• 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.

• 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.

• 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.

• 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 Korean Society for Quality Management
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• v.9 no.2
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• pp.26-30
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• 1981

A typical industrial data - monitoring scheme often requires trend detection Trend detection can be accomplished in many ways. Common statistical methods are the sign test, the run test, and the trend test. Graphical methods include various smoothing schemes and the cusum. The cusum has established itself as an efficient method of detecting changes in the mean level of a process being monitored. The cusum requires a "target value" with which the raw data are compared. At production start - up it is often difficult to designate the target value. This paper offers a means of initiating the cusum technique without a target value.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.4
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• pp.1-7
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• 2002

Statistical process control is used widely as an effective tool to solve the quality problems in practice fields. All the control charts used in statistical process control are parametric methods, suppose that the process distributes normal and observations are independent. But these assumptions, practically, are often violated if the test of normality of the observations is rejected and/or the serial correlation is existed within observed data. Thus, in this study, to screening process, the Combined Shewhart - CUSUM quality control chart is described and evaluated that used bootstrap method. In this scheme the CUSUM chart will quickly detect small shifts form the goal while the addition of Shewhart limits increases the speed of detecting large shifts. Therefor, the CSC control chart is detected both small and large shifts in process, and the simulation results for its performance are exhibited. The bootstrap CSC control chart proposed in this paper is superior to the standard method for both normal and skewed distribution, and brings in terms of ARL to the same result.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2007.11a
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• pp.169-170
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• 2007

본 연구에서 반도체 플라즈마 장비 감시를 위한 CUSUM 제어 차트 설계기법에 관해 연구하였다. CUSUM 제어차트에 관여하는 설계변수의 다양한 조합에 대하여 플라즈마 장비의 감시 성능을 평가하였다. 평가를 위해 RF 정합망 감시시스템을 이용하여 플라즈마 임피이던스 정합에 관여하는 정합변수에 대한 실시간 데이터를 수집하였으며, 여기에는 임피이던스와 상위치에 대한 전기적 정보, 그리고 반사전력에 대한 정보가 포함된다. CUSUM 설계변수에 따른 감시와 진단성능을 평가하였으며, 최적화된 설계변수의 결정으로 감시와 진단성능을 증진시킬 수 있었다. 한편, 고정설계변수에 비해 가변 설계변수가 감시성능을 증진하느데 더 효과적임을 알 수 있었다. 평가에 이용된 데이터는 소스전력이 500 W, 압력이 15 mTorr, $O_2$ 유량이 75 socm일 때 수집하였다.

• 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.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.823-833
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• 2016

The lifetime is a key characteristic of product quality. It is best to obtain the lifetime data of all samples, but they are often censored due to time or expense limitations. In this paper, we propose a binomial cumulative sum (CUSUM) chart to monitor the mean of type I right-censored Weibull lifetime data, for a xed value of the Weibull shape parameter. We compare the performance of the proposed binomial CUSUM chart with CUSUM charts studied previously using the steady-state average run length (ARL). The results show that the performance of the binomial CUSUM chart is better when the censoring rate is high and/or the sample size is small.

• 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.