An Improved Parameter Estimation Method for Three-Parameter Weibull Distribution in the Life Analysis of Rolling Bearing

2012 ◽  
Vol 569 ◽  
pp. 442-446 ◽  
Author(s):  
Feng Long Yin ◽  
Ya Shun Wang ◽  
Chun Hua Zhang ◽  
Xiang Po Zhang
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rolling Bearing ◽  
Accurate Estimate ◽  
Distribution Model ◽  
Bearing Life ◽  
Mechanical Products ◽  
Life Analysis

Three-parameter Weibull distribution is playing a more and more important role in the reliability analysis of mechanical products. It can provide higher accuracy and better reflection of reliability in operating situation concerning fitting and parameter estimation for the rolling bearing life data. This paper focuses on the theory derivation of the maximum likelihood estimation of the three-parameter Weibull distribution, puts forward an improved method for the model parameter estimation and draws the life distribution model. Following that, the method has been proved to be correct and accurate by practical examples.The proposed method can provide a more accurate estimate way for the life analysis of rolling bearing based on three-parameter Weibull distribution.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

Maximum Likelihood Method for Parameter Estimation of Weibull Distribution Model Based on Fruit Fly Optimization Algorithm

2014 ◽  
Vol 602-605 ◽  
pp. 3508-3511 ◽  
Author(s):  
Xiang Ping Meng ◽  
Chuan Qi Zhao ◽  
Lei Huo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Optimization Algorithm ◽  
Likelihood Estimation ◽  
Fruit Fly ◽  
Distribution Model ◽  
Fruit Fly Optimization Algorithm ◽  
Fruit Fly Optimization

It is difficult to estimate the parameters of Weibull distribution model using Maximum Likelihood Estimation based on Ant Colony Algorithm (ACA) or Particle Swarm Optimization theory (PSO) for which is easy to fall into premature and needs more variables, thus Fruit Fly Optimization Algorithm (FOA) theory is introduced into maximum likelihood estimation, and a parameter estimation method based on FOA theory is proposed, an example has been simulated to verify the feasibility and effectiveness of this method by comparing with ACA and PSO.

Optimization of Distribution Model for CNC Lathes Early Failures

2009 ◽  
Vol 407-408 ◽  
pp. 107-111
Author(s):  
Dian Sheng Chen ◽  
Tian Shan Lv
Keyword(s):  
Weibull Distribution ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Distribution Model ◽  
Early Failure ◽  
Index Method ◽  
Failure Data ◽  
Failure Distribution ◽  
Early Failures

To eliminate early failures of CNC lathes, it is necessary to study the early failure distribution to establish accurate early failure distribution model of CNC lathes. During the modeling process, the same group of failure data obeys Weibull distribution, exponential distribution, super-exponential distribution and gamma distribution at the same time. To optimize the failure distribution model, this paper used “relevant index” method by comparing the distribution function curve fitting and determined that this group of failure data fitted Weibull distribution using maximum likelihood estimation method with its shape parameter k 0.8706 and scale parameter b142.6991.

scholarly journals Parameter Estimation of Three-Parameter Weibull Distribution of Gas Turbine Blades Using TPC Windchill Quality Solutions

2020 ◽  
pp. 31-40
Author(s):  
Erhuvwu Totore ◽  
Joseph E. Udumebraye ◽  
William E. Odinikuku
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Turbine Blades ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Weibull Analysis ◽  
Analysis Software ◽  
Gas Turbine Blades

The maximum likelihood estimation method is an effective technique for estimating the parameters of the Weibull distribution. However, it is an arduous task to compute the parameters of the Weibull distribution using numerical methods, hence; various reliability software packages have been developed to address this difficulty. In this study, an attempt is made to obtain the estimates of three-parameter Weibull distribution through the application of Weibull analysis software TPC Windchill Quality Solutions 11. The study involves the analysis of the failure times of ten identical gas turbines blades over a period of ten years. From the results obtained, it was found that the gas turbine blades were in their wear-out period. The results obtained in the study were compared with Weibull analysis software Minitab 19 and the values of the Weibull estimates obtained were found to be close. This shows that the software is suitable for the parameter estimation of three-parameter Weibull distribution.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

scholarly journals PARAMETER ESTIMATION FOR COMPLICATED NOISE ENVIRONMENT

2019 ◽  
Vol 6 (125) ◽  
pp. 15-25
Author(s):  
Serhii Vovk
Keyword(s):  
Parameter Estimation ◽  
Optimization Problem ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Optimal Estimation ◽  
Optimization Methods ◽  
Noise Distribution ◽  
Method Performance ◽  
Noise Environment ◽  
M Estimator

For a complicated noise environment the use of M-estimator faces a problem of choosing a cost function yielding the best solution. To solve this problem it is proposed to use a superset of cost functions. The superset capabilities provide constructing a parameter estimation method for complicated noise environment. It consists in tuning the generalized maximum likelihood estimation to the current noise environment by setting values of three free superset parameters related to the scale, the tail heaviness and the form of noise distribution, as well as to the anomaly values that presence in data. In general case, this method requires to solve the optimization problem with a non-unimodal objective function, and it can be mostly implemented by using the zero-order optimization methods. However, if the noise environment has known statistics, the proposed method leads to the optimal estimation. If the noise environment is complicated or does not have a complete statistics, the proposed method leads to the more effective estimates comparing to those of mean, median, myriad and meridian estimators. Numerical simulations confirmed the method performance.

scholarly journals The Modified Kumaraswamy Weibull Distribution: Properties and Applications in Reliability and Engineering Sciences

2020 ◽  
pp. 433-446
Author(s):  
M. E. Mead ◽  
Ahmed Afify ◽  
Nadeem Shafique Butt
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Hazard Rates ◽  
Alpha Power ◽  
Mathematical Properties ◽  
Engineering Sciences ◽  
Maximum Likelihood Estimation Method

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone  and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications.

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

Sign in / Sign up

Export Citation Format

Share Document