• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.197-201
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• 2005

In this article, we will compare the performance of the mean control chart, the median control chart, the transformed mean control chart, the transformed median control chart, and the precedence control chart by simulation study. For control charts with transformed data, Yeo-Johnson transformation is used. Under the in-control condition, ARL's in all control charts coincide with the designed ARL in the normal distribution, but in the other distributions, only the precedence control chart provides the in-control ARL as designed. Under the out-of-control condition, the mean control chart is preferred in the normal distribution and the median control chart is preferred in the heavy-tailed distribution and the precedence control chart outperforms in the short-tailed distribution.

• Communications for Statistical Applications and Methods
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• 제20권2호
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• pp.107-113
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• 2013

This study reviews several well-known control charts for the location parameter with a discussion of the relationship between the maintenance of the control chart and a series of hypotheses testing. As a by-product, we then propose a new median control chart with the sign test statistic. We also modify the nonparametric control charts to easily understand the relation. Then we illustrate the construction of several median control charts with the industrial data and compare the efficiency among several control charts. Finally, we discuss some interesting features for the median control charts as concluding remarks.

• 품질경영학회지
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• 제14권2호
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• pp.2-8
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• 1986

This thesis is concerned with the design of control chart based on the sample median which is easy to use in practical situations and to analyze the properties for non-normally distributed Weibull process. In this cases are use to the quality characteristics of the process are not normally distributed but skewed due to the intermitted production, small lot size and sample size is small one n=3 or n=5, etc. And when it relates unsymmetrically distributed process, model designed median control chart is more effective than Shewhart $\bar{x}$-chart which assumed on normal distribution, when we exactly should be known Weibull distribution or estimated. The median control chart in this thesis is more robustness compared with other conventionally developed control chart.

• 기술사
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• 제20권3호
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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.

• 산업경영시스템학회지
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• 제10권16호
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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.

• 기술사
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• 제21권4호
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• pp.19-32
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• 1988

Whereas is non-symmetrical distribution manufacturing process the traditional X-chart by Shewhart is not plotted relatively on the central line but plotted on the skew of upper-hand side or lower-hand side. That is to say, for the purpose of producing either upper-specification-oriented items or lower-specification-oriented items, and when we carry out tighter control so as to have them pass only its specifications, the distribution shape naturally has a non-normal distribution. In the Shewhart X-chart, which is the most widely used one in Korea, such skewed distributions make tile 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 short comings is non-normally distributed processes, a distribution-free type of confidence interval can be used, which should be haled 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 non-normal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, and Truncated-normal distributions, may be easily analyzed. To enhance this improvement, I proved the property of practical applications of control chart method by comparing and analyzing the case studies of practical application of special purpose control chart method, and also by introducing the new designed median control chart.

• 한국국방경영분석학회지
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• 제22권2호
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• pp.126-138
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• 1996

The statistical control chart has been proven to be the effective tool most widely used in the manufacturing industry for monitoring and controlling the manufacturing processes. However, the Shewhart chart sometimes gives us false information when the distribution of quality characteristics is skewed. Therefore, it cannot serve as the universal quality control chart if there exist odd events in the manufacturing process. The objective of this study is thus to develop the new technique for constructing the limits of quality control chart based on a sample median and range when the distribution of the underlying population is skewed. This new control chart can effectively solve and manage the processes which have the non-normally distributed quality characteristics frequently occurring in the practical situation.

• 품질경영학회지
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• 제15권2호
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• pp.10-19
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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 $\overline{X}$-chart, X-chart, $\widetilde{X}$-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 the Shewhart $\overline{X}$-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 the more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, and Truncated-normal distributions.

• Journal of the Korean Data and Information Science Society
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• 제27권6호
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• pp.1487-1498
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• 2016

관리도를 사용하여 공정을 관리할 때, 일반적으로 공정 모수의 정확한 값은 알 수 없기 때문에 제1국면의 표본을 통하여 이를 추정해서 사용하고 있다. 또한 추정된 공정 모수를 이용하여 관리도를 설계하는 경우 관리한계는 관리상태에서의 런길이의 평균인 ARL (average run length)이 미리 지정한 값을 만족하도록 설정하고 있다. 그러나 런길이의 분포는 일반적으로 치우쳐져 있기 때문에, 런길이의 평균 대신 중위수를 사용하는 것이 바람직할 수 있다. 이 논문에서는 제1국면에서 추정한 모수를 사용하는 경우 부그룹의 크기에 따른 $\bar{X}$ 관리도의 성능에 대해 연구하였고, 이때 공정 평균에 대한 추정량은 전체 표본평균을 사용하고 공정 표준편차에 대해서는 5가지 추정량을 사용하여 이에 대한 영향을 살펴보았다. 기존 연구와 다른 점은 여러 가지의 부그룹 크기에 대해 모수 추정의 영향을 ARL 대신 런길이의 중위수인 MRL (median run length)에 기초하여 살펴보았으며, 두 가지 방법에 대해 그 결과를 비교하였다.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.365-376
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• 2007

This research considers to propose the control charts using median for the location parameter. In order to decide the control limits, we apply several bootstrap methods through the approach obtaining the confidence interval except the standard bootstrap method. Then we illustrate our procedure using an example and compare the performance among the various bootstrap methods by obtaining the length between control limits through the simulation study. The standard bootstrap may be apt to yield shortest length while the bootstrap-t method, the longest one. Finally we comment briefly about some specific features as concluding remarks.