• Title/Summary/Keyword: Weibull distribution

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Statistical Analysis for Fatigue Lifetime of Ceramics (세라믹스의 피로수명에 대한 통계적 분석)

  • 박성은;김성욱;이홍림
    • Journal of the Korean Ceramic Society
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    • v.34 no.9
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    • pp.927-934
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    • 1997
  • Static and cyclic fatigue tests were carried out for alumina specimen to study the statistical analyses (normal, lognormal and Weibull distribution) of fatigue lifetime data and nominal initial crack length data. Fatigue lifetime data followed Weibull distribution better than normal or lognormal distribution, for the shape parameter of the notched specimen was larger than that of the unnotched specimen. The nominal initial crack length data obtained from fatigue lifetime followed the lognormal and Weibull distribution better than normal distribution, for the coefficient of variation of the unnotched specimen was larger than that of the notched specimen, and shape parameter of unnotched specimen was smaller than that of the notched specimen.

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고장 보고율을 이용한 현장 수명자료 분포의 모수추정

  • Park, Tae-Ung;Kim, Yeong-Bok;Lee, Chang-Hun
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2005.05a
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    • pp.678-685
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    • 2005
  • Estimating parameters of the lifetime distribution is investigated when field failure data are not completely reported. To take into account the reality and the accuracy of the estimates in such a case, the failure reporting probability is incorporated in estimating parameters. Firstly, method of maximum likelihood estimate(MLE) is used to estimate parameters of the lifetime distribution when failure reporting probability is known. Secondly, Expectation and Maximization(EM) algorithm is used to estimate the failure reporting probability and parameters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both case, procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simulation results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

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Analysis of Insulating Reliability in Epoxy Composites using Weibull Distribution Equation (와이블 분포식을 이용한 에폭시 복합체의 절연 신뢰도 분석)

  • Park, No-Bong;Lim, Jung-Kwan;Park, Yong-Pil
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2003.05a
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    • pp.813-816
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    • 2003
  • The dielectric breakdown of epoxy composites used for transformers was experimented and then its data were applied to Weibull distribution probability. First of all, speaking of dielectric breakdown properties, the more hardener increased, the stronger breakdown strength became at low temperature because of cross-linked density by the virtue of ester radical. The breakdown strength of specimens with filler was lower than it of non-filler specimens because it is believed that the adding filler forms interface and charge is accumulated in it, therefore the molecular motility is raised and the electric field is concentrated. In the case of filled specimens with treating silane, the breakdown strength become much higher. Finally, according to Weibull distribution analysis, reducing breakdown probability of equipment insulation lower than 0.1 % level requires the allowable field intensity values to be kept under 21.5 MV/cm.

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A Study on the Reliability of Helical Gear System Using Renewal Theory (재생이론에 의한 헬리컬 기어장치의 신뢰성에 관한 연구)

  • 김하수;양성모
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.6
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    • pp.90-96
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    • 1998
  • Helical gear system is widely used to transmit heavy duty power with harmonies and silences between parallel shafts. This paper predicts a life with Weibull distribution and estimates a reliability based on recycle principle of helical gear systems. 2-parameter Weibull distribution is generally adopted to estimate the mechanical life and the reliability of most gear systems, because this Weibull distribution is proper to explain a characteristics or a life of parts of gear systems with linearity of probability density data on weibull data sheet. For a high reliability, this paper estimates a number of overhaul times and a number of needed substitutes (exchange attachment,1 or parts) with following renewal theory, One is make an exchange of whole module include failure attachments/parts and second estimating method is only exchange of a failure attachments / parts.

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Analysis of Insulating Reliability in Epoxy Composites Using Weibull Distribution Equation (와이블 분포식을 이용한 Epoxy 복합체의 절연 신뢰도 해석)

  • 임중관;박용필;이준웅
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.14 no.8
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    • pp.647-651
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    • 2001
  • The dielectric breakdown of epoxy composites used for transformers was experimented and then its data were applied to Weibull distribution probability. First of all, speaking of dielectric breakdown properties, the more hardener increased, the stronger breakdown strength became at low temperature because of cross-linked density by the virtue of ester radical. The breakdown strength of specimens with filler was lower than it of non-filler specimens because it is believed that the adding filler forms interface and charge is accumulated in it, therefore the molecular motility is raised and the electric filed is concentrated. In the case of filled specimens with treating silane, the breakdown strength become much higher. Finally, from the analysis of weibull distribution, it was confirmed that to low allowed breakdown probability under 0,.1%, the applied field value needed to be under 21.5MV/cm.

