• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.107-114
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• 2013

Modelling of failures is an important element of reliability modelling. Empirical modelling approach suitable for complex item is explored in this paper. First step of the empirical modelling approach is to plot hazard function, density function, Weibull probability plot as well as cumulative intensity function to see which model fits best for the given data. Next step of the empirical modelling approach is select appropriate model for the data and fit the parametric model accordingly and estimate the parameters.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.385-396
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• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.201-206
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• 2003

This study is test for STS304 specimen using bending and torsion state. Rounded specimen and notched specimen including fracture surface investigation was comparatively experimented, fatigue life according to degree of surface finishing was examined. Fatigue fracture probability of notched canilever specimens were predicted by P-S-N curve, median rank and Weibull distribution. And at the relation with the rotational speed and stress, the fatigue life of the test specimen was higher at high speed than low speed If summarize STS304 torsion result of fatigue test, is as following. Fatigue life prediction was available by Weibull statistics distribution, and 50% breakdown probability correlation equation was appeared as following.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.3
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• pp.105-111
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• 2013

Probability distribution of microbes in wastewater is a crucial factor to be determined for microbial risk assessment associated with its reuse. The objective of this study was to investigate probability distribution of an indicator microorganism in wastewater. Daily total coliform counts measured from nationwide wastewater treatment plants in 2010 by the Ministry of Environment were used for statistical analysis. Basic statistics and probability distributions were estimated in the three different spatial scales using the MS Excel software and FARD2006 model. Overall, wastewater from manure and livestock treatment plants demonstrated greater median coliform counts than from sewage and village treatment plants. Generalized logistic (GLO) and 2-parameter Weibull (WBU2) appeared to be the two probability distributions that fitted best for total coliform numbers in wastewater. The study results of microbial statistics and probability distributions would provide useful data for quantitative assessment of microbial risk from agricultural wastewater reuse.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.11a
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• pp.285-286
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• 2008

Recently, epoxy based nano-composites are being increasingly investigated for their electrical properties, since the introduction of nano fillers demonstrate several advantages in their properties when compared with the similar properties obtained for epoxy systems with micrometer sized fillers. We calculated scale and shape parameter using dielectric strength. In this paper, it is investigated that the allowable' breakdown probability of specimens is stable at some value using Weibull statistics. Therefore we found that breakdown probability of specimens is stable until 20 [%].

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09b
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• pp.1146-1147
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• 2006

Diamond segments were fabricated by cold pressing and sintering under pressure at the temperature up to $750^{\circ}C$. Based on the results of this investigation, it can be concluded that the segments containing 39wt.% cobalt in the matrix material have the highest bending strength at a fracture probability of 50 % due to the weibull distribution method. According to the weibull statistics, it was also determined that the transverse rupture strength was the best for 39 wt.% cobalt ratio in the matrix material for the fracture probability when the other variables are the same.

• Journal of Power System Engineering
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• v.21 no.5
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• pp.79-85
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• 2017

Vickers hardness is an important material in the design and reliability is required. Therefore, these values are very important as the basic data for design, manufacture and development, and the identification of quantitative probability distribution characteristics such as mean and dispersion is a very important parameter in design. In this study, Vickers hardness was measured after artificially heat-treated in the temperature range 753K, where chrome depletion near the grain boundary occurred for three kinds of stainless steels, and the Vickers hardness were evaluated. From the results, Vickers hardness increased with increasing heat treatment temperature. In Weibull distribution for Vickers hardness, the dispersion of STS310S at 813K and 873K was small, and the dispersion of STS316L at 753K, 933K and 993K was small. Also, STS347H exhibited the lowest dispersion at 753K in three kinds of stainless steels. The scale parameter increased with increasing heat treatment temperature in three kinds of stainless steels.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2184-2187
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• 2003

Quantizers for digital coding systems are usually optimized with respect to a model of the probability density function of the random variable to be quantized. Thus a mismatch of the quantizer relative to the actual statistics of the random variable may be unavoidable. This paper presents the results of an experimental investigation of mismatched quantizers. For the modeling of the source statistics, various types of the Weibull distribution are used, and the optimization of the quantizer is carried with respect to the minimum mean-square error (mse) criterion. The goal of this paper is to find an estimate formula for the mismatched quantizer on Weibull sources.

• Communications for Statistical Applications and Methods
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• v.30 no.2
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• pp.191-213
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• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.