae for Vmax. In the case of the normalised bias (NBIAS), the distribution methods underestimated Vmax by −21% (Weibull) and −31% (Exponential) whereas the new formula yielded NBIAS = −6%.

Penaksiran Parameter Distribusi Weibull Menggunakan Algoritma Genetika dan Particle Swarm Optimization

This study aims toestimate and compare the results of the estimated parameters of the Weibull distributionusing the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The Weibull distribution used is a two-parameter Weibull distribution and a three-parameterWeibull distribution. In the GA Algorithm, there are evolution operators such as crossover and mutation. Meanwhile, in PSO algorithm doesn’t. The evolution operators that can optimize complex problems and a very wide search space Evaluation of the two method is carried out by observing the difference in the resulting fitness values.Based on the simulation data from the estimator obtained using the R program, it is found that the two-parameter Weibull distribution parameter and a three-parameterWeibull distribution using a AG algorithm are both used in this distribution. This is supported by the small difference in the fitness value of the GA algorithm obtained compared to the PSO algorithm. The sample space also affects the difference in fitness. The large the sample space, the greater the fitness.

Analysis of adaptive type-II progressively hybrid censoring with binomial removals

Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed.

New insights in the probability distributions of wave-by-wave overtopping volumes at vertical breakwaters

Advances in the development of prediction tools for wave overtopping allow now for overtopping volumes to be estimated with good accuracy, with the combined use of mean overtopping rates and maximum wave by wave overtopping volumes in a sequence of wave overtopping events. While previous literature has tended to focus on mean overtopping rates at coastal structures, limited studies have investigated the wave by wave overtopping volumes at coastal sea defences; in particular, a paucity of studies have focussed on the prediction of the shape parameter in the Weibull distribution (i.e., Weibull b) of overtopping volumes. This study provides new insights on the probability distribution of individual wave overtopping volumes at plain vertical seawalls by analysing the measured Weibull b values derived from a series of laboratory experiments on seawalls performed on a wide range of wave conditions and crest freeboards. The influence of wave conditions (wave steepness, significant wave height), structural parameters (crest freeboard, toe water depth), impulsiveness, probability of overtopping waves, and overtopping discharge on Weibull b parameter were examined, and then compared with the well-established empirical formulae. For the conditions covered within this study, it was found that the probability distribution of wave-by-wave overtopping volumes follow a 2-parameter Weibull distribution. No apparent differences in Weibull b values were reported with the variation of incident wave steepness and impulsiveness parameter. Results of this study revealed that Weibull b values at vertical walls, subjected to non-impulsive wave conditions, can be predicted reasonably well using relative freeboard and relative overtopping rates. A new unified formula is proposed for the estimation of Weibull b values at vertical walls under impulsive and non-impulsive wave attack.

Using the Bayes estimator for Weibull parameters estimation taking into account left-truncated and rightcensored data

Today, when operation of commercial plants is organised, they are expected to comply to constantly increasing requirements for safety, dependability and efficiency of operation. The methods and procedures that are employed for the purpose of improving the safety and dependability of commercial plants are based on the information on the dependability of components, systems and equipment. In order to identify the objective dependability characteristics of such facilities, their behaviour in operation is monitored. In the course of facility operation monitoring, periods of continuous fault-free operation, periods of downtime, causes of downtime, failures, defects and malfunctions of items, frequency and depth of preventive maintenance of elements and systems, as well as other information are recorded. It should be noted that elements and systems of today’s industrial facilities, such as nuclear power plants, petrochemical complexes, etc., are classified as highly dependable equipment. Failures of such equipment are rare. The number of same-type facilities is extremely small. Aim. Given the above, the problem arises of developing methods for reliable estimation if item dependability characteristics on the basis of limited statistical information. Method. The paper examines a method for calculating facility dependability indicators on the basis of statistical information obtained in operation, i.e. a method for minimising the risk function while taking into account left-truncated and right-censored data for the purpose of Weibull distribution parameter estimation. Conclusions. By way of example, the authors refer to a method for evaluating dependability indicators based on complete, right-censored and left-truncated operation times, as, in practice, such combination is quite common. The form of likelihood functions for the Weibull distribution is given. A test case is examined, whereas, using the risk function minimisation, estimates of the Weibull distribution parameters are obtained for a sample that contains full, left-truncated and right-censored data. The authors examined the variation in the Weibull distribution values and their accuracy depending on the proportion of truncated and censored data.

A Mathematical Model Analysis for Estimating Stock Market Price Changes

In this paper, different methods for estimation of parameters of Weibull distribution were examined using Mean Square Error (MSE) as a criterion for selecting the best model. The Method of Moments exceeded other methods. In the same circumstance, the estimated results were logically extended to form a matrix that would help in predicting different commodity price processes by exploring the properties of fundamental matrix solution where we obtained predicted stock prices and asset returns for 12 months. Finally, from the fundamental matrix system a theorem was developed and proved to show different levels of changes as it affects stock market in terms of short-run and long-run respectively

Comparison of eight methods of Weibull distribution for determining the best-fit distribution parameters with wind data measured from the met-mast.

In order to assess the wind characteristics of a specified region, a pre-analysis of the region can be made with different numerical methods. For instance, the two-parameter Weibull distribution is widely used in wind energy studies and the wind energy sector to obtain information about the wind characteristics of the specified region. The main goal of this study is to perform a detailed analysis of the data obtained from the wind measurement sensors on a meteorological mast with a height of 80m to determine the wind characteristics and wind energy potential of a region in Osmaniye, Turkey. The suitability of the two-parameter Weibull distribution, which is the most popular probability distribution model, was investigated to evaluate the distribution of these wind data. In the precise determination of the Weibull distribution parameters (k and c), the suitability of eight different numerical methods, namely, graphical (GM), empirical of Justus (EMJ), empirical of Lysen (EML), power density (PDM), moment (MoM), maximum likelihood (MLM), modified maximum likelihood (MMLM), and alternative maximum likelihood (AMLM) methods, was examined. Root-mean-square error (RMSE), chi-square (X2), and analysis of variance (R2) were used to compare and verify the performance of these models. The best and worst performances in these eight methods were MMLM and GM, compared with the actual measured data. Also, wind power density was calculated considering these methods and prevailing wind directions.

Reliability for Weibull Distribution using Ms-Excel

The weibull distribution is mostly used in reliability analysis life data analysis due to its versatility. Depending on the values of the parameters, the weibull distribution can be used to model a variety of life behaviors. The three parameter weibull distribution can estimate the probability of null wind speed and gives greater weight to low wind speeds. We also discuss least square method of estimation problems and hypothesis testing issues, with the emphasis on graphical methods and some weibull analysis software are also provided. The analysis is also applicable in the design stage and in-service time as well and it is not only limited to the production stage. Now, the techniques to perform the Weibull analysis process are done by statistical software programs.