• Geomechanics and Engineering
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• v.34 no.3
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• pp.285-301
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• 2023

During the construction of E75 highway through Grdelica gorge in Serbia, a major failure occurred in the zone of reinforced rock slope. Excavation was performed in highly anisotropic Paleozoic schist rock formation. The reinforcement consisted of the two rows of micropile wall with pre-stressed anchors. Forces in anchors were monitored with load cells while benchmarks were installed for superficial displacement measurements. The aim of the study is to investigate possible causes of instability considering different probability distributions of the strength of discontinuities and anchor bond strength by applying different optimization techniques for finding the critical failure surface. Even though the deterministic safety factor value is close to unity, the probability of failure is governed by variability of shear strength of anisotropic planes and optimization method used for locating the critical sliding surface. The Cuckoo search technique produces higher failure probabilities compared to the others. Depending on the assigned statistical distribution of input parameters, various performance functions of the factor of safety are obtained. The probability of failure is insensitive to the variation of bond strength. Different sampling techniques should yield similar results considering that the sufficient number of safety factor evaluations is chosen to achieve converged solution.

• The Journal of Engineering Geology
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• v.16 no.4 s.50
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• pp.337-349
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• 2006

Seven hundred and fifty one fractures of the rhyolitic tuffaceous rock masses were mapped using 6 scanlines placed on rock slope exposures that were within 8.02 km of Busan-Ulsan highway. These data were analyzed to find the number of fracture sets that exist in the rock slopes and the probability distributions of orientation, spacing, trace length and fracture size in 3-D for each of the fracture sets. All the fracture set orientation distributions exhibit high variability. The Fisher distributions were found to be unsuitable to represent the statistical distribution of orientation for most of the fracture sets. The probability distributions, gamma, exponential and lognormal were found to be highly suitable to represent the distribution of spacing and semi-trace length of fracture sets. In obtain-ing these distributions, corrections were applied for sampling biases associated with spacing and trace length. The generated fracture system in 3-D was used to make predictions of fracture traces for each fracture set on 2-D win-dows. Developed stochastic 3-D fracture network for the rock mass was validated by comparing statistical proper-ties of the observed fracture traces on scanlines with the predicted fracture traces on the scanlines. This exercise fumed out to be successful.

• Journal of Korea Water Resources Association
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• v.39 no.10 s.171
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• pp.891-904
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• 2006

The estimation of the probability precipitation is essential for the design of hydrologic projects. The techniques to calculate the probability precipitation can be determined by the point frequency analysis and the regional frequency analysis. The regional frequency analysis includes index-flood technique and L-moment technique. In the regional frequency analysis, even if the rainfall data passed homogeneity, suitable distributions can be different at each point. However, the regional frequency analysis can supplement the lacking precipitation data. Therefore, the regional frequency analysis has weaknesses compared to parametric point frequency analysis because of suppositions about probability distributions. Therefore, this paper applies kernel density function to precipitation data so that homogeneity is defined. In this paper, The data from 16 rainfall observatories were collected and managed by the Korea Meteorological Administration to achieve the point frequency analysis and the regional frequency analysis. The point frequency analysis applies parametric technique and nonparametric technique, and the regional frequency analysis applies index-flood techniques and L-moment techniques. Also, the probability precipitation was calculated by the regional frequency analysis using variable kernel density function.

• Journal of Food Hygiene and Safety
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• v.27 no.3
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• pp.312-316
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• 2012

This study was to present the proper probability distribution models that based on the data for surveys of food cold storage temperatures as the input variables to the further MRA (Microbial risk assessment). The temperature was measured by directly visiting 7 food plants. The overall mean temperature for food cold storages in the survey was $2.55{\pm}3.55^{\circ}C$, with 2.5% of above $10^{\circ}C$, $-3.2^{\circ}C$ and $14.9^{\circ}C$ as a minimum and maximum. Temperature distributions by space-locations was $0.80{\pm}1.69^{\circ}C$, $0.59{\pm}1.68^{\circ}C$, and $0.65{\pm}1.46^{\circ}C$ as an upper (2.4~4 m), middle (1.5~2.4 m), and lower (0.7~1.5 m), respectively. Probability distributions were also created using @RISK program based on the measured temperature data. Statistical ranking was determined by the goodness of fit (GOF) to determine the proper probability distribution model. This result showed that the LogLogistic (-4.189, 5.9098, 3.2565) distribution models was found to be the most appropriate for relative MRA conduction.

