scholarly journals Estimation on Reliability Models of Bearing Failure Data

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Xia Xintao ◽  
Chang Zhen ◽  
Zhang Lijun ◽  
Yang Xiaowei
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Distribution Model ◽  
Bearing Failure ◽  
Analysis Model ◽  
Failure Data ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter

The failure data of bearing products is random and discrete and shows evident uncertainty. Is it accurate and reliable to use Weibull distribution to represent the failure model of product? The Weibull distribution, log-normal distribution, and an improved maximum entropy probability distribution were compared and analyzed to find an optimum and precise reliability analysis model. By utilizing computer simulation technology and k-s hypothesis testing, the feasibility of three models was verified, and the reliability of different models obtained via practical bearing failure data was compared and analyzed. The research indicates that the reliability model of two-parameter Weibull distribution does not apply to all situations, and sometimes, two-parameter log-normal distribution model is more precise and feasible; compared to three-parameter log-normal distribution model, the three-parameter Weibull distribution manifests better accuracy but still does not apply to all cases, while the novel proposed model of improved maximum entropy probability distribution fits not only all kinds of known distributions but also poor information issues with unknown probability distribution, prior information, or trends, so it is an ideal reliability analysis model with least error at present.

scholarly journals Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution

2020 ◽  
Vol 14 (4) ◽  
pp. 293-302
Author(s):  
Bin Deng ◽  
Xingang Wang ◽  
Danyu Jiang ◽  
Jianghong Gong
Keyword(s):  
Weibull Distribution ◽  
Normal Distribution ◽  
Fracture Probability ◽  
Strong Correlations ◽  
Strength Data ◽  
Statistical Variations ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter ◽  
Measured Strength

It is generally assumed that the measured strength of brittle ceramics follows a Weibull distribution. However, there seems to be few sound and direct evidences to support this assumption. Several previous studies have shown that other distributions, such as normal distribution and log-normal distribution may describe more appropriately the strength data than Weibull distribution. In this paper, the efficiency of using a normal distribution to describe the strength which follows a Weibull distribution is examined based on Monte-Carlo simulations. It was shown that there exist strong correlations between the parameters of normal distribution and those of Weibull distribution. For the designed fracture probability not lower than 0.01, analyses based on both normal distribution and Weibull distribution may give nearly identical predictions for the applicable stress levels. For lower fracture probabilities, the differences between the predictions of both distributions are not significant. It was suggested that, if there is no evidence to confirm that the measured strength follows a certain distribution, normal distribution and Weibull distribution seem to have the same efficiency in analysing the statistical variations in the measured strength of ceramics.

A Log-Normal Distribution Model for the Molecular Weight of Aquatic Fulvic Acids

2000 ◽  
Vol 34 (6) ◽  
pp. 1103-1109 ◽  
Author(s):  
Stephen E. Cabaniss ◽  
Qunhui Zhou ◽  
Patricia A. Maurice ◽  
Yu-Ping Chin ◽  
George R. Aiken
Keyword(s):  
Molecular Weight ◽  
Normal Distribution ◽  
Fulvic Acids ◽  
Distribution Model ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Normal Distribution Model

Comprehensive Source Identification and Apportionment Analysis of five Heavy Metals in Soils in Wenzhou City, China

2020 ◽  
Author(s):  
Shuai Shao ◽  
Bifeng Hu ◽  
Yin Zhou ◽  
Zhou Shi
Keyword(s):  
Heavy Metals ◽  
Normal Distribution ◽  
Source Identification ◽  
Mixture Distribution ◽  
Anthropogenic Sources ◽  
Distribution Model ◽  
Auxiliary Variables ◽  
Industrial Emissions ◽  
Log Normal ◽  
Log Normal Distribution

<p>Source identification and apportionment of heavy metals (HMs) has been a vital issue of soil contamination restoration. In this study, qualitive approaches (Finite mixture distribution model (FMDM) and raster based principal components analysis (RB-PCA)) as well as quantitative approach (positive matrix factorization (PMF)) were composed to identify and apportion sources of five HMs (Cd, Hg, As, Pb, Cr) with the help of several crucial auxiliary variables in Wenzhou City, China. The result of FMDM showed Cd, and Pb fitted for single log-normal distribution, while Hg fitted for double log-normal mixed distribution, and As, Cr presented triple log-normal distribution. Each element was identified and separated from natural or anthropogenic sources. An improved score interpolation map of PCA attached with corresponded auxiliary variables analysis suggested three main contribution sources including parental materials, mines exploiting and industrial emissions contributes most in the whole study area. Each element was further discussed for quantitative contributions through PMF model. Parental materials contributed to all elements (Cd, Hg, As, Pb, Cr) as 89.22%, 84.81%, 7.31%, 35.84%, 27.42%. Industrial emissions had a contribution as 2.94%, 80.77%, 15.93%, 4.79%, 25.63% for each element respectively. While Mine exploiting mixed with fertilizers inputs has dedicated for such five HMs as 7.84%,11.92%, 48.23%, 10.40% and 46.95%. Such results could efficiently be devoted to scientific decisions and strategies making regarding HMs pollution regulation in soils.</p>

scholarly journals Analysis of Probability Distribution of Muzzle Velocity for Chrome Plated Barrel

2021 ◽  
Vol 24 (4) ◽  
pp. 401-407
Author(s):  
Jaekab Kim ◽  
Jaehoon Kim
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Distribution Model ◽  
Statistical Parameters ◽  
Chrome Plating ◽  
Fitness Test ◽  
Muzzle Velocity ◽  
Probability Paper ◽  
Statistical Program

To confirm the change of muzzle velocity and the most suitable probability distribution model of the 155 mm K9 howitzer barrel with chrome plating and changed rifling. Using a statistical program, the muzzle velocity were plotted on a normal distribution, a 2-parameter and 3-parameter Weibull distribution on a probability paper. Also, statistical parameters were estimated and muzzle velocity fitness test and probability of K676 charge were plotted. In both the chrome-plated with standard rifling and changed rifling for K9 barrel, the 2-parameter and 3-parameter Weibull distribution were skewed to the left compared to the normal distribution. It was confirmed that the muzzle velocity of the K9 barrel with chromium-plated is suitable for the normal distribution and 3-parameter Weibull distribution model.

scholarly journals Distribution of Earthquake Magnitude Levels in Bangladesh

2019 ◽  
Vol 11 (3) ◽  
pp. 15
Author(s):  
Md. Habibur Rahman ◽  
Md. Moyazzem Hossain
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Earthquake Magnitude ◽  
Human Beings ◽  
Richter Scale ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Best Fit

Earthquakes are one of the main natural hazards which seriously make threats the life and property of human beings. Different probability distributions of the earthquake magnitude levels in Bangladesh are fitted. In terms of graphical assessment and goodness-of-fit criterion, the log-normal distribution is found to be the best fit probability distributions for the earthquake magnitude levels in Bangladesh among the probability distribution considered in this study. The average earthquake magnitude level found 4.67 (in Richter scale) for log-normal distribution and the approximately forty-six percent chance is predicted to take place earthquake magnitude in the interval four to five.

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