• Journal of the Korean Professional Engineers Association
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• v.20 no.3
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• pp.15-25
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• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the X-chart, X-chart, X-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In Shewhart X-chart, which is the most widely used one in Korea, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for tile more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the X-chart, the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the X-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based on a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $X^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the propose4 median chart and the X chart was also performed with these examples and the median chart turned out to be superior to the X-chart.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.101-106
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• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the $\bar{X}$-chart, $\bar{X}$-chart, $\bar{X}$-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In Shewhart $\bar{X}$-chart. which is the most widely used one in Kora, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for the more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the $\bar{X}$-chart; the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the $\bar{X}$-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based oh a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $\chi$$^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the proposed median chart and the $\bar{X}$ chart was also performed with these examples and the median chart turned out to be superior to the $\bar{X}$-chart.

• Nuclear Engineering and Technology
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• v.54 no.3
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• pp.1016-1023
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• 2022

In proton therapy, a highly conformal proton dose can be delivered to the tumor by means of the steep distal dose penumbra at the end of the beam range. The proton beam range, however, is highly sensitive to range uncertainty, which makes accurately locating the proton range in the patient difficult. In-vivo range verification is a method to manage range uncertainty, one of the promising techniques being prompt gamma imaging (PGI). In earlier studies, we proposed gamma electron vertex imaging (GEVI), and constructed a proof-of-principle system. The system successfully demonstrated the GEVI imaging principle for therapeutic proton pencil beams without scanning, but showed some limitations under clinical conditions, particularly for pencil beam scanning proton therapy. In the present study, we upgraded the GEVI system in several aspects and tested the performance improvements such as for range-shift verification in the context of line scanning proton treatment. Specifically, the system showed better performance in obtaining accurate prompt gamma (PG) distributions in the clinical environment. Furthermore, high shift-detection sensitivity and accuracy were shown under various range-shift conditions using line scanning proton beams.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Progress in Medical Physics
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• v.21 no.1
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• pp.78-85
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• 2010

The compatibility with GammaMed-12i brachytherapy machine for an Ir-192 encapsulated source (IRRS20, KAERI, Korea) manufactured by Korea atomic energy research institute (KAERI) has been investigated. As a mechanical testing of compatibility, precise measurement of step movement with channels, measurement of curvature of radius for wire, and emergency return testing were performed. Periodic measurements of air kerma strength for 45 days were carried out to evaluate decay characteristics of Ir-192 radioisotope and comparison of dose distributions in phantom between KAERI and old sources previously used were performed by film dosimetry. KAERI source has a good compatibility with GammaMed12i machine as a result of mechanical testing. There are in good agreement with calculated values in activity characteristics and there were small differences in dose distributions around the source in comparison between KAERI and old source.

• Journal of Korean Neurosurgical Society
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• v.64 no.1
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• pp.13-22
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• 2021

Objective : High precision and accuracy are expected in gamma knife radiosurgery treatment. Because of the requirement of clinically applying complex radiation and dose gradients together with a rapid radiation decline, a dedicated quality assurance program is required to maintain the radiation dosimetry and geometric accuracy and to reduce all associated risk factors. This study investigates the validity of Leksell Gamma plan (LGP)10.1.1 system of 5th generation Gamma Knife Perfexion as modified variable ellipsoid modeling technique (VEMT) method. Methods : To verify LGP10.1.1 system, we compare the treatment plan program system of the Gamma Knife Perfexion, that is, the LGP, with the calculated value of the proposed modified VEMT program. To verify a modified VEMT method, we compare the distributions of the dose of Gamma Knife Perfexion measured by Gafchromic EBT3 and EBT-XD films. For verification, the center of an 80 mm radius solid water phantom is placed in the center of all sectors positioned at 16 mm, 4 mm and 8 mm; that is, the dose distribution is similar to the method used in the x, y, and z directions by the VEMT. The dose distribution in the axial direction is compared and analyzed based on Full-Width-of-Half-Maximum (FWHM) evaluation. Results : The dose profile distribution was evaluated by FWHM, and it showed an average difference of 0.104 mm for the LGP value and 0.130 mm for the EBT-XD film. Conclusion : The modified VEMT yielded consistent results in the two processes. The use of the modified VEMT as a verification tool can enable the system to stably test and operate the Gamma Knife Perfexion treatment planning system.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.9
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• pp.551-557
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• 2017

