• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.459-465
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• 2009

For an inverse double Weibull distribution which is symmetric about zero, we obtain distribution and moment of ratio of independent inverse double Weibull variables, and also obtain the cumulative distribution function and moment of a skew-symmetric inverse double Weibull distribution. And we introduce a skew-symmetric inverse double Weibull generated by a double Weibull distribution.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.859-870
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• 2009

We obtain a skewed double Weibull distribution by a double Weibull distribution, and evaluate its coefficient of skewness. And we obtain the approximate maximum likelihood estimator(AML) and moment estimator of skew parameter in the skewed double Weibull distribution, and hence compare simulated mean squared errors(MSE) of those estimators. We compare simulated MSE of two proposed reliability estimators in two independent skewed double Weibull distributions each with different skew parameters. Finally we introduce a skewed double Weibull distribution generated by a uniform kernel.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.93-109
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• 2007

In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.333-348
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• 2015

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

• Computers and Concrete
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• v.21 no.3
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• pp.291-298
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• 2018

In this study, the flexural fatigue performance of concrete beams made with 100% Coarse Recycled Concrete Aggregates (RCA) and 100% Coarse Natural Aggregates (NA) were statistically commanded. For this purpose, the experimental fatigue test results of earlier researcher were investigated using two parameter Weibull distribution. The shape and scale parameters of Weibull distribution function was evaluated using seven numerical methods namely, Graphical method (GM), Least-Squares (LS) regression of Y on X, Least-Squares (LS) regression of X on Y, Empherical Method of Lysen (EML), Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM). The average of Weibull parameters was used to incorporate survival probability into stress (S)-fatigue life (N) relationships. Based on the Weibull theory, as single and double logarithm fatigue equations for RCA and NA under different survival probability were provided. The results revealed that, by considering 0.9 level survival probability, the theoretical stress level corresponding to a fatigue failure number equal to one million cycle, decreases by 8.77% (calculated using single-logarithm fatigue equation) and 6.62% (calculated using double logarithm fatigue equation) in RCA when compared to NA concrete.

• Tunnel and Underground Space
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• v.13 no.6
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• pp.444-454
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• 2003

Rock fragmentation technique by cutter penetration has widely been used in the mechanical tunnel excavation. Microcracks propagate and interact because of locally concentrated high stress induced by cutter penetration. which is caused by heterogeneity of rocks. In this study Weibull distribution function and degradation index are used to consider the strength heterogeneity of a rock and the degradation of rock properties after failure. Through the numerical analyses, it is shown that the lateral pressure has an important influence on the rock fragmentation. In the single cutter penetration, large chips are formed as lateral pressure increase. The cutter spacing is also an important factor that affects the rock fragmentation in the double cutter penetration. The fragmentation efficiency of the double cutter penetration is better when cutter spacing is 70 mm than 40 mm and 100 mm. From the results, it is expected that this study can be applied to a TBM tunnel design by understanding of chipping process and mechanism of rock due to cutter penetration.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.1-16
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• 2007

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

• Journal of the Korean Institute of Gas
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• v.22 no.6
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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.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.6
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• pp.1-8
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• 1994

To enhance the strength of gears for transmission, Generally caburizing heat treatment is applied. But there are some problems in this technology the distortion of gears during heat treatment process, and the discontinuity of manufacturing process. For these reasons, the high frequency induction hardening process is widely used. This method is one of the surface hardening process to improve the wear resistance and fatigue life of the machine components. In this study, to compare the bending fatigue strength of caburized gear with that of induction hardened gear, bending fatigue testing of gears with two different cases was performed by using an electrohydraulic servo-controlled fatigue testing machine and double tooth bending fatigue test fixture. Fatigue life distributions at constant stress levels were established directly from fatigue data. For gear design, the fatigue strength distribution at specified life is more important. This distribution is obtained by statical transformation from fatigue life distribution. Reliability of bending fatigue strength was estimated by P-S-N curves and Weibull distribution.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.4
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• pp.147-153
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• 2000

This paper presents a design method using CAE(Computer Aided Engineering ) with the consideration of reliability for optimal gear driving system. This method considered a configuration of the intermediate shaft. There are four mounting types, such as double straddle, double overhung, output gear overhung, and input ger overhung in the intermediate shaft. The reliability and life analysis are based on the two-parameter Weigbull distribution lives of the gears and bearing . The validity and feasibility of the proposed method are verified by the application to transmission of a industry machine.