• International Journal of Quality Innovation
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• v.1 no.1
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• pp.81-88
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• 2000

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.135-148
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• 1989

Cumulative sum schemes based on a weighted score are considered for controlling the mean of a continuous production process; in which both the one-sided and two-sided schemes are proposed. The average run lengths and the run length distributions for the proposed schemes are obtained by the Markov chain approach. Comparisons by the average run length show that the proposed schemes perform nearly as well as the standard cumulative sum schemes in detecting changes in the process mean. Comparisons of the one-sided schemes by the run length distribution are also presented.

• Journal of the Korean Statistical Society
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• v.23 no.1
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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.

• 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.

• Journal of Integrative Natural Science
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• v.12 no.3
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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).

• 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.35 no.6
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• pp.725-737
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• 2022

In the standard assumption of statistical process monitoring (SPM) under consideration, the in-control region of the control parameter of quality characteristic consists of a single point. However, if small deviations from the ideal situation may not be of practical importance, the parametric space can consist of three regions: In-control, indifference, and out-of-control. In this paper, we propose two exponentially weighted moving average (EWMA) charting procedures applicable to the situation with three parameter regions, and compare the efficiency of the proposed procedures with the Shewhart chart and the cumulative sum (CUSUM) chart.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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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.

• The Korean Journal of Applied Statistics
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• v.3 no.1
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• pp.105-120
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• 1990

In this paper, a sequential test procedure is defined by using cumulative sum (CUSUM) of statistics. The properties as well as the efficiency of the CUSUM test are studied in comparison with the sequential probability ratio test (SPRT). It was shown that, the operating characteristic function and the average sample numbrer can be derived by Wald and Wiener process approximations. Also it was shown that the statistics used in the CUSUM test is determined to provide asymtotically equivalent efficiency compared to the SPRT. The efficiency of the CUSUM test and the SPRT are cpmpared by an example for some limited number of cases in the exponential distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.3
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• pp.52-61
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• 2012

The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.