• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• International Journal of Quality Innovation
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• 제1권1호
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• pp.81-88
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• 2000

• Communications for Statistical Applications and Methods
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• 제29권4호
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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.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.523-530
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• 2016

Most classical control charts assume that processes are serially independent, and autocorrelation among variables makes them unreliable. To address this issue, a variety of statistical approaches has been employed to estimate the serial structure of the process. In this paper, we propose a multioutput least squares support vector regression and apply it to construct a residual multivariate cumulative sum control chart for detecting changes in the process mean vector. Numerical studies demonstrate that the proposed multioutput least squares support vector regression based control chart provides more satisfying results in detecting small shifts in the process mean vector.

• 품질경영학회지
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• 제33권3호
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• pp.126-134
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• 2005

This paper proposes a selectively cumulative sum(S-CUSUM) control chart for detecting shifts in the process mean. The basic idea of the S-CUSUM chart is to accumulate previous samples selectively in order to increase the sensitivity. The S-CUSUM chart employs a threshold limit to determine whether to accumulate previous samples or not. Consecutive samples with control statistics out of the threshold limit are to be accumulated to calculate a standardized control statistic. If the control statistic falls within the threshold limit, only the next sample is to be used. During the whole sampling process, the S-CUSUM chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L -consecutive control statistics fall outside the threshold limit. The number L is a decision variable and is called a 'control length'. A Markov chain approach is employed to describe the S-CUSUM sampling process. Formulae for the steady state probabilities and the Average Run Length(ARL) during an in-control state are derived in closed forms. Some properties useful for designing statistical parameters are also derived and a statistical design procedure for the S-CUSUM chart is proposed. Comparative studies show that the proposed S-CUSUM chart is uniformly superior to the CUSUM chart or the Exponentially Weighted Moving Average(EWMA) chart with respect to the ARL performance.

• 통합자연과학논문집
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• 제12권3호
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• pp.78-84
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• 2019

In many cases, the quality of a product is determined by several correlated quality variables. Control charts have been used for a long time widely to control the production process and to quickly detect the assignable causes that may produce any deterioration in the quality of a product. Numerical switching performances of multivariate cumulative sum control chart for simultaneous monitoring all components in the dispersion matrix ${\Sigma}$ under multivariate normal process $N_p({\underline{\mu}},{\Sigma})$ are considered. Numerical performances were evaluated for various shifts of the values of variances and/or correlation coefficients in ${\Sigma}$. Our computational results show that if one wants to quick detect the small shifts in a process, CUSUM control chart with small reference value k is more efficient than large k in terms of average run length (ARL), average time to signal (ATS), average number of switches (ANSW).

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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• pp.560-570
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• 2006

This paper proposes a selectively cumulative sum (S-CUSUM) control chart with variable sampling intervals (VSI) for detecting shifts in the process mean. The basic idea of the VSI S-CUSUM chart is to adjust sampling intervals and to accumulate previous samples selectively in order to increase the sensitivity. The VSI S-CUSUM chart employs a threshold limit to determine whether to increase sampling rate as well as to accumulate previous samples or not. If a standardized control statistic falls outside the threshold limit, the next sample is taken with higher sampling rate and is accumulated to calculate the next control statistic. If the control statistic falls within the threshold limit, the next sample is taken with lower sampling rate and only the sample is used to get the control statistic. The VSI S-CUSUM chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L-consecutive control statistics fall outside the threshold limit. The number L is a decision variable and is called a 'control length'. A Markov chain model is employed to describe the VSI S-CUSUM sampling process. Some useful formulae related to the steady state average time-to signal (ATS) for an in-control state and out-of-control state are derived in closed forms. A statistical design procedure for the VSI S-CUSUM chart is proposed. Comparative studies show that the proposed VSI S-CUSUM chart is uniformly superior to the VSI CUSUM chart or to the Exponentially Weighted Moving Average (EWMA) chart with respect to the ATS performance.

• 통합자연과학논문집
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• 제5권4호
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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.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.21-29
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• 2002

Several different control statistics to simultaneously monitor dispersion matrix of several quality variables are presented since different control statistics can be used to describe variability. Multivariare cumulative sum (CUSUM) control charts are proposed and the performances of the proposed CUSUM charts are evaluated in terms of average run length (ARL). Multivariate Shewhart charts are also proposed to compare the properties of the proposed CUSUM charts. The numerical results show that multivariate CUSUM charts are more efficient than multivariate Shewhart charts for small or moderate shifts. And we also found that small reference value of the CUSUM chart is more efficient for small shift.

• Communications for Statistical Applications and Methods
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• 제21권1호
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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.