• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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• pp.311-319
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• 2001

All indices that are now in use assume normally distributed data, and any use of the indices on non-normal data results in inaccurate capability measurements. Therefore, $C_{s}$ is proposed which extends the most useful index to date, the Pearn-Kotz-Johnson $C_{pmk}$, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness. Therefore we propose, a new process capability index $C_{psk}$( WV) applying the weighted variance control charting method for non-normally distributed. The main idea of the weighted variance method(WVM) is to divide a skewed or asymmetric distribution into two normal distribution from its mean to create two new distributions which have the same mean but different standard distributions. In this paper we propose an example, a distribution generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and the Wright methods. This example shows that the weighted valiance-based indices are more consistent than the other two methods In terms of sensitivity to departure to the process mean/median from the target value for non-normal process.s.s.s.

• Proceedings of the Korean Geotechical Society Conference
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• 1997.03a
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• pp.161-168
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• 1997

The purpose of this study is to evaluate the possibility of normalization of the distibutions of soil parameters taken from soft ground and the reliability of the safety factors of specific objects on it, including sanitary landfill. Through this study it is found that distributions of soil parameters could be adjusted to appropriate normal distributions as possibility density functions(PDF), and that especially the group of initial cohesions and the coresponding safety factors has a perfect linear correlation. According to those results the PDF to initial cohesion as possibility parameter can not only be tmsformed to the PDF to safety factor but also, conseqently, the reliability of the safety factor(SF) simply based on the mean value of soil parameter(Co) can be calculated or easily picked up from the standrad normal distribution table. It is therefore concluded that even though calculated values of safety factors are over any standard requirements some possibility of risk both to the objects and natural soft ground could be still existing, and also a new standard value for this slope stability control system should be derived just by adjusting old one according to the magnitude of risk possibility.

• Water for future
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• v.26 no.4
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• pp.73-83
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• 1993

This study focuses on the separation effect analysis of rainfall data for 2-parameter log-normal, 3-parameter log-normal, type-extreme value, 2-parameter gamma, 3-parameter gamma, log-Pearson type-III, and general extreme value distribution functions. Difference in the relationship between the mean and standard deviation of skewness for historical data and relations derived from 7 distribution functions are analyzed suing the Monte Carlo experiment. The results show that rainfall data has the separation effect for 6 distribution functions except 3-parameter gamma distribution function.

• Journal of the Korea Society of Computer and Information
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• v.21 no.7
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• pp.85-92
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• 2016

The law of large numbers, central limit theorem, and connection among binomial distribution, normal distribution, and statistical estimation require dynamics of continuous visualization for students' better understanding of the concepts. During this visualization process, the differences and similarities between statistical probability and mathematical probability that students should observe need to be provided with the intermediate steps in the converging process. We propose a visualization method that can integrate intermediate processes and results through Excel. In this process, students' experiences with dynamic visualization help them to perceive that the results are continuously changed and extracted from multiple situations. Considering modeling as a key process, we developed a classroom exercise using Excel to estimate the population mean and standard deviation by using a sample mean computed from a collection of data out of the population through sampling.

• Journal of The Korean Society of Agricultural Engineers
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• v.60 no.4
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• pp.83-91
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• 2018

Land reclamation, coastal construction, coastline extension and port construction, all of which involve dredging, are increasingly required to meet the growing economic and societal demands in the coastal zone. During the land reclamation, a portion of landfills are lost from the desired location due to a variety of causes, and therefore prediction of sediment transport is very important for economical and efficient land reclamation management. In this study, laboratory disposal tests were performed using an open channel, and suspended sediment transport was analyzed according to flow velocity and grain size. The relationships between the average and standard deviation of the deposition distance and the flow velocity were almost linear, and the relationships between the average and standard deviation of deposition distance and the grain size were found to have high non-linearity in the form of power law. The deposition distribution of sediments was demonstrated to have log-normal distributions regardless of the flow velocity. Based on the experimental results, modeling of suspended sediment transport was performed using deep neural network, one of deep learning techniques, and the deposition distribution was reproduced through log-normal distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.16 no.28
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• pp.137-143
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• 1993

Generally there are three methods to derive an approximation formula: 1) approching standard normal distribution by appropriate changing variable 2) using standardization variable for expansion 3) deriving approximation formula by direct method. This paper present correction terms having the form of $C_{1/v^{n/2}}/{\;}+{\;}C_2{\;}(n=1,2)$ with respect to $x^2_{\alpha}(v)$ distribution (${\nu}{\;}{\leq}{\;}30$), which minimize the error by EDA method and least square method.