• Journal of Food Hygiene and Safety
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• v.34 no.2
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• pp.199-204
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• 2019

This study aimed to generate a probability distribution model based on temperature data of frozen food storage facility as input variables for microbial risk assessment (MRA). We visited 8 food-handling businesses to collect temperature data from their cold storage warehouses. The overall mean temperature inside the storage facilities was $-20.48{\pm}3.08^{\circ}C$, with 20.4% of the facilities having above $-18^{\circ}C$, with minimum and maximum temperature values of -10.3 and $-25.80^{\circ}C$ respectively. Temperature distributions by space locations of natural and forced convection were $-22.57{\pm}0.84$ and $-17.81{\pm}1.47^{\circ}C$, $-22.49{\pm}1.05$ and $-17.94{\pm}1.44^{\circ}C$, and $-22.68{\pm}1.03$ and $-18.08{\pm}1.42^{\circ}C$ in the upper (2.4~4 m), middle (1.5~2.4 m), and lower (0.7~1.5 m) shelves, respectively. Probability distributions from the temperature data were obtained using the program @RISK. Statistical ranking was determined using goodness of fit to determine the probability distribution model. Our results show that a log-normal distribution [5.9731, 3.3483, shift (-26.4281)] is most appropriate for relative MRA conduction.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.59-68
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• 2017

Random process plays a major role in wireless communication system to analytically derive the probability distribution function of the various statistical distribution. In this paper, we derive the decreasing function of the exponential distribution under the given condition which is expressed as wireless channel condition. The probability distribution function of Gaussian, Laplacian, Rayleigh and Nakagami distribution are also derived. Extensive simulation results of these statistical distributions are provided to prove that random process has a significant role in the wireless communications. In addition, the Rayleigh and Rician channels show specific examples of visible distance communication and invisible distance channel environment. This paper is motivated by that we assume a block fading channel model, where the channel is constant during a transmission block and changes independently between consecutive transmission block, can achieve a better performance in high SNR regime with i.i.d channel. This algorithm for realizing these transforms can be applied to the Kronecker MIMO channel.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.5A
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• pp.425-431
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• 2010

The phase distribution in a multi-phase material strongly affects its material properties. Therefore, a proper method to describe the phase distribution of a material is needed. In this research, probability distribution functions, two-point correlation and lineal-path functions, are used to represent the probabilistic phase distributions of a material. The probability distribution function is calculated using a numerical method and is described as an analytical form via exponential curve fitting with three parameters. Application of analytical form of probability distribution function is investigated using two-phase polycrystalline solids and soil samples. It is confirmed that the probability distribution functions can be represented as an exponential form using curve fitting which helps identifying the applicability of a representative volume element(RVE).

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.3
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• pp.109-123
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• 1999

Fleet sizing and empty equipment redistribution are two of the most critical problems in managing a fleet of equipment over a transportation network. Where the demand pattern followed the compound Poisson process(CPP) which can be generated one or more at a time under homogeneous Poisson process(HPP), this paper presented a mathematical model to determine control parameters of a decentralized distribution policy and fleet size in case of the pure hub-and-spoke system, a popular form of a logistics system. and validated this model by simulation. That is, where the number of demanded equipments followed geometric and binomial distributions, respectively, cost models on the pure hub-and-spoke logistics system with deterministic trans-portation times, which could be solved analytically, were established and analyzed. We also compared the deterministic case with stochastic one that the transportation time follows some probability distributions.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.7
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• pp.71-79
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• 2015

This paper is on the development of computer software which can be utilized as a power system analysis tool for reliability assessment education. The input data of the developed software are so simple that even a non-expert easily understand how to use it. The software provides not only reliability indices but also their distributions, moreover, it provides the factors those effect the indices, which made the software even more useful for educational purpose. The developed software utilized Monte-carlo simulation based on the state duration sampling, therefore it can manage various probability distributions such as exponential, Weibull, gamma and lognormal distribution. Within the software, the parameters of the distribution can be decided automatically from its mean and variance, that is another advantage as an educational software.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.421-433
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• 1998

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.