• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.219-226
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• 2004

In this paper, we consider two-components system which the lifetimes have a bivariate Weibull distribution with bivariate random censored data. Here the bivariate censoring times are independent of the lifetimes of the components. We obtain estimators and approximated confidence intervals for the reliability of series system based on likelihood function and relative frequency, respectively. Also we present a numerical study.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.819-829
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• 2024

This paper delves into an examination of both non-Bayesian and Bayesian estimation techniques for determining the Topp-leone inverse Weibull distribution parameters based on progressive Type-II censoring. The first approach employs expectation maximization (EM) algorithms to derive maximum likelihood estimates for these variables. Subsequently, Bayesian estimators are obtained by utilizing symmetric and asymmetric loss functions such as Squared error and Linex loss functions. The Markov chain Monte Carlo method is invoked to obtain these Bayesian estimates, solidifying their reliability in this framework.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.463-473
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• 2017

Reinforced concrete is a complex material to be modeled in finite element domain. A proper material model is necessary to represent the nonlinear behaviour accurately. Though the nonlinear analysis of RC structures evolved long back, still an accurate and reliable model to predict the realistic behaviour of components are limited. It is observed from literature that there are three well-known models to represent the nonlinear behaviour of concrete. These models include Chu model (1985), Hsu model (1994) and Saenz model (1964).A new stress-strain model based on Weibull distribution has been proposed in the present study. The objective of the present study is to analyze a reinforced concrete beam under flexural loading by employing all the models. Nonlinear behaviour of concrete is considered in terms of stress vs. strain, damage parameter, tension stiffening behaviour etc. The ductility of the RC beams is computed by using deflection based and energy based concepts. Both deflection ductility and energy based ductility is compared and energy based concept is found to be in good correlation with the experiments conducted. The behavior of RC beam predicted using ABAQUS has been compared with the corresponding experimental observations. Comparison between numerical and experimental results confirms that these four constitutive models are reliable in predicting the behaviour of RC structures and any of the models can be employed for analysis.

• Journal of Electrical Engineering and Technology
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• 제9권3호
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• pp.957-963
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• 2014

Converter transformers play important roles in high-voltage direct current transmission systems. This paper presents experimental and analysis results of the combined electrical and thermal aging of oil-impregnated paper at pulsating DC voltages. Breakdown voltages and time-to-breakdown of oil-paper specimens were measured by using short-time and constant-stress tests. The breakdown characteristics of combined electrical and thermal aging on insulation system were discussed. According to the relationship between failure time and aging temperature, the two-parameter Weibull model was improved. On the basis of the competing risk algorithm and the improved Weibull model, the two factors failure model was calculated. And the influence of temperature in the insulation system has been analyzed. This model performs better than the two-parameter Weibull model when both time and temperature are considered as variables in estimating the lifetime of oil-paper insulation.

• Journal of the Korean Institute of Gas
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• 제22권6호
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• pp.40-43
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• 2018

For pressure safety valves, open failure and close failure are partially dependent on each other. A method is proposed in this work that uses a Markov process model and a Weibull distribution model in order to construct a reliability model for two kinds of failure. A pressure safety valve model is obtained from a known open failure model, an induced close failure model, and a simultaneous failure model that reproduces recently reported inspection results. It is expected that the application of the proposed method can be expanded to quantitative risk assessment of various systems that have partially dependent multiple failure states.

• Journal of Korean Society of Forest Science
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• 제101권4호
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• pp.599-605
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• 2012

The purpose of this study is to estimate diameter distribution, volume per hectare, and carbon stock for Quercus variabilis stand. 354 Quercus variabilis stands were selected on the basis of age and structure, the data and samples for these stands are collected. For the prediction of diameter distribution, Weibull model was applied and for the estimation of the parameters, a simplified method-of-moments was applied. To verify the accuracy of estimates, models were developed using 80% of the total data and validation was done on the remaining 20%. For the verification of the model, the fitness index, the root mean square error, and Kolmogorov-Smirnov statistics were used. The fitness index of the site index, height, and volume equation estimated from verification procedure were 0.967, 0.727, and 0.988 respectively and the root mean square error were 2.763, 1.817, and 0.007 respectively. The Kolmogorov-Smirnov test applied to Weibull function resulted in 75%. From the models developed in this research, the estimated volume and above-ground carbon stock were derived as $188.69m^3/ha$, 90.30 tC/ha when site index and stem number of 50-years-old Quercus variabilis stand show 14 and 697 respectively. The results obtained from this study may provide useful information about the growth of broad-leaf species and prediction of carbon stock for Quercus variabilis stand.

• Journal of Korean Society for Quality Management
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• 제40권2호
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• pp.186-198
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• 2012

Since Duncan(1956) first proposed an economic design of $\bar{X}$-control charts, most of the succeeding works on economic design of control charts assumed the exponential failure model like Duncan. Hu(1984), however, assumed a more versatile Weibull failure model to develop an economic design of $\bar{X}$-control charts and Banerjee and Rahim(1988) further improved Hu's design by changing the assumption of fixed-length sampling intervals to variable-length ones. In this article we follow the approach of Banerjee and Rahim(1988) but include a pair of warning limits inside the control limits in order to search for a failure without stopping the process when the sample mean falls between warning and control limits. The computational results indicate that the proposed model gives a lower cost than Banerjee and Rahim's model unless the early failure probability of a Weibull distribution is relatively large. The reduction in cost is shown to become larger as the cost of production loss outweighs the cost of searches for a failure.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.13-30
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• 1993

We propose the ordered least squares estimators(OLSE's) of the parameters and the p-th quantiles for the two-parameter Weibull regression model under the Type II censoring, The Monte Carlo simulations are performed to compare the proposed estimators with the maximum likelihood estimators(MLE's), and it is shown that the proposed estimators are slightly better than MLE's as the censoring rate goes up.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.131-136
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• 1993

We shall consider the trends of correlation coefficient between the smallest and largest observations in the Weibull model in the presence of an unidentified outlier, and derive the density functions of order statistics by the permanent theory.

• Journal of the Korea Safety Management & Science
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• 제1권1호
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• pp.135-143
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• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected bum-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.