• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.91-105
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• 2019

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

• Journal of Korean Society of Water and Wastewater
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• v.25 no.2
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• pp.141-152
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• 2011

In this study, we extracted effective factors of pipe burst from the status data of water asset, operating data of pressure, volume and etc. and 7 years' pipe burst and repair records. The extracted factors were sorted by each attribution and then a statistical analysis was performed to generate a pipe burst probability function using the logistic regression model. As the result, material, diameter, length, laying year, pressure and road width affected to pipe burst significantly. Especially, in case of small diameter, laying year was most effective factor and in case of steel pipe, external loading was main cause of burst, and in case of cast iron, PE, PC, HP pipes, the deterioration of joint was main cause. The other side, as a result of Hosmer-Lemeshow goodness of fit test the models are turned out significant statistically. Also the classification criteria were determined to minimize the total cost from classification errors, when the predicted probability was more than 18% this pipe could have a chance of burst.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.12
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• pp.3275-3295
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• 2012

In this paper, we analyze the performance of an amplify-and-forward (AF) two-way relaying system, where two sources exchange information via the aid of an intermediate relay that is selected among multiple relays according to max-min criterion. We consider a practical scenario, where one source-relay link undergoes Rician fading, and the other source-relay link is subject to Rayleigh fading. To be specific, we derive a tight lower bound for the outage probability. From this lower bound, the asymptotic outage probability and average symbol error rate (SER) expressions are derived to gain insight into the system performance at high signal-to-noise ratio (SNR) region. Furthermore, we investigate the optimal power allocation (PA) with fixed relay location (RL), optimal RL with fixed PA and joint optimization of PA and RL to minimize the outage probability and average SER. The analytical expressions are verified through Monte Carlo simulations, where the positive impact of Rician factor on the system performance is also illustrated. Simulation results also validate the effectiveness of the proposed PA and relay positioning schemes.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• Journal of the Korean Society of Safety
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• v.34 no.5
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• pp.87-94
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• 2019

This study deals with the reliability analysis approach of the temporary structure that can consider the uncertainty in rotational stiffness at the joints of the members, for which the semi-rigid connections are modelled as rotational spring and its coefficient is treated as a random variable following uniform distribution. In addition, this study introduces a computational procedure of the effective length coefficient for more accurate buckling load according to connection conditions of the supporting members attached to the joint. From the results of this study, it can be seen that the failure probability of the joint-hinge model (Case 1) presented in the design standard is higher than that of the practical model (Case 5) considering the rotational stiffness at the joints. This implies that the design standard leads to a conservative design of the temporary structure. The results also confirmed that the failure probability of the vertical member, i.e., the most critical member, can be further reduced when the base connection is provided with a fixed end. The comparative results between FORM, SORM and MCS further demonstrated that FORM can have a high level of numerical efficiency while ensuring the accuracy of the solution, compared with SORM and MCS. Based on these results, the proposed approach can be used as an accurate and efficient reliability analysis method of the three dimensional temporary structure.

• Journal of Welding and Joining
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• v.17 no.1
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• pp.124-132
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• 1999

Thermal fatigue strength of the solder joints is the most critical issue for TSOP(Thin Small Outline Package) because the leads of this package are extremely short and thermal deformation cannot be absorbed by the deflection of the lead. And the TSOP body can be subject to early fatigue failures in thermal cycle environments. This paper was discussed distribution of thermal stresses at near the joint between silicon chip and die pad and investigated their reliability of solder joints of TSOP with 42 alloy clad lead frame on printed circuit board through FEM and 3 different thermal cycling tests. It has been found that the stress concentration around the encapsulated edge structure for internal crack between the silicon chip and Cu alloy die pad. And using 42 alloy clad, The reliability of TSOP body was improved. In case of using 42 alloy clad die pad(t=0.03mm). $$\sigma$_{VMmax}$ is 69Mpa. It is showed that 15% improvement of the strength in the TSOP body in comparison with using Cu alloy die pad $($\sigma$_{VMmax}$=81MPa). In solder joint of TSOP, the maximum equivalent plastic strain and Von Mises stress concentrate on the heel of solder fillet and crack was initiated in it's region and propagated through the interface between lead and solder. Finally, the modified Manson-Coffin equation and relationship of the ratio of $N_{f}$ to nest(η) and cumulative fracture probability(f) with respect to the deviations of the 50% fracture probability life $(N_{f 50%})$ were achieved.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.4
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• pp.291-297
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• 2017

