• 산업경영시스템학회지
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• 제27권3호
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• pp.14-20
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• 2004

The coefficient of variation(CV) which is a relatively dimensionless measure of variability is widely used to describe the variation of sample data. However, the properties of CV distribution are little available and few research has been done on estimation and interpretation of CV. In this paper, we give an outline of statistical properties of coefficient of variation and design of control chart based on this statistic. Construction procedures of control chart are presented. The proposed control chart is an efficient method to monitor a process variation for short production run situation. Futhermore, we evaluated the performance of CV control chart by average run length(ARL).

• 산업경영시스템학회지
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• 제39권1호
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• pp.116-122
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• 2016

Recently, the production cycle in manufacturing process has been getting shorter and different types of product have been produced in the same process line. In this case, the control chart using coefficient of variation would be applicable to the process. The theory that random variables are located in the three times distance of the deviation from mean value is applicable to the control chart that monitor the process in the manufacturing line, when the data of process are changed by the type of normal distribution. It is possible to apply to the control chart of coefficient of variation too. ${\bar{x}}$, s estimates that taken in the coefficient of variation have just used all of the data, but the upper control limit, center line and lower control limit have been settled by the effect of abnormal values, so this control chart could be in trouble of detection ability of the assignable value. The purpose of this study was to present the robust control chart than coefficient of variation control chart in the normal process. To perform this research, the location parameter, ${\bar{x_{\alpha}}}$, $s_{\alpha}$ were used. The robust control chart was named Tim-CV control chart. The result of simulation were summarized as follows; First, P values, the probability to get away from control limit, in Trim-CV control chart were larger than CV control chart in the normal process. Second, ARL values, average run length, in Trim-CV control chart were smaller than CV control chart in the normal process. Particularly, the difference of performance of two control charts was so sure when the change of the process was getting to bigger. Therefore, the Trim-CV control chart proposed in this paper would be more efficient tool than CV control chart in small quantity batch production.

• Journal of the Korean Statistical Society
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• 제35권3호
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• pp.331-341
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• 2006

An approximate distribution of the plug-in estimator of the squared coefficient of variation ($CV^2$) is derived by using Edgeworth expansions under general population models. Also bias of the estimator is investigated for several important distributions. Under the normal distribution, we proposed the new estimator for $CV^2$ based on median of the sampling distribution of plug-in estimator.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.42-47
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• 1984

In this paper, the means of the estimators for the coefficient of variation (CV) in an underlying Pareto distribution are expressed in terms of confluent hypergeometric functions. The numericla values of the biases for the CV estimators in the Pareto distribution are also obtained.

• 산업경영시스템학회지
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• 제29권2호
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• pp.97-103
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• 2006

Recently, the control chart is developed for monitoring processes with normal short production runs by the coefficient of variation(CV) characteristic for a normal distribution. This control chart does not work well in non-normal short production runs. And most of industrial processes are known to follow the non-normal distribution. Therefore, the control chart is required to be developed for monitoring the processes with non-normal short production runs by the CV characteristics for a non-normal distribution. In this paper, we suggest the control chart for monitoring the processes with a gamma short runs by the CV characteristics for a gamma distribution. This control chart is denoted by the gamma CV control chart. Futhermore evaluated the performance of the gamma CV control chart by average run length(ARL).

• 품질경영학회지
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• 제38권3호
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• pp.313-321
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• 2010

The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from each other. Recently, the CV control chart is developed for monitoring processes in such situations. However, the CV control chart has low performance in detecting small shift. Due to the development of equipment and technique, currently, small shift of process occurs more frequently than large shift. In this paper, we proposes the CV-CUSUM control chart using CUSUM scheme which is cumulative sum of the deviations between each data point and a target value to detect a small shift in the process. We also found that the FIR(fast initial response) CUSUM control chart is especially valuable at start-up or after a CV-CUSUM control chart has signaled out-of-control.

