• Proceedings of the Korean Society for Quality Management Conference
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• 2004.04a
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• pp.57-63
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• 2004

CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts, however, are less effective in detecting for recurring cycles or frequent small shifts in the process. With Shewhart control charts, we have applied the variety of run rules to check the stability of process in addition to the situations that some points fall outside the control limits. In this paper, we propose the Z-CUSUM control chart for monitoring the process with recurring cycles or frequent small shifts by use of the zone concept as like the Shewhart control charts.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.787-796
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• 2014

Situations where sample size is not constant are common when monitoring a process with Poisson count data. In this paper, we propose a generalized likelihood ratio(GLR) control chart to detect shifts in the Poisson rate when the sample size varies. The performance of the proposed GLR chart is compared with the performance of several cumulative sum(CUSUM) type charts. It is shown that the overall performance of the GLR chart is comparable with CUSUM type charts and is significantly better in cases where the actual value of the shift is different from the pre-specified value in CUSUM type charts.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.2
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• pp.9-17
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• 2010

Complex products may present more than one type of defects and these defects are not always of equal severity. These defects are classified according to their seriousness and effect on product quality and performance. So, demerit systems are very effective systems to monitor the different types of defects. Recently, Kang et al.(2009) proposed the revised Demerit-CUSUM for the evaluation of the Demerit-CUSUM control chart performance exactly. In this paper, we present an advanced Demerit control chart using the double EWMA technique. The double EWMA technique is very efficient and strong method for process control where defects and nonconformities occur with various defect types. Moreover, we compare exact performance of Demerit-CUSUM, Demerit-EWMA and Demerit-DEWMA control chart according to changing sample size or mean shifts magnitude. By the result, we confirm that the performance of Demerit-DEWMA control chart is more than the performance of the Demerit-CUSUM and Demerit-EWMA control chart.

• Journal of Korean Society for Quality Management
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• v.49 no.4
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• pp.539-550
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• 2021

Purpose: The purpose of this study is to propose a multivariate CUSUM control chart that can detect the out-of-control state fast while monitoring the cross- and auto- correlated multivariate time series data. Methods: We first build models to estimate the observation data and calculate the corresponding residuals. After then, a multivariate CUSUM chart is applied to monitor the residuals instead of the original raw observation data. Vector Autoregression and Artificial Neural Net are selected for the modelling, and Separated-MCUSUM chart is selected for the monitoring. The suggested methods are tested under a number of experimental settings and the performances are compared with those of other existing methods. Results: We find that Artificial Neural Net is more appropriate than Vector Autoregression for the modelling and show the combination of Separated-MCUSUM with Artificial Neural Net outperforms the other alternatives considered in this paper. Conclusion: The suggested chart has many advantages. It can monitor the complicated multivariate data with cross- and auto- correlation, and detects the out-of-control state fast. Unlike other CUSUM charts finding their control limits by trial and error simulation, the suggested chart saves lots of time and effort by approximating its control limit mathematically. We expect that the suggested chart performs not only effectively but also efficiently for monitoring the process with complicated correlations and frequently-changed parameters.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.123-142
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• 1999

Conventional SPC assumes that observations are independent. Often in industrial practice, however, observations are not independent. A common approach to building control charts for autocorrelated data is to apply conventional SPC to the residuals from a time series model of the process or is to apply conventional SPC to the weighted or unweighted subgroup means. In this paper, we propose a robust CUSUM control scheme for the detection of level change, without model identification or subgrouping of autocorrelated data. The proposed CUSUM chart and other conventional control charts are compared by a Monte Carlo simulation. It is shown that the proposed CUSUM chart is more effective than conventional CUSUM chart when the process is autocorrelated.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.29-35
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• 2011

In statistical process control, the primary method used to monitor the number of nonconformities is the c-chart. The conventional c-chart is based on the assumption that the occurrence of nonconformities in samples is well modeled by a Poisson distribution. When the Poisson assumption is not met, the X-chart is often used as an alternative charting scheme in practice. And CUSUM-chart is used when it is desirable to detect out of control situations very quickly because of sensitive to a small or gradual drift in the process. In this paper, I compare CUSUM-chart to X-chart for the Katz family covering equi-, under-, and over-dispersed distributions relative to the Poisson distribution.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.126-142
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• 1998

Traditional statistical process control(SPC) assumes that consective observations from a process are independent. In industrial practice, however, observations are ofter serially correlated. A common a, pp.oach to building control charts for autocorrelatd data is to a, pp.y classical SPC to the residuals from a time series model fitted. Unfortunately, one cannot completely escape the effects of autocorrelation by using charts based on residuals of time series model. For the detection of variance change in the process we propose a CUSUM of squares control chart which does not require the model identification. The proposed CUSUM of squares chart and the conventional control charts are compared by a Monte Carlo simulation. It is shown that the CUSUM of squares chart is more effective in the presence of dependency in the processes.

• Journal of Korean Society for Quality Management
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• v.33 no.3
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.487-498
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• 2022

Social network analysis (SNA) techniques have recently been developed to monitor and detect abnormal behaviors in social networks. As a useful tool for process monitoring, control charts are also useful for network monitoring. In this paper, the degree and closeness centrality measures, in which each has global and local perspectives, respectively, are applied to an exponentially weighted moving average (EWMA) chart and a multinomial cumulative sum (CUSUM) chart for monitoring undirected weighted networks. In general, EWMA charts monitor only one variable in a single chart, whereas multinomial CUSUM charts can monitor a categorical variable, in which several variables are transformed through classification rules, in a single chart. To monitor both degree centrality and closeness centrality simultaneously, we categorize them based on the average of each measure and then apply to the multinomial CUSUM chart. In this case, the global and local attributes of the network can be monitored simultaneously with a single chart. We also evaluate the performance of the proposed procedure through a simulation study.