• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.69-80
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• 2014

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both a sustained shift and a linear drift. The design and application of a generalized likelihood ratio (GLR) chart for simultaneously monitoring a sustained shift and a linear drift are evaluated. The GLR chart has the advantage that when we design this chart, we do not need to specify the size of the parameter change. The performance of the GLR chart is compared with that of other control charts, such as the standard cumulative sum (CUSUM) charts and the cumulative score (CUSCORE) charts. And we compare the proposed GLR chart with the GLR charts designed for monitoring only a sustained shift and for monitoring only a linear drift. Finally, we also compare the proposed GLR chart with the chart combinations. We show that the proposed GLR chart has better overall performance for a wide range of shift sizes and drift rates relative to other control charts, when a special cause produces a sustained shift and/or a linear drift in the process mean.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.169-183
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• 2004

The synthetic control chart (SCC) proposed by Wu and Spedding (2000) is to detect shifts in the process mean. The performance was re-evaluated by Davis and Woodall (2002), and the steady-state average run length (ARL) performance was shown to be inferior to cumulative sum (CUSUM) or exponentially weighted moving average (EWMA) chart This paper proposes a simple adaptive scheme to improve the performance of the synthetic control chart. That is, once a non-conforming (NC) sample occurs, we investigate the next L-consecutive samples with larger sample sizes and shorter sampling intervals. We employ a Markov chain model to derive the ARL and the average time to s19na1 (ATS). We also propose a statistical design procedure for determining decision variables. Comprehensive comparative study shows that the proposed control chart is uniformly superior to the original SCC or double sampling (DS) Χ chart and comparable to the EWMA chart in ATS performance.

• Journal of Integrative Natural Science
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• v.5 no.4
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• pp.246-252
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• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.465-470
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• 2012

EWMA(exponentially weighted moving average) charts and CUSUM(cumulative sum) charts are very effective to detect small shifts in the process mean. These charts have some control-chart parameters that allow the charts and be tuned and be more sensitive to certain shifts. The EWMA chart requires users to specify the value of a smoothing parameter, which can also be designed for the size of the mean shift. However, the size of the mean shift that occurs in applications is usually unknown and EWMA charts can perform poorly when the actual size of the mean shift is significantly different from the assumed size. In this paper, we propose the design procedure to find the optimal smoothing parameter of the EWMA chart when the size of the mean shift is unknown.

• Journal of the Korea Society of Computer and Information
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• v.25 no.12
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• pp.73-82
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• 2020

Most process date such as semiconductor and petrochemical processes, autocorrelation often exists between observed data, but when the existing SPC(Statistical process control) is applied to these processes, it is not possible to effectively detect the average change of the process. In this paper, when the average change of a certain size occurs in the process data following a specific time series model, the average of the residuals changes according to the passage of time, and the change pattern of the average is introduced around the ARMA(1,1) process. Based on this result, the reference value required in the design process of the CUSUM (Cumulative sum) control chart is appropriately considered by considering the type of the time series model of the process data of the CUSUM control chart that can detect small mean changes in the process and the width of the process mean change of interest. It was confirmed through simulation that it should be selected and used.

• Management Science and Financial Engineering
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• v.6 no.1
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• pp.1-19
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• 2000

This papeer proposes a general approach of the multivariate expontially weighted moving average(MEWMA) chart, in which the smoothing matrix has full elements instead of only diagonal elements. The average run length (ARL) properties of this scheme are examined for a diverse set of quality control environments and the information to design the chhart is provied. Performance of the scheme is measured by estmating ARL and compared to those of two group cumulative sum (CUSUM) chats. The comparison resullts show that the MEWMA chart can improve its ARL performance in detecting a small shifts out-of-control in the start-up stage, the general MEWMA chart of a full smoothing matrix appears to offer an exceptional protection aginst departures from control in the process mean.

• Journal of Korean Society for Quality Management
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• v.38 no.3
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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.

• Journal of Korean Society for Quality Management
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• v.43 no.4
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• pp.521-532
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• 2015

Purpose: The purpose of this study is to compare two multivariate cumulative sum (MCUSUM) charts designed for spatio-temporal surveillance in terms of not only temporal detection performance but also spatial detection performance. Method: Experiments under various configurations are designed and performed to test two CUSUM charts, namely SMCUSUM and RMCUSUM. In addition to average run length(ARL), two measures of spatial identification accuracy are reported and compared. Results: The RMCUSUM chart provides higher level of spatial identification accuracy while two charts show comparable performance in terms of ARL. Conclusion: The RMCUSUM chart has more flexibility, robustness, and spatial identification accuracy when compared to those of the SMCUSUM chart. We recommend to use the RMCUSUM chart if control limit calibration is not an urgent task.

• 한국데이터정보과학회:학술대회논문집
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• 2003.05a
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• pp.89-95
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• 2003

Cumulative sum(CUSUM) control charts for monitoring dispersion matrix under multivariate normal process are proposed. Performances of the proposed CUSUM charts are measured in terms of average run length(ARL) by simulation. Numerical results show that small reference values of the proposed CUSUM chart is more efficient for small shifts in the production process.

• Journal of the Korean Society of Safety
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• v.31 no.4
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• pp.35-41
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• 2016

In order to guarantee the process safety and prevent accidents, the deviations from normal operating conditions should be monitored and their root causes have to be identified as soon as possible. The statistical theories-based method among various fault diagnosis methods has been gaining popularity, due to simplicity and quickness. However, according to fault magnitudes, the scalar value generated by statistical methods can be changed and this point can lead to produce wrong information. To solve this difficulty, this work employs PCA (Principal Component Analysis) based method with qualitative information. In the case study of our previous study, the number of assumed faults is much smaller than that of process variables. In the case study of this study, the number of predefined faults is 19, while that of process variables is 6. It means that a fault diagnosis becomes more difficult and it is really hard to isolate a single fault with a small number of variables. The PCA model is constructed under normal operation data in order to get a loading vector and the data set of assumed faulty conditions is applied with PCA model. The significant changes on PC (Principal Components) axes are monitored with CUSUM (Cumulative Sum Control Chart) and recorded to make the information, which can be used to identify the types of fault.