• International Journal of Reliability and Applications
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• v.9 no.2
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• pp.167-182
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• 2008

The objective of this paper is to discuss the stochastic analysis and the statistical inference of a three-states semi-Markov reliability model. Using the maximum likelihood procedure, the parameters included in this model are estimated. Based on the assumption that the lifetime and repair time of the system are gener-alized Weibull random variables, the reliability function of this system is obtained. Then, the distribution of the first passage time of this system is derived. Many important special cases are discussed. Finally, the obtained results are compared with those available in the literature.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.6
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• pp.899-908
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• 1995

In this paper, the probabilistic relations of dual morphological operations, such as dilation and erosion, closing and opening, and close- open and open-close, and the statistical properties for a continuous stationary lst order Gauss-Markov source are analyzed. The result is that the dual filters have symmetrical means and skews, and equal variances. Also, the statistics of morphological filters are very similar with those of input source, as correlation coefficient increases.

• International Journal of Reliability and Applications
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• v.6 no.1
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• pp.13-29
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• 2005

This paper deals with the stochastic analysis of a three-states semi-Markov reliability model. Using both the maximum likelihood and Bayes procedures, the parameters included in this model are estimated. Next, assuming that the lifetime and repair time are generalized exponential random variables, the reliability function of this system is obtained. Then, the distribution of the first passage time of this system is discussed. Finally, some of the obtained results are compared with those available in the literature.

• Water for future
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• v.14 no.1
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• pp.51-58
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• 1981

This study attempts to examine and estabilish a simulation model from the stochastic analysis of daily streamflow. Daily streamflow records obstained at the main gauging stations along the Han, Nakdong and Geum River were used in the analysis. The following results were abtained. From the analysis of time series of streamflow by the correlogram and spectraal density, The serial component of one-year periodicity, serial correlation and irregular or random component were found. The coefficient of determination R2 of multilag model remaine a plateau at log-two, so that second order mu.ltilag model was Known to fit in the simulation of daily streamflow, Consequently, multilag and recised Markov model of the sewnd order give the best results in simulatin of daily streamflow. But the former generally gives better results than the latter. And theoretical markev model is unfit in the simulation of daily series without modification.

• Journal of Information Processing Systems
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• v.18 no.4
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• pp.457-469
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• 2022

Hydraulic concrete buildings in the northwest of China are often subject to the combined effects of low-temperature frost damage, during drying and wetting cycles, and salt erosion, so the study of concrete deterioration prediction is of major importance. The prediction model of the relative dynamic elastic modulus (RDEM) of four different kinds of modified concrete under the special environment in the northwest of China was established using Grey residual Markov theory. Based on the available test data, modified values of the dynamic elastic modulus were obtained based on the Grey GM(1,1) model and the residual GM(1,1) model, combined with the Markov sign correction, and the dynamic elastic modulus of concrete was predicted. The computational analysis showed that the maximum relative error of the corrected dynamic elastic modulus was significantly reduced, from 1.599% to 0.270% for the BS2 group. The analysis error showed that the model was more adjusted to the concrete mixed with fly ash and mineral powder, and its calculation error was significantly lower than that of the rest of the groups. The analysis of the data for each group proved that the model could predict the loss of dynamic elastic modulus of the deterioration of the concrete effectively, as well as the number of cycles when the concrete reached the damaged state.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1241-1250
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• 1996

The characteristics of fatigue cumulative damage and fatigue life of 8-harness satin woven CFRP composites with a circular hole under constant amplitude and 2-level block loading are estimated by Stochastic Makov chain model. It is found in this study that the fatigue damage accumulation behavior is very random and the fatigue damage is accumulated as two regions under constant amplitude fatigue loading. In constant amplitude fatigue loading the predicted mean number of cycles to a specified damage state by Markov chain model shows a good agreement with the test result. The predicted distribution of the fatigue cumulative damage by Markov chain model is similar to the test result. The fatigue life predictions under 2-level block loading by Markov chain model revised are good fitted to the test result more than by 2-parameter Weibull distribution function using percent failure rule.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.228-240
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• 1991

Many experimental data of fatigue crack propagation show that the fatigue crack propagation process is stochastic. Therefore, the study on the crack propagation must be based on the probabilistic approach. In the present paper, fatigue crack propagation process is assumed to be a discrete Markov process and the method is developed, which can evaluate the reliability of the structural component by using Markov chain model(Unit step B-model) suggested by Bogdanoff. In this method, leak failure, plastic collapse and brittle fracture of the critical component are taken as failure modes, and the effects of initial crack distribution, periodic and non-periodic inspection on the probability of failure are considered. In this method, an equivalent load value for random loading such as wave load is used to facilitate the analysis. Finally some calculations are carried out in order to show the usefulness and the applicability of this method. And then some remarks on this method are mentioned.

• Water for future
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• v.14 no.4
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• pp.19-26
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• 1981

The auto-and cross-correlation function, power spectrum, coherence function and Markov model are applied to investigate the statistical characteristics of discharge and each factor of water quality and the interrelation-ship between the variation of discharge and water quality factors. The analysis of discharge, dissolved oxygen and electric conductivity, which were only obtainable data at the Indogyo gagining station in the downstream of the Han River, clearly showed that they hace distinct period of 12 months and three different periods of 6, 4 and 3 months weaker than the former. The cross-correlation between the discharge and water quality(DO, COND) is rather weak and the crosscorrelation function has its peak at lag one. It is considered therefrom that the variation of discharge behaves on water quality facotrs with one day's difference. In the examination of linear regression model for the serial generation and predictive measures, discharge series is fit to first and second order Markov model and DO, COND to first order Markov model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.4B
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• pp.383-392
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• 2008

It is not always easy to estimate the parameters in hydrologic models due to insufficient hydrologic data when hydraulic structures are designed or water resources plan are established. Therefore, uncertainty analysis are inevitably needed to examine reliability for the estimated results. With regard to this point, this study applies a Bayesian Markov Chain Monte Carlo scheme to the NWS-PC rainfall-runoff model that has been widely used, and a case study is performed in Soyang Dam watershed in Korea. The NWS-PC model is calibrated against observed daily runoff, and thirteen parameters in the model are optimized as well as posterior distributions associated with each parameter are derived. The Bayesian Markov Chain Monte Carlo shows a improved result in terms of statistical performance measures and graphical examination. The patterns of runoff can be influenced by various factors and the Bayesian approaches are capable of translating the uncertainties into parameter uncertainties. One could provide against an unexpected runoff event by utilizing information driven by Bayesian methods. Therefore, the rainfall-runoff analysis coupled with the uncertainty analysis can give us an insight in evaluating flood risk and dam size in a reasonable way.

• Proceedings of the Korean Information Science Society Conference
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• 2007.06c
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• pp.263-266
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• 2007

This paper discusses the Bayesian statistical inference. This paper discusses the Bayesian inference, MCMC (Markov Chain Monte Carlo) integration, MCMC method, Metropolis-Hastings algorithm, Gibbs sampling, Maximum likelihood estimation, Expectation Maximization algorithm, missing data processing, and BMA (Bayesian Model Averaging). The Bayesian statistical inference is used to process a large amount of data in the areas of biology, medicine, bioengineering, science and engineering, and general data analysis and processing, and provides the important method to draw the optimal inference result. Lastly, this paper discusses the method of principal component analysis. The PCA method is also used for data analysis and inference.