Reliability analysis of a mechanical system has been developed in order to consider the uncertainties in the product design that may occur from the tolerance of design variables, uncertainties of noise, environmental factors, and material properties. In most of the previous studies, the reliability was calculated independently for each performance of the system. However, the conventional methods cannot consider the correlation between the performances of the system that may lead to a difference between the reliability of the entire system and the reliability of the individual performance. In this paper, the joint probability density function (PDF) of the performances is modeled using a copula which takes into account the correlation between performances of the system. The system reliability is proposed as the integral of joint PDF of performances and is compared with the individual reliability of each performance by mathematical examples and two-bar truss example.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.9
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• pp.1513-1527
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• 2011

This paper investigates the capacity rate problems for a joint decode-and-forward (JDF) based two-way relaying with network coding. We first characterize the achievable rate region for a conventional three-node network scenario along with the calculation of the corresponding maximal sum-rate. Then, for the goal of maximizing the system sum-rate, opportunistic relay selection is examined for multi-relay networks. As a result, a novel strategy for the implementation of relay selection is proposed, which depends on the instantaneous channel state and allows a single best relay to help the two-way information exchange. The JDF scheme and the scheme using relay selection are analyzed in terms of outage probability, after which the corresponding exact expressions are developed over Rayleigh fading channels. For the purpose of comparison, outage probabilities of the amplify-and-forward (AF) scheme and those of the scheme using relay selection are also derived. Finally, simulation experiments are done and performance comparisons are conducted. The results verify that the proposed strategy is an appropriate method for the implementation of relay selection and can achieve significant performance gains in terms of outage probability regardless of the symmetry or asymmetry of the channels. Compared with the AF scheme and the scheme using relay selection, the conventional JDF scheme and that using relay selection perform well at low signal-to-noise ratios (SNRs).

• Journal of the Korea Society for Simulation
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• v.28 no.1
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• pp.99-107
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• 2019

Until now it has had the limitation of the target in the US JMEM to calculate the Pk with the existing method by our study. In this study, we focused on deriving a method to calculate the Pk of the actual targets except JMEM targets using ANN. We study the initial predictive model of ANN(Artificial Neural Network) from the targets data of the specification and the vulnerable area in the US JMEM(Joint Munitions Effectiveness Manuals), and calculate the actual targets vulnerable area by using this method. Finally, we propose a method to calculate the Pk by applying those data to the existing method of us.

• Geomechanics and Engineering
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• v.36 no.6
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• pp.601-618
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• 2024

The joint probability distribution of uncertain geomechanical parameters of geotechnical strata is a crucial aspect in constructing the reliability functional function for roof structures. However, due to the limited number of on-site exploration and test data samples, it is challenging to conduct a scientifically reliable analysis of roof geotechnical strata. This study proposes a Copula method based on small sample exploration and test data to construct the intensity characteristics of roof geotechnical strata. Firstly, the theory of multidimensional copula is systematically introduced, especially the construction of four-dimensional Gaussian copula. Secondly, data from measurements of 176 groups of geomechanical parameters of roof geotechnical strata in 31 coal mines in China are collected. The goodness of fit and simulation error of the four-dimensional Gaussian Copula constructed using the Pearson method, Kendall method, and Spearman methods are analyzed. Finally, the fitting effects of positive and negative correlation coefficients under different copula functions are discussed respectively. The results demonstrate that the established multidimensional Gaussian Copula joint distribution model can scientifically represent the uncertainty of geomechanical parameters in roof geotechnical strata. It provides an important theoretical basis for the study of reliability functional functions for roof structures. Different construction methods for multidimensional Gaussian Copula yield varying simulation effects. The Kendall method exhibits the best fit in constructing correlations of geotechnical parameters. For the bivariate Copula fitting ability of uncertain parameters in roof geotechnical strata, when the correlation is strong, Gaussian Copula demonstrates the best fit, and other Copula functions also show remarkable fitting ability in the region of fixed correlation parameters. The research results can offer valuable reference for the stability analysis of roof geotechnical engineering.