• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.4
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• pp.134-139
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• 2008

Most approaches for continuous review inventory problem need tables for loss function and cumulative standard normal distribution. Furthermore, it is time-consuming to calculate order quantity (Q) and reorder point (r) iteratively until required values are converged. The purpose of this paper is to develop a direct method to get the solution without any tables. We used approximation approaches for loss function and cumulative standard normal distribution. The proposed method can get the solution directly without any iterative procedure for Q, r and without any tables. The performance of the proposed approach is tested by using numerical examples. The budget constraint of this paper assumes that purchasing costs are paid at the time an order is arrived. This constraint can be easily replaced by capacity constraint or budget constraint in which' purchasing costs are paid at the time an order is placed.

• Journal of KIEE
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• v.11 no.1
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• pp.69-77
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• 2001

This paper describes an image processing algorithm capable of recognizing road lanes by using a CDF(cumulative distribution function). The CDF is designed for the model function of road lanes. Based on the assumptions that there are no abrupt changes in the direction and location of road lanes and that the intensity of lane boundaries differs from that of the background, we formulated the CDF, which accumulates the edge magnitude for edge directions. The CDF has distinctive peak points at the vicinity of lane directions due to the directional and the positional continuities of a lane. To obtain lane-related information a scatter diagram was constructed by collecting edge pixels, of which the direction corresponds to the peak point of the CDF, then the principal axis-based line fitting was performed for the scatter diagram. Noises can cause many similar features to appear and to disappear in an image. Therefore, to reduce the noise effect a recursive estimator of the CDF was introduced, and also to prevent false alarms or miss detection a scene understanding index (DUI) was formulated by the statistical parameters of the CDF. The proposed algorithm has been implemented in real time on video data obtained from a test vehicle driven on a typical highway.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.237-244
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• 2014

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1276-1282
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• 2013

This paper proposes a stochastic modeling of plug-in electric vehicles (PEVs) distribution in power systems, and analyzes the corresponding clustering characteristic. It is essential for power utilities to estimate the PEV charging demand as the penetration level of PEV is expected to increase rapidly in the near future. Although the distribution of PEVs in power systems is the primary factor for estimating the PEV charging demand, the data currently available are statistics related to fuel-driven vehicles and to existing electric demands in power systems. In this paper, we calculate the number of households using electricity at individual ending buses of a power system based on the electric demands. Then, we estimate the number of PEVs per household using the probability density function of PEVs derived from the given statistics about fuel-driven vehicles. Finally, we present the clustering characteristic of the PEV distribution via case studies employing the test systems.

• Journal of ILASS-Korea
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• v.20 no.3
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• pp.175-180
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• 2015

A series of sprinkler discharging tests was conducted to measure the droplet size and its distribution of residential fire sprinkler heads. Droplet sizes in sprinkler spray were measured using a laser diffraction method for the flush, circular and pendent type sprinkler head. In this study, the $D_{v,50}$ of the flush type sprinkler heads were ranged between $530{\sim}1040{\mu}m$ and those of circular and pendent type were $988{\mu}m$ and $916{\mu}m$, respectively. The measured cumulative volume distributions were followed by a combination of the log-normal and Rosin-Rammler distribution which is widely used in the computational fire analysis and the parameters of distribution function were obtained from the best fit line through the measured data.

• The Korean Journal of Ecology
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• v.23 no.6
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• pp.435-438
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• 2000

Diameter distributions describe forest stand structure information. Prediction equations for percentiles of diameter distribution and parameter recovery procedures for the Weibull distribution function based on four percentile equations were applied to develop prediction system of even-aged slash pine stand structure development in terms of the number of stems per diameter class changes. Four percentiles of the cumulative diameter distribution were predicted as a function of stand characteristics. The predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level. Statistically, no significant differences were detected based on the data from 236 evaluation data sets. This stand level diameter distribution prediction system will be useful in slash pine stand structure modeling and in updating forest inventories for the long-term forest management planning.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.227-240
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• 2017

In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1908-1918
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• 1991

Fatigue tests have been carried out to measure the degradation of the residual strength and the fatigue life in carbon/epoxy (0/45/90/-45)$_{2s}$ composite materials. Theoretical predictions of residual strength and fatigue life were compared with experimental results. Distribution characteristics were studied using the probability of failure based on the cumulative distribution function and median rand. The static ultimate strength of carbon/epoxy composites used herein is observed to be relatively higher than that of existing similar composites ; while fatigue life is shorter due to the brittleness of matrix. The fatigue life obtained in these experiments is shorter than that estimated by residual strength degradation model when the stress level above 0.6 For the stress level of 0.6, the experimental value was abruptly increased. The cumulative distribution function for the static ultimate strength is well correlated to that for the strength converted from the measured fatigue life. Also, the predicted distribution of residual strength shows good agreement with the experimental results. Therefore, it is proven that the residual strength degradation model is reasonable.e.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.277-286
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• 2012

For credit assessment models, the ROC curves evaluate the classification performance using two univariate cumulative distribution functions of the false positive rate and true positive rate. In this paper, it is extended to two bivariate normal distribution functions of default and non-default borrowers; in addition, the bivariate ROC curves are proposed to represent the joint cumulative distribution functions by making use of the linear function that passes though the mean vectors of two score random variables. We explore the classification performance based on these ROC curves obtained from various bivariate normal distributions, and analyze with the corresponding AUROC. The optimal threshold could be derived from the bivariate ROC curve using many well known classification criteria and it is possible to establish an optimal cut-off criteria of bivariate mixture distribution functions.

• Journal of the Korean Geotechnical Society
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• v.24 no.5
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• pp.129-137
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• 2008

An active application of concrete track is being expected far the future constructions of Korean railroad. In comparison with the existing ballasted tract, a concrete track is very susceptible for the settlement, since its rehabilitation requires much time and cost. When a concrete track is constructed on fine-grained subgrade soil, excessive cumulative plastic settlements due to repetitive train road may occur. In this case, the settlement of the concrete track may be effectively reduced by installing a small number of small-diameter piles beneath the track. This paper presents the effect of pile installation on the reduction of cumulative plastic settlement of concrete track. A method combining experiential equation and numerical method is proposed. Using an existing experiential equation and the estimated earth pressure distribution, the cumulative plastic strain was calculated. From the results, it is verified that the effects of the pile installation is significant to effectively reduce the cumulative plastic settlement of concrete track. The reduction effects of the cumulative plastic settlement according to the pile number and pile arrangement are presented.