• Journal of Environmental Health Sciences
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• v.45 no.5
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• pp.497-510
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• 2019

Objectives: The aim of this study was to secure the reliability of using the CalTOX model when evaluating LADD (or ADD) and Risk (or HQ) among local residents for the emission of BTEX (Benzene, Toluene, Ethylbenzene, Xylene) and by closely examining the difference in the confidence interval of the assessment outcomes according to the difference in the probability density function of input variables. Methods: The assessment was made by dividing it according to the method ($I^{\dagger}$) of inputting the probability density function in meteorological variables of the model with log-normal distribution and the method of inputting ($II^{\ddagger}$) after grasping the optimal probability density function using @Risk. A T-test was carried out in order to analyze the difference in confidence interval of the two assessment results. Results: It was evaluated to be 1.46E-03 mg/kg-d in LADD of Benzene, 1.96E-04 mg/kg-d in ADD of Toluene, 8.15E-05 mg/kg-d in ADD of Ethylbenzene, and 2.30E-04 mg/kg-d in ADD of Xylene. As for the predicted confidence interval in LADD and ADD, there was a significant difference between the $I^{\dagger}$ and $II^{\ddagger}$ methods in $LADD_{Inhalation}$ for Benzene, and in $ADD_{Inhalation}$ and ADD for Toluene and Xylene. It appeared to be 3.58E-05 for risk in Benzene, 3.78E-03 for HQ in Toluene, 1.48E-03 for HQ in Ethylbenzene, and 3.77E-03 for HQ in Xylene. As a result of the HQ in Toluene and Xylene, the difference in confidence interval between the $I^{\dagger}$ and $II^{\ddagger}$ methods was shown to be significant. Conclusions: The human risk assessment for BTEX was made by dividing it into the method ($I^{\dagger}$) of inputting the probability density function of meteorological variables for the CalTOX model with log-normal distribution, and the method of inputting ($II^{\ddagger}$) after grasping the optimal probability density function using @Risk. As a result, it was identified that Risk (or HQ) is the same, but that there is a significant difference in the confidence interval of Risk (or HQ) between the $I^{\dagger}$ and $II^{\ddagger}$ methods.

• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.245-255
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• 2011

There are two nonparametric methods that use empirical distribution functions and probability density estimators for the test of the distribution change of data. In this paper we investigate the two methods precisely and summarize the results of previous research. We assume several probability models to make a simulation study of the change point analysis and to examine the finite sample behavior of the two methods. Empirical powers are compared to verify which is better for each model.

• Geomechanics and Engineering
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• v.5 no.5
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• pp.485-497
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• 2013

The factor of safety is the most common measure of the safety margin for slopes. When the traditionally defined factor is used in kinematic approach of limit analysis, calculations can become elaborate, and iterative methods have to be used. To avoid this inconvenience, the safety factor was defined in terms of the work rates that are part of the work balance equation used in limit analysis. It was demonstrated for two simple slopes that the safety factors calculated according to the new definition fall close to those calculated using the traditional definition. Statistical analysis was carried out to find out whether, given normal distribution of the strength parameters, the distribution of the safety factor can be approximated with a well-defined probability density function. Knowing this function would make it convenient to calculate the probability of failure. The results indicated that the normal distribution could be used for low internal friction angle (up to about $16^{\circ}$) and the Johnson distribution could be used for larger angles ${\phi}$. The data limited to two simple slopes, however, does not allow assuming these distributions a priori for other slopes.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.9
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• pp.616-623
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• 2001

Effects of the grating period fluctuation on the wavelength distribution have been studied by an effective index transfer matrix method in quarter wavelength shifted (QWS) DFB lasers. The wavelength distribution is expressed by a probability density that is an analytical function of the correlation coefficient and normalized standard deviation of the grating period fluctuation. The probability density function of wavelength distribution is shown to be nearly Gaussian, and its standard deviation increases with normalized standard deviation of the grating period fluctuation, and decreases with the negative correlation between adjacent half-periods.

• Korean Journal of Agricultural Science
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• v.50 no.3
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• pp.469-477
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• 2023

This study was conducted to evaluate the spraying performance according to the flight conditions of agricultural drones for the development of a variable control system. The analyzed flight conditions comprised six factors: spraying direction, flight speed, altitude, wind speed, wind direction, and rotor rotational speed. The ratio of the area sprayed on the water-sensitive paper was used as the coverage, and the distribution and amount of the coverage were evaluated. The coverage distribution based on the distance from the drone was used to evaluate a spray pattern, and the distribution was expressed as a Gaussian function approximation. In addition, the probability distribution based on coverage was expressed as the cumulative probability via Gamma function approximation to analyze the spraying efficiency in the target area. The results showed that the averaged coverage decreased significantly as the flight speed and wind speed increased, and the wind direction changed the spray pattern without a coverage decrease. This study contributes to the development of a control technique for the precision control system of agricultural drones.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1281-1288
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• 2010

We consider Yut board game with four Yut sticks which are of the same shape and the same size so that they have the same probability of showing back when they are tossed. Since, in Yut board game, a player have to toss four sticks one more when sawi Mo or sawi Yut appears, the player may be interested in the distance which Mal can move in one's turn. Therefore, the probability mass function of the distance is obtained and probabilities with several values of back probability are summarized in a table. Also, the expectation, the variance, the skewness, and the kurtosis of the distribution are calculated and their values are also tablized for some values of back probability.

• ETRI Journal
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• v.32 no.1
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• pp.145-147
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• 2010

In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.6 s.171
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• pp.183-191
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• 2005

Axiomatic design offers a scientific base for design in an efficient way. It is well known that it has two axioms: the Independence Axiom and the Information Axiom. Many applications of the Independence Axiom have been published, however, the Information Axiom has been mainly applied to IFR (functional requirement) - 1DP (design parameter) problems except fer a few case studies. This research presents various methods for calculation of information content. Generally, the information content is evaluated by the probability of success. The probability of success is calculated in two ranges: the FR range and the DP range. In the FR range, the graphical method is utilized with uniform distribution of the DP. In the FP range, the integration method is employed. It is noted that any distribution function of the DP can be accommodated in the integration method. The developed method can be applied to a decoupled design with multiple FRs and DPs. The developed method is extended to a coupled design and a design with a hierarchical structure of axiomatic design.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• Geomechanics and Engineering
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• v.29 no.6
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• pp.599-614
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• 2022

In this study, the reliability analysis of internal and external stabilities of Reinforced Soil Walls (RSWs) under static and seismic loads are investigated so that it can help the geotechnical engineers to perform the design more realistically. The effect of various variables such as angle of internal soil friction, soil specific gravity, tensile strength of the reinforcements, base friction, surcharge load and finally horizontal earthquake acceleration are examined assuming the variables uncertainties. Also, the correlation coefficient impact between variables, sensitivity analysis, mean change, coefficient of variation and type of probability distribution function were evaluated. In this research, external stability (sliding, overturning and bearing capacity) and internal stability (tensile rupture and pull out) in both static and seismic conditions were investigated. Results of this study indicated sliding as the predominant failure mode in the external stability and reinforcing rupture in the internal stability. First-Order Reliability Method (FORM) are applied to estimate the reliability index (or failure probability) and results are validated using the Monte Carlo Simulation (MCS) method. The results showed among all variables, the internal friction angle and horizontal earthquake acceleration have dominant impact on the both reinforced soil wall internal and external stabilities limit states. Also, the type of probability distribution function affects the reliability index significantly and coefficient of variation of internal friction angle has the greatest influence in the static and seismic limits states compared to the other variables.