• The Journal of the Korean life insurance medical association
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• v.3 no.1
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• pp.103-141
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• 1986

The present study was undertaken to establish the decision standard of builds for the insured by using the ratio of weight-for-height as build index. Materials being examined were the ratio of weight-for-height being calculated from the actually measured heights and weights of a total of 15,838 insured persons who were examined medically at Honam Medical Department of Dong Bang Life Insurance Company, Ltd. from June, 1979 to September, 1985. The ratio of weight-for-height is calculated by the following formula. The ratio of weight-for-height(%)=$\frac{weight(kg){\times}100}{\{height(cm)-100\}{\times}0.9(kg)$ The results were as follows: 1. The distribution of the ratio of weight. for-height of the 15,838 insureds follows Log normal distribution being skewed to the left(the direction of underweight). 2. The ratio of weight-for-height were Log transformed to lead to a sym metrical pattern of distribution in which statistical rules are known to be applied more exactly. Thereafter, the establishment of dicision standard of builds was undertaken by using the log of the ratio of weight-for-height as build index. Through all ages in male, the ratio of weight-for-height indicating the range of standard lives including slight overweighted and underweighted lives besides normal lives is 80-130%, and corresponds to $"M-2{\delta}"-"M+1.5{\delta}"$ and to $M{\pm}20%$ ; in female, 85-135%, and corresponds to $"M-2{\delta}"-"M+1.5{\delta}"$ and to $M{\pm}20%$. Through all ages in male, the ratio of weight-for-height indicating the initial level of super-overweighted and super-underweighted lives is 130-150% and 75-80%,and corresponds to $M+3{\delta}\;and\;M-3{\delta}$ and to M+40% and M-25% respectively;in female, 140-160% and 75-80%, and corresponds to $M+3{\delta}\;and\;M-3{\delta}$ and to M+40%-+50% and M-25% respectively. 3. Author's rating table model for builds(a table of weight per height) is proposed. On the table, the ratings for builds, i. e. standard, super-weighted and super-underweighted lives, are listed.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.479-483
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• 2004

A new calculation method of expected overtopping probability of rubble mound breakwater considering real tide occurrence has been proposed. A calculation method of expected overtopping probability of rubble mound breakwater was proposed by Kweon and Suh (2003). In their calculation, the fluctuation of tidal elevation was expressed by the sinusoidal change that yields the uniform distribution of occurrence frequency. However, the realistic distribution of tidal elevation should influence on the overtopping chance. In this study, the occurrence frequency of tidal elevation obtained from the real sea is included. The tidal elevation used in this study is collected from the east coastal part of Korean peninsular. Analyzing the annual data of the tidal fluctuation measured hourly during 355 days, the distribution of occurrence frequency is formulated utilizing by the normal distribution with one peak. Among the calculation procedures of annual maximum wave height, wave height-period joint distribution, wave run-up height and occurrence frequency of tide, only the annual maximum wave height is again chosen randomly from normal distribution to consider the uncertainty. The others are treated by utilizing the distribution function or relationship itself, It is found that the inclusion of the variability of tidal elevation has great influence on the computation of the expected overtopping probability of rubble mound breakwater. The bigger standard deviation of occurrence frequency is, the lower the overtopping probability of rubble mound breakwater is.

• Journal of Power System Engineering
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• v.22 no.6
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• pp.67-73
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• 2018

Gasoline that meets the quality standards is distributed in Korea. However, consumers who use toluene or solvent mixed with gasoline have appeared due to rising crude oil prices and for the purpose of tax evasion. Gasoline quality standard is enacted by the domestic and international research reference. A wrong fuel can influence automobile performance or environmental issue. Thus, empirical data from this issue is necessary. Therefore, this research observed catalyst influence by gasoline property change and inspect influence of environment. In this study, fuel property evaluation, lean-burn evaluation, and real vehicle exhaust emission test were performed. In the result of fuel property, the fuel "A" was measured to be up to 27% less octane than the normal gasoline and the distillation property was measured 24% higher than normal gasoline. In the test result of single cylinder engine lean-burn test, the fuels "A" and "B" show torque value 20% less than the normal gasoline. As a result of vehicle test using the catalyst, the fuel "A" was increased more than the normal gasoline with 83% THC, 1,806% CO and 128% NOx, and the fuel "B" was increased more than normal gasoline with 1.6% THC, 391% CO and 142% NOx.

• Journal of the Korea Convergence Society
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• v.10 no.11
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• pp.303-308
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• 2019

This study suggests a method for deriving earthquake response based on log-normal distribution in order to obtain realistic and reliable probability and statistical seismic response of structures. The development of three earthquake suites were presented, with a brief description of 2%, 10%, and 50% in 50 years probability of exceedance according the USGS Los Angeles probabilistic seismic hazard maps. In order to analyze the basic dynamic behavior, a Single-Degree-of-Freedom (SDOF) structure was selected and the seismic response spectrum representing the response of each natural period was plotted. Overall, the mean response values presented through the log-normal distribution is lower than the standard normal distribution. Thus, it is considered that the former method can be provided as the effective cost on performance-based seismic design more than the latter one.