• Journal of the Korean Data and Information Science Society
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• 제25권3호
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• pp.611-622
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• 2014

The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2016년도 학술발표회
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• 콘크리트학회논문집
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• 제16권5호
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• pp.581-589
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• 2004

본 논문에서는 일정진폭 휨인장 및 쪼갬인장 반복하중을 받는 콘크리트의 피로신뢰성과 모델제안을 위하여 도로포장에 사용되는 콘크리트를 대상으로 연구하였다. 실험데이터는 2-모수 Weibull 확률분포함수를 사용하여 신뢰성 해석을 수행하였고, 적합도 검정을 통하여 이를 기반으로 한 모델을 제시하였다. 피로실험은 $150 mm{\times}75 mm$ 시험체의 쪼갬인장피로 실험방법과 $150 mm{\times}150 mm{\times}550 mm$ 시험체의 휨인장피로 실험방법을 적용였으며 일정 진폭 피로하중에 대하여 수행하였다. 두 가지의 실험방법에 대하여 응력 수준 90, 80, $70\%$로 변화하여 실험하고 이때 적용한 응력비는 0.1, 하중재하속도 20Hz, 정현파(sine)를 적용하였다. 연구결과 콘크리트 피로데이터의 분산성으로 인하여 보다 정확한 해석을 위해 두 가지의 해석 기준을 설정하여 제시하였으며, 그래픽방법, 모멘트방법 및 최우도법에 의해 2-모수 Weibull의 매개변수 $\alpha$와 u를 계산하고 이를 이용하여 확률밀도함수(P.D.F)와 누적분포함수(C.D.F)를 도시하였다. 또한, Weibull의 확률분포함수를 이용한 신뢰성 해석은 Kolmogorov-Smirnov의 방법을 사용하여 $5\%$의 유의수준에서 적합도 검정을 수행한 결과 채택되는 것으로 나타났다. 이러한 해석에 기초하여 쪼갬인장피로실험과 휨인장피로 실험에 대한 피로모델을 제시하고 응력수준에 따른 피로수명과 200만회 및 1,000만회에서의 피로강도를 산정하여 제시하였으며 국외의 주요 피로모델과 비교하였다.

• 대한조선학회논문집
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• 제58권3호
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• pp.137-143
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• 2021

In this study, the fracture strength of Flexible Secondary Barrier (FSB) composites was standardized by conducting a distribution analysis of the fracture probability, considering that the fracture strength of FSB composites such as glass fiber reinforced composites is relatively large. As the mechanical performance of FSB composites varies with the fiber direction, 20 replicate uniaxial tensile tests were performed for different temperatures ranging from the ambient to cryogenic conditions, considering the actual operating environment of liquefied natural gas. For the probability statistical analysis, the Weibull distribution analysis derived from the weakest link theory was used, considering the large variance in the fracture strength and brittle fracture behavior. The results of the Weibull distribution analysis were used to calculate the standard fracture strength of the FSB composites for different fiber directions. The findings can help ensure the reliability of the FSB mechanical properties in different fiber directions in the design of the secondary barrier and structural analyses.

• 전기학회논문지
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• 제58권2호
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• pp.308-313
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• 2009

This paper presents a reliability analysis of S-bonds for AF track circuits, which detect train movement and transmit a speed control signal to the train. Field survey shows that S-bonds are exposed to very large vibrations transferred from rail, and suffer from frequent failures when they were installed on ballasted track. We collected the time-to-failure data of S-bonds from the maintenance field of Seoul metro line 2, and made a parametric approach to estimate the statistical distribution that fits the time-to-failure data. The analysis shows that S-bonds have time-to-failure characteristics described by Weibull distribution. The estimated shape parameter of Weibull distribution is 1.1, which means the distribution has constant failure rate characteristics like exponential distribution. The reliability function, hazard function, percentiles and mean lifetime are derived for maintenance support.

• 한국태양에너지학회 논문집
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• 제32권2호
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• pp.95-104
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• 2012

This study purposed to predict wind energy for small size wind power generators at 50m above the ground in each area using mean wind speed data for 10 minutes collected from 2001 to 2011 by meteorological data in large cities having over 60% of 15 story (50m) or higher apartments including Seoul, Daejeon, Gwangju and Daegu representing the inland region, and Busan, Incheon and Ulsan representing the coastal region. In the results of analysis, we confirmed close agree ment between observatory weather data and probability density distribution obtained using Weibull's parameters, and this suggests that Weibull's parameter is applicable to the estimation of wind energy. Hourly output energy using the mean wind speed for 10 minutes and output energy obtained from Weibull's parameter showed an error less than 5%, and thus it was found that wind energy can be evaluated using Weibull's modulus.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2005년도 춘계학술대회 논문집
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• pp.114-118
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• 2005

In this study, the DC dielectric breakdown of epoxy composites used for molding material was experimented and then its data were simulated by Weibull distribution equation. From the analysis of Weibull distribution, it was confirmed that as the allowed breakdown probability was given by 0.1[%], the applied field value needed to be under 21.5[kV/mm].

• International Journal of Reliability and Applications
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• 제14권2호
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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.

• 대한치과기공학회지
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• 제43권1호
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• pp.13-18
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• 2021

Purpose: This study aimed to compare the flexural properties and perform the Weibull analysis of photo-curing three-dimensional (3D) printing resin. Methods: Photo-curing temporary resin (3D polymer) was used as a printing resin. Specimens (65 × 10 × 3.3 ㎣) were prepared following the ISO 20975-1 guidelines and according to the different printing orientations using a digital light processing 3D printer (D2 120; Dentium). The flexural strength (FS), flexural modulus, and work of fracture (WOF) were measured using a universal testing machine (Instron 3344; Instron) at a crosshead speed of 5 mm/min. Results: In this study, the 0° orientation exhibited higher FS and WOF than the 45° orientation. Significant differences were found among the printing orientations (p<0.05). Specimens printed at the 0° orientation were the most accurate. In the Weibull analysis, 0° showed the greatest Weibull modulus (m), which represents a higher reliability. Conclusion: 3D printing should be selected and used by considering flexural properties, size accuracy, and reliability.

• 대한의용생체공학회:의공학회지
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• 제37권1호
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• pp.21-30
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• 2016

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.