• 산업경영시스템학회지
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• 제31권4호
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• pp.114-120
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• 2008

The control chart is widely used statistical process control(SPC) tool that searches for assignable cause of variation and detects any change of process. Generally, ${\bar{X}}-R$ control chart and ${\bar{X}}-S$ are most frequently used. When the production run is short and process parameter changes frequently, it is difficult to monitor the process using traditional control charts. In such a case, the coefficient of variation (CV) is very useful for monitoring the process variability. The CV control chart is an effective tool to control the mean and variability of process simultaneously. The CV control chart, however, is not sensitive at small shift in the magnitude of CV. In this paper, we propose an CV-EWMA (exponentially weighted moving average) control chart which is effective in detecting a small shift of CV. Since the CV-EWMA control chart scheme can be viewed as a weighted average of all past and current CV values, it is very sensitive to small change of mean and variability of the process. We suggest the values of design parameters and show the results of the performance study of CV-EWMA control chart by the use of average run length (ARL). When we compared the performance of CV-EWMA control chart with that of the CV control chart, we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

• 산업경영시스템학회지
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• 제33권3호
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• pp.146-153
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• 2010

When the production run is short and process parameters change frequently, it is difficult to monitor the process using traditional control charts. In such a case, the coefficient of variation (CV) is very useful for monitoring the process variability. The CV control chart is an effective tool to control the mean and variability of process simultaneously. The CV control chart, however, is not sensitive at small shifts in the magnitude of CV. The CV-EWMA(exponentially weighted moving average) control chart which was developed recently is effective in detecting a small shifts of CV. Since the CV-EWMA control chart scheme can be viewed as a weighted average of all past and current CV values, it is very sensitive to small change of mean and variability of the process. In this paper, we propose an FIR(Fast initial response) CV-EWMA control chart to improve the sensitivity of a CV-EWMA scheme at process start-up or out-of-control process. Moreover, we suggest the values of design parameters and show the results of the performance study of FIR CV-EWMA control chart by the use of average run length(ARL). Also, we compared the performance of FIR CV-EWMA control chart with that of the CV-EWMA control chart and we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

• 폴리머
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• 제32권4호
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• pp.377-384
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• 2008

본 연구에서는 UV 조사와 alkoxy 가수분해 법을 이용하여 구형 마이크로 실리콘 고분자 비드를 합성하였다. 구형 실리콘 고분자 비드의 입자들의 coefficient of variation(CV)은 UV 조사량의 세기와 조사시간, 반응온도가 증가함에 따라 감소하였다. 합성된 비드의 평균 입경, 굴절률, pH는 각각 $4.1{\mu}m$, 1.43, 7.5이었으며 진비중, 겉보기 비중은 1.30, 0.40이었으며, 수분함량은 2%이하였다. Hexamethyldisilazane(HMDS) 농도가 0.1 wt%일 때 입자크기와 CV는 가장 작았고, 진원도는 $0.95{\sim}0.98{\mu}m$이었다. UV 조사량과 조사시간이 450 W, 90 min일 때 CV는 4.92%이었다. Methyltrimethoxysilane(MTMS)의 농도가 20 wt%일 때 수율은 총 충전량 대비 11.3%까지 증가하였으며 입자의 평균직경은 교반속도와 온도가 증가함에 따라 작아졌다.

• Journal of Preventive Medicine and Public Health
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• 제32권1호
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• pp.80-87
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• 1999

Objectives. The Study of Small Area Variation(SAV) is most interesting issue in the health care researches. Most studies of SAV have been concluded the existences of variation on the basis of the magnitude of variation without statistical testing. But it is difficult to explain the existence of variation with this way because variation indicies are easily influenced by several parameters and also their distribution are skewed. So, it needs for the study to investigate the distribution of these indices and develop the statistical testing model. Methods. This study was planned to analyze on the distribution of variation indices such as Extremal Quotient(EQ), Coefficient of Variation(CV), Systematic Component of Variation(SCV) and compare the statistical power among indicies. The simulations was performed on the basis of several assumptions and compared to the empirical data. Results. Main findings can be summarized as follows. 1. If other conditions are constant, the more number of regions, the larger 95 percentile of EQ. But under same situation, 95 percentile of CV and SCV were slightly decreased. 2. If the size of regional population or utilization rate were increased, 95 percentile of all statistics were decreased. Also in the cases of small population size and low utilization rate, 95 percentiles of EQ showed various change contrast to the little change of CV. 3. If the difference at the size of regional population were increased, 95 percentiles of EQ and SCV were increased contrast to the little different of CV. 4. If the utilization rate were increased, 95 percentiles of all indicies were increased. But under the same difference of utilization rate, the power of CV and SCV were increased comparing to no change of the power of EQ. 5. Usually the power of EQ were lower than that of CV or SCV and it is similar between CV and SCV. Conclusions. Therefore, we suggest that in selecting the variation indicies at the SAV, CV or SCV are superior than EQ in terms of significance level and power.