A Simple Estimator of the Shape Factor of the Two-Parameter Weibull Distribution

1987 ◽  
Vol 26 (2) ◽  
pp. 323-325 ◽  
Author(s):  
Rolan D. Christofferson ◽  
Dale A. Gillette
Keyword(s):  
Weibull Distribution ◽  
Shape Factor ◽  
Two Parameter

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

scholarly journals Bayesian Method for Estimating Weibull Parameters for Wind Resource Assessment in the Equatorial Region: a Comparison Between Two-parameter and Three-parameter Weibull Distributions

2021 ◽  
Author(s):  
M. G. M. Khan ◽  
M. Rafiuddin Ahmed
Keyword(s):  
Weibull Distribution ◽  
Bayesian Approach ◽  
Resource Assessment ◽  
Equatorial Region ◽  
Weibull Parameters ◽  
Wind Speeds ◽  
Wind Resource Assessment ◽  
Low Wind Speeds ◽  
Wind Resource ◽  
Two Parameter

Abstract The two-parameter Weibull distribution has garnered much attention in the assessment of wind energy potential. The estimation of the shape and scale parameters of the distribution has brought forth a successful tool for the wind energy industry. However, it may be inappropriate to use the two-parameter Weibull distribution to accurately characterize wind speed at every location, especially at sites where the frequency of low speed is high, such as the Equatorial region. In this work, for the robustness in wind resource assessment, we first propose a Bayesian approach in estimating Weibull parameters. Secondly, we compare the techniques of wind resource assessment using both two and three-parameter Weibull distributions for different sites in the Equatorial region. The Bayesian inference approach is adopted using Markov Chain Monte Carlo (MCMC) algorithms. Simulation studies conducted in this research confirms that the Bayesian approach seems to be a new robust alternative technique for accurate estimation of Weibull parameters. An appropriate Weibull distribution and the application of the Bayesian approach in estimating distribution parameters were determined using data from six sites in the Equatorial region from 1° N of Equator to 19° South of Equator. Results revealed that a three-parameter Weibull distribution is a better fit for wind data having a greater percentage of low wind speeds (0-1 m/s) and low skewness. However, wind data with a smaller percentage of low wind speeds and high skewness showed better results using a two-parameter Weibull distribution. The results also demonstrate that the proposed Bayesian approach to estimate Weibull parameters is extremely useful in the analysis of wind power potential, as it provides more accurate results while characterizing lower wind speeds.

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

A New Technique for Optimization of Product Acceptance Process in Terms of Misclassification Probability

2018 ◽  
pp. 1-32
Author(s):  
Nicholas A. Nechval ◽  
Konstantin N. Nechval
Keyword(s):  
Weibull Distribution ◽  
Optimization Technique ◽  
Parametric Uncertainty ◽  
Lifetime Distribution ◽  
Statistical Quality Control ◽  
Misclassification Probability ◽  
Distribution Parameters ◽  
A New Technique ◽  
Two Parameter

A product acceptance process is an inspecting one in statistical quality control or reliability tests, which are used to make decisions about accepting or rejecting lots of products to be submitted. This process is important for industrial and business purposes of quality management. To determine the optimal parameters of the product acceptance process under parametric uncertainty of underlying lifetime models (in terms of misclassification probability), a new optimization technique is proposed. The most popular lifetime distribution used in the field of product acceptance is a two-parameter Weibull distribution, with the assumption that the shape parameter is known. Such oversimplified assumptions can facilitate the follow-up analyses, but may overlook the fact that the lifetime distribution can significantly affect the estimation of the failure rate of a product. Therefore, the situations are also considered when both Weibull distribution parameters are unknown. An illustrative numerical example is given.

scholarly journals Probabilistic Fracture Energy Assessment of Natural Fibre Reinforced Concrete by Two Parameter Weibull Distribution

2018 ◽  
Vol 7 (3.12) ◽  
pp. 407
Author(s):  
Neha P Asrani ◽  
Murali G ◽  
Arthika J ◽  
Karthikeyan. K ◽  
Haridharan. M.K
Keyword(s):  
Weibull Distribution ◽  
Fracture Energy ◽  
Plain Concrete ◽  
Natural Fibre ◽  
Test Results ◽  
Specific Fracture Energy ◽  
Energy Assessment ◽  
Experimental Process ◽  
Specific Fracture ◽  
Two Parameter

