scholarly journals Robust explicit estimators of Weibull parameters

Metrika ◽  
2009 ◽  
Vol 73 (2) ◽  
pp. 187-209 ◽  
Author(s):  
Kris Boudt ◽  
Derya Caliskan ◽  
Christophe Croux
Keyword(s):  
Weibull Parameters ◽  
Explicit Estimators

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

scholarly journals The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters

2018 ◽  
Vol 7 (2) ◽  
pp. 139-150 ◽  
Author(s):  
Adekunlé Akim Salami ◽  
Ayité Sénah Akoda Ajavon ◽  
Mawugno Koffi Kodjo ◽  
Seydou Ouedraogo ◽  
Koffi-Sa Bédja
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Time Series Data ◽  
Empirical Method ◽  
Likelihood Method ◽  
Series Data ◽  
New Approach ◽  
Weibull Parameters ◽  
Distribution Histogram ◽  
Mean Wind Speed

In this article, we introduced a new approach based on graphical method (GPM), maximum likelihood method (MLM), energy pattern factor method (EPFM), empirical method of Justus (EMJ), empirical method of Lysen (EML) and moment method (MOM) using the even or odd classes of wind speed series distribution histogram with 1 m/s as bin size to estimate the Weibull parameters. This new approach is compared on the basis of the resulting mean wind speed and its standard deviation using seven reliable statistical indicators (RPE, RMSE, MAPE, MABE, R2, RRMSE and IA). The results indicate that this new approach is adequate to estimate Weibull parameters and can outperform GPM, MLM, EPF, EMJ, EML and MOM which uses all wind speed time series data collected for one period. The study has also found a linear relationship between the Weibull parameters K and C estimated by MLM, EPFM, EMJ, EML and MOM using odd or even class wind speed time series and those obtained by applying these methods to all class (both even and odd bins) wind speed time series. Another interesting feature of this approach is the data size reduction which eventually leads to a reduced processing time.Article History: Received February 16th 2018; Received in revised form May 5th 2018; Accepted May 27th 2018; Available onlineHow to Cite This Article: Salami, A.A., Ajavon, A.S.A., Kodjo, M.K. , Ouedraogo, S. and Bédja, K. (2018) The Use of Odd and Even Class Wind Speed Time Series of Distribution Histogram to Estimate Weibull Parameters. Int. Journal of Renewable Energy Development 7(2), 139-150.https://doi.org/10.14710/ijred.7.2.139-150

Nondestructive Photoelastic and Machine Learning Characterization of Surface Cracks and Prediction of Weibull Parameters for Photovoltaic Silicon Wafers

2021 ◽  
pp. 1-40
Author(s):  
Logan Rowe ◽  
Alexander J. Kaczkowski ◽  
Tung-Wei Lin ◽  
Gavin Horn ◽  
Harley Johnson
Keyword(s):  
Machine Learning ◽  
Learning Algorithm ◽  
Tensile Load ◽  
Silicon Wafers ◽  
Uniaxial Tensile ◽  
Support Vector ◽  
Weibull Parameters ◽  
Bulk Stress ◽  
Wire Motion

Abstract A nondestructive photoelastic method is presented for characterizing surface microcracks in monocrystalline silicon wafers, calculating the strength of the wafers, and predicting Weibull parameters under various loading conditions. Defects are first classified from through thickness infrared photoelastic images using a support vector machine learning algorithm. Characteristic wafer strength is shown to vary with the angle of applied uniaxial tensile load, showing greater strength when loaded perpendicular to the direction of wire motion than when loaded along the direction of wire motion. Observed variations in characteristic strength and Weibull shape modulus with applied tensile loading direction stem from the distribution of crack orientations and the bulk stress field acting on the microcracks. Using this method it is possible to improve manufacturing processes for silicon wafers by rapidly, accurately, and nondestructively characterizing large batches in an automated way.

scholarly journals Predicting How Crack Tip Residual Stresses Influence Brittle Fracture

2002 ◽  
Author(s):  
Saeid Hadidimoud ◽  
Ali Mirzaee-Sisan ◽  
Chris E. Truman ◽  
David J. Smith
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Experimental Studies ◽  
Crack Tip ◽  
Distribution Model ◽  
Relative Importance ◽  
Local Approach ◽  
Weibull Parameters ◽  
Experimental Scatter ◽  
Crack Tip Blunting

A probability distribution model, based on the local approach to fracture, has been developed and used for estimating cleavage fracture following prior loading (or warm pre-stressing) in two ferritic steels. Although there are many experimental studies it is not clear from these studies whether the generation of local residual stress and/or crack tip blunting as a result of prior loading contribute to the enhancement in toughness. We first identify the Weibull parameters required to match the experimental scatter in lower shelf toughness of the candidate steels. Second we use these parameters in finite element simulations of prior loading on the upper shelf followed by unloading and cooling to lower shelf temperatures to determine the probability of failure. The predictions are consistent with experimental scatter in toughness following WPS and provide a means of determining the relative importance of the crack tip residual stresses and crack tip blunting. We demonstrate that for our steels the crack tip residual stress is the pivotal feature in improving the fracture toughness following WPS. The paper finally discusses these results in the context of the non-uniqueness and the sensitivity of the Weibull parameters.

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