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A Probabilistic Analysis on Fracture Strength of Ceramics (세라믹스의 파괴강도에 관한 확률론적 해석)

  • 김선진
    • Journal of Ocean Engineering and Technology
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    • v.10 no.2
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    • pp.61-68
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    • 1996
  • Weibull distribution function is applied very successfully to the strength of brittle materials such as ceramics and the weakest link model is applied to explain the ovents. This paper deals with the effect of specimen size on the strength of ceramics. The values of tensile strength were calculated by the Monte-Calro simuation. The tensile strength obtained was plotted on Weibull probabillity papers and represented by the 3-parameter Weibull distribution. The strength distribution function was compared with the theoretical weibull distribution. As a result, it was found that the Weibull shape parameter was changed due to the size and there was a possibility of a false indication as if the weakest link model holds good. We should be very careful when we apply the Weibull statistics to estimate the strength of products.

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On the maximum likelihood estimators for parameters of a Weibull distribution under random censoring

  • Kim, Namhyun
    • Communications for Statistical Applications and Methods
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    • v.23 no.3
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    • pp.241-250
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    • 2016
  • In this paper, we consider statistical inferences on the estimation of the parameters of a Weibull distribution when data are randomly censored. Maximum likelihood estimators (MLEs) and approximate MLEs are derived to estimate the parameters. We consider two cases for the censoring model: the assumption that the censoring distribution does not involve any parameters of interest and a censoring distribution that follows a Weibull distribution. A simulation study is conducted to compare the performances of the estimators. The result shows that the MLEs and the approximate MLEs are similar in terms of biases and mean square errors; in addition, the assumption of the censoring model has a strong influence on the estimation of scale parameter.

Mathematical modeling of wind power estimation using multiple parameter Weibull distribution

  • Chalamcharla, Seshaiah C.V.;Doraiswamy, Indhumathy D.
    • Wind and Structures
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    • v.23 no.4
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    • pp.351-366
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    • 2016
  • Nowadays, wind energy is the most rapidly developing technology and energy source and it is reusable. Due to its cleanliness and reusability, there have been rapid developments made on transferring the wind energy systems to electric energy systems. Converting the wind energy to electrical energy can be done only with the wind turbines. So installing a wind turbine depends on the wind speed at that location. The expected wind power can be estimated using a perfect probability distribution. In this paper Weibull and Weibull distribution with multiple parameters has been used in deriving the mathematical expression for estimating the wind power. Statistically the parameters of Weibull and Weibull distribution are estimated using the maximum likelihood techniques. We derive a probability distribution for the power output of a wind turbine with given rated wind speeds for the regions where the wind speed histograms present a bimodal pdf and compute the first order moment of this distribution.

Goodness-of-fit tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples

  • Kang, Suk-Bok;Han, Jun-Tae;Seo, Yeon-Ju;Jeong, Jina
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.4
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    • pp.903-914
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    • 2014
  • The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

Inference for exponentiated Weibull distribution under constant stress partially accelerated life tests with multiple censored

  • Nassr, Said G.;Elharoun, Neema M.
    • Communications for Statistical Applications and Methods
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    • v.26 no.2
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    • pp.131-148
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    • 2019
  • Constant stress partially accelerated life tests are studied according to exponentiated Weibull distribution. Grounded on multiple censoring, the maximum likelihood estimators are determined in connection with unknown distribution parameters and accelerated factor. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample size. However, it is not possible to obtain the Bayes estimates in plain form, so we apply a Markov chain Monte Carlo method to deal with this issue, which permits us to create a credible interval of the associated parameters. Finally, based on constant stress partially accelerated life tests scheme with exponentiated Weibull distribution under multiple censoring, the illustrative example and the simulation results are used to investigate the maximum likelihood, and Bayesian estimates of the unknown parameters.