Fracture energy is the post-crack energy absorption ability of the material that represents the energy absorbed by the structure at the time of failure. Its analysis has gained importance and hence requires a powerfulmethod for its development. A two parameter Weibull distribution proves to be an efficient tool in analysing the scattered experimental test results. In this paper, the specific fracture energy of plain concrete and concrete reinforced with natural fibres of hemp, wheat straw and elephant grass are statistically analysed by two parameter Weibull distribution by using graphical method. For determining Weibull parameters, 21 equations have been used and the best equation is taken for the reliability analysis. A Weibull reliability curve is plotted, which shows the specific fracture energy at each reliability level. This curve enables an engineer to choose the fracture energy of a particular mix based on its reliability requirement and safety limit. Therefore, reliability curves are a pioneer in statistical analysis as they eliminate the time-consuming and costly experimental process. This method can be applied in areas with similar uncertainties.  

scholarly journals Experimental Investigation on the Impact Resistance of Carbon Fibers Reinforced Coral Concrete

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4000 ◽  
Author(s):  
Bing Liu ◽  
Jingkai Zhou ◽  
Xiaoyan Wen ◽  
Jianhua Guo ◽  
Xuanyu Zhang ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Carbon Fibers ◽  
Impact Test ◽  
Concrete Strength ◽  
Impact Resistance ◽  
Initial Crack ◽  
Drop Weight ◽  
Weight Impact ◽  
The Impact ◽  
Two Parameter

In this study, the impact resistance of coral concrete with different carbon fiber (CF) dosages subjected to drop-weight impact test was investigated. For this purpose, three concrete strength grades (C20, C30, C40) and six CF dosages (0.0%, 0.3%, 0.6%, 1.0%, 1.5%, and 2.0% by weight of the binder) were considered, and a total of 18 groups of carbon fibers reinforced coral concrete (CFRCC) were cast. For each group, eight specimens were tested following the drop-weight impact test suggested by CECS 13. Then, the two-parameter Weibull distribution theory was adopted to statistically analyze the variations in experimental results. The results indicated that the addition of CFs could transform the failure pattern from obvious brittleness to relatively good ductility and improve the impact resistance of coral concrete. Moreover, the impact resistance of CFRCC increases with the CF dosage increasing. The statistical analysis showed that the probability distribution of the blow numbers at the initial crack and final failure of CFRCC approximately follows the two-parameter Weibull distribution.

Statistical Distribution of Tapered Roller Bearing Fatigue Lives at High Levels of Reliability

2005 ◽  
Author(s):  
Michael N. Kotzalas
Keyword(s):  
Weibull Distribution ◽  
Roller Bearing ◽  
Rolling Element Bearing ◽  
Mathematical Methods ◽  
Data Set ◽  
Tapered Roller Bearing ◽  
Roller Bearings ◽  
Tapered Roller ◽  
Tapered Roller Bearings ◽  
Two Parameter

The original two-parameter Weibull distribution used for rolling element bearing fatigue tends to greatly underestimate life at high levels of reliability. This fact has been proven for through hardened ball, cylindrical and spherical roller bearings, as well as linear ball bearings, by other researchers. However, to date this has not been done with tapered roller bearings (TRB) or case carburized materials, and as such this study was conducted. First, the three-parameter Weibull distribution was utilized to create a mathematical model, and statistical data analysis methods were put into place. This algorithm was then investigated as to its ability to discern the shape of the reliability distribution using known, numerically generated, data sets for two and three-parameter Weibull distributions. After validation, an experimental data set of 9702 TRB’s, 98% of which were case carburized, was collected. Using the developed algorithm on this data set, the overall RMS error was reduced from 26.0% for the standard, two-parameter to 12.2% for the three-parameter Wiebull distribution. Also, the error at 99.9% reliability was reduced from 95.8% to 37%. However, as the results within varied from previously published values at high reliabilities, there is likely a difference in the underlying population and/or dependency on the statistical and mathematical methods utilized. Therefore, more investigation should be conducted in this area to identify the underlying variables and their effects on the results.

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