• 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.

• Journal of Korean Society of Transportation
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• v.5 no.2
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• pp.73-80
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• 1987

Various procedures for evaluation of traffic noise annoyance have been proposed. However, most of the studies of this type are restricted for improving traffic flow. In this paper, a method to predict the road traffic noise is proposed in terms of equivalent continuous A-Weighted sound pressure level (Leq), based on a probability model. First, distribution of the road traffic noise level are investigated. second, the weibull distribution parameters are estimated by using the quantification theory. Finally, a prediction model of the road traffic noise is proposed based on the weibull distribution model The predicted values of the Leq are closely matched the measured data.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.3
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• pp.109-115
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• 2006

The Weibull distribution is a good candidate for accurate probabilistic model with its rich shape-forming ability and relatively simple CDF(cumulative distribution function). If there are sufficient information to get convincible mean and variance for a probabilistic event, reliable parameters of the Weibull distribution can be determined uniquely. However, sufficient information is not given as usual. There needs more deliberate model building method for that case. This Paper presents an effective parameter estimation technique for Weibull distribution with limited failure data.

• 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.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.359-370
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• 1999

We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.

• Nuclear Engineering and Technology
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• v.55 no.5
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• pp.1924-1934
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• 2023

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F_en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.399-409
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• 2016

Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modified Weibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modified Weibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• The KIPS Transactions:PartD
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• v.11D no.4
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• pp.885-892
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• 2004

Weibull distribution Iincluding Rayleigh and Exponential distribution is a typical model to estimate the effort distribution which is committed to the software testing phase. This model does not represent standpoint that many efforts are committed actually at the test beginning point. Moreover, it does not properly represent the various distribution form of actual test effort. To solve these problems, this paper proposes the Sigmoid model. The sigmoid function to be applicable in neural network transformed into the function which properly represents the test effort of software in the model. The model was verified to the six test effort data which were got from actual software projects which have various distribution form and verified the suitability. The Sigmoid model nay be selected by the alternative of Weibull model to estimate software test effort because it is superior than the Weibull model.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.