It is extremely important to improve methodologies for the lifetime assessment of porcelain insulators. While there has been a considerable amount of work regarding the phenomena of lifetime distributions, most of the studies assume that aging distributions follow the Weibull distribution. However, the true underlying distribution is unknown, giving rise to unrealistic inferences, such as parameter estimations. In this article, we review several distributions that are commonly used in reliability and survival analysis, such as the exponential, Weibull, log-normal, and gamma distributions. Some properties, including the characteristics of failure rates of these distributions, are presented. We use a Bayesian approach for model selection and parameter estimation procedures. A well-known measure, called the Bayes factor, is used to find the most plausible model among several contending models. The posterior mean can be used as a parameter estimate for unknown parameters, once a model with the highest posterior probability is selected. Extensive simulation studies are performed to demonstrate our methodologies.

• Journal of The Korean Society of Agricultural Engineers
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• v.51 no.3
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• pp.53-62
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• 2009

This study was carried out to select optimal probability distribution based on design accumulated monthly mean inflow from the viewpoint of drought by Gamma (GAM), Generalized extreme value (GEV), Generalized logistic (GLO), Generalized normal (GNO), Generalized pareto (GPA), Gumbel (GUM), Normal (NOR), Pearson type 3 (PT3), Wakeby (WAK) and Kappa (KAP) distributions for the observed accumulative monthly mean inflow of Chungjudam. L-moment ratio was calculated using observed accumulative monthly mean inflow. Parameters of 10 probability distributions were estimated by the method of L-moments with the observed accumulated monthly mean inflow. Design accumulated monthly mean inflows obtained by the method of L-moments using different methods for plotting positions formulas in the 10 probability distributions were compared by relative mean error (RME) and relative absolute error (RAE) respectively. It has shown that the design accumulative monthly mean inflow derived by the method of L-moments using Weibull plotting position formula in WAK and KAP distributions were much closer to those of the observed accumulative monthly mean inflow in comparison with those obtained by the method of L-moment with the different formulas for plotting positions in other distributions from the viewpoint of RME and RAE.

• Journal of Korean Neurosurgical Society
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• v.43 no.1
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• pp.26-30
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• 2008

Objective : The authors developed a stereotactic device for irradiation of small animals with Leksell Gamma Knife Model C. Development and verification procedures were described in this article. Methods : The device was designed to satisfy three requirements. The mechanical accuracy in positioning was to be managed within 0.5 mm. The strength of the device and structure were to be compromised to provide enough strength to hold a small animal during irradiation and to interfere the gamma ray beam as little as possible. The device was to be used in combination with the Leksell G-$frame^{(R)}$ and $KOPF^{(R)}$ rat adaptor. The irradiation point was determined by separate imaging sequences such as plain X-ray images. Results : The absolute dose rate with the device in a Leksell Gamma Knife was 3.7% less than the value calculated from Leksell Gamma $Plan^{(R)}$. The dose distributions measured with $GAFCHROMIC^{(R)}$ MD-55 film corresponded to those of Leksell Gamma $Plan^{(R)}$ within acceptable range. The device was used in a series of rat experiments with a 4 mm helmet of Leksell Gamma Knife. Conclusion : A stereotactic device for irradiation of small animals with Leksell Gamma Knife Model C has been developed so that it fulfilled above requirements. Absorbed dose and dose distribution at the center of a Gamma Knife helmet are in acceptable ranges. The device provides enough accuracy for stereotactic irradiation with acceptable practicality.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.