• Journal of Advanced Marine Engineering and Technology
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• v.23 no.4
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• pp.453-461
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• 1999

The estimation of fatigue life at the design stage is very important in order to arrive at feasible and cost effective solutions considering the total lifetime of the structure and machinery compo-nents. In this study the practical procedure of prediction of fatigue life by use of cumulative damage factors based on Miner-Palmgren hypothesis and probability density function is shown with a $135,000m^3$ LNG tank being used as an example. In particular the parameters of Weibull distribution taht determine the stress spectrum are dis-cussed. At the end some of uncertainties associated with fatigue life prediction are discussed. The main results obtained from this study are as follows: 1. The practical procedure of prediction of fatigue life by use of cumulative damage factors expressed in combination of probability density function and S-N data is proposed. 2. The calculated fatigue life is influenced by the shape parameter and stress block. The conser-vative fatigue design can be achieved when using higher value of shape parameter and the stress blocks divded into more stress blocks.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.423-431
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• 2005

Some recent inequalities for expectation and cumulative distribution function are improved.

• Journal of Ocean Engineering and Technology
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• v.13 no.3 s.33
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• pp.29-35
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• 1999

At the design of Mark III membrane type LNG tank, an analytical and experimental approach on the fatigue strengths of membrane and its welds are very important in order to assist designers and surveyors. In this study, fatigue tests of lap weld of Mark III membrane type LNG tank were carried out and cumulative damage factor was calculated in order to estimate the fatigue life by probability density function and rule methods. It contained the following tests and reviews : 1) The fatigue tests of lap weld of stainless steel according to statistical testing method recommended by JSME, 2)Preparation of S-N curve for lap welds considering the statistical properties of the results of fatigue tests. 3) Procedure for estimating the initiation life of fatigue crack of lap welds under variable loads by the rule lf classification society and probability density function, 4) Guideline for inspection of lap welds fo membrane type LNG tank.

• Korean Journal of Metals and Materials
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• v.46 no.9
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• pp.554-562
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• 2008

The distribution and prediction interval for the misorientation angle of grain boundary at which $Cr_2N$ was precipitated during heating at $900^{\circ}C$ for $10^4$ sec were newly estimated, and followed by the estimation of mathematical and median rank methods. The probability density function of the misorientation angle can be estimated by a statistical analysis. And then the ($1-{\alpha}$)100% prediction interval of misorientation angle obtained by the estimated probability density function. If the estimated probability density function was symmetric then a prediction interval for the misorientation angle could be derived by the estimated probability density function. In the case of non-symmetric probability density function, the prediction interval could be obtained from the cumulative distribution function of the estimated probability density function. In this paper, 95, 99 and 99.73% prediction interval obtained by probability density function method and cumulative distribution function method and compared with the former results by median rank regression or mathematical method.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.6
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• pp.993-999
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• 2004

The estimation of fatigue life at the design stage of membrane type LNG tank is very important in order to arrive at feasible and cost effective solutions considering the total lifetime of the tank. In this study, the practical procedure of fatigue life prediction by use of cumulative damage factors based on Miner-Palmgren hypothesis and probability density function has been shown with the corner region of Gaz Transport Membrane type LNG tank being used as an example. In particular the parameters of Weibull distribution that determine the stress spectrum are discussed. The main results obtained from this study are as follows: 1. The recommended value for the shape parameter of Weibull distribution for the LNG tank is 1.1 in case of using the direct calculation method proposed in this study. 2. The calculated fatigue life is influenced by the shape parameter of Weibull distribution and stress block. The safe fatigue design can be achieved by using higher value of shape parameter and the stress blocks divided into more stress blocks.

• Computers and Concrete
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• v.8 no.2
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• pp.163-176
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• 2011

By virtue of chord-length density function from the field of statistical physics, this paper introduced a quantitative approach to estimate the distribution of cement paste thickness between aggregates in concrete. Dynamics mixing method based on molecular dynamics was employed to generate one model structure, then image analysis algorithm was used to obtain the distribution of thickness of cement paste in model structure for the purpose of verification. By comparison of probability density curves and cumulative probability curves of the cement paste thickness among neighboring aggregates, it is found that the theoretical results are consistent with the simulation. Furthermore, for the model mortar and concrete mixtures with practical volume fraction of Fuller-type aggregate, this analytical formula was employed to predict the influence of aggregate volume fraction and aggregate fineness. And evolution of its mean values were also investigated with the variation of volume fraction of aggregate as well as the fineness of aggregates in model mortars and concretes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.3
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• pp.147-160
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• 2020

A stochastic probabilistic model for harbor structures such as rubble-mound breakwater has been formulated by using the generalized Wiener process considering the nonlinearity of damage drift and its nonlinear uncertainty, by which the damage path with real-time can be tracked, the residual useful lifetime at some age can also be analyzed properly. The formulated stochastic model can easily calculate the probability of failure with the passage of time through the probability density function of cumulative damage. In particular, the probability density functions of residual useful lifetime of the existing harbor structures can be derived, which can take into account the current age, its present damage state and the future damage process to be occurred. By using the maximum likelihood method and the least square method together, the involved parameters in the stochastic model can be estimated. In the calibration of the stochastic model presented in this paper, the present results are very well similar with the results of MCS about tracking of the damage paths as well as evaluating of the density functions of the cumulative damage and the residual useful lifetime. MTTF and MRL are also evaluated exactly. Meanwhile, the stochastic probabilistic model has been applied to the rubble-mound breakwater. The related parameters can be estimated by using the experimental data of the cumulative damages of armor units measured as a function of time. The theoretical results about the probability density function of cumulative damage and the probability of failure are very well agreed with MCS results such that the density functions of the cumulative damage tend to move to rightward and the amounts of its uncertainty are increased as the elapsed time goes on. Thus, the probabilities of failure with the elapsed time are also increased sharply. Finally, the behaviors of residual useful lifetime have been investigated with the elapsed age. It is concluded for rubble-mound breakwaters that the probability density functions of residual useful lifetime tends to have a longer tail in the right side rather than the left side because of the gradual increases of cumulative damage of armor units. Therefore, its MRLs are sharply decreased after some age. In this paper, the special attentions are paid to the relationship of MTTF and MRL and the elapsed age of the existing structure. In spite of that the sum of the elapsed age and MRL must be equal to MTTF deterministically, the large difference has been shown as the elapsed age is increased which is due to the uncertainty of cumulative damage to be occurred in the future.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• International Journal of Reliability and Applications
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• v.14 no.2
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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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.3
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• pp.1-8
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• 2016

We propose an adaptive histogram stretching algorithm for application to a car's personal recorder. The algorithm was used for pre-processing to detect the license plate region in an image from a personal recorder. The algorithm employs a Probability Density Function (PDF) and Cumulative Distribution Function (CDF) to analyze the distribution diagram of the images. These two functions are calculated using an image obtained by sampling at a certain pixel interval. The images were subjected to different levels of stretching, and experiments were done on the images to extract their characteristics. The results show that the proposed algorithm provides less deterioration than conventional algorithms. Moreover, contrast is enhanced according to the characteristics of the image. The algorithm could provide better performance than existing algorithms in applications for detecting search regions for license plates.