• 품질경영학회지
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• 제49권4호
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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.

• 품질경영학회지
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• 제32권2호
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• pp.132-153
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• 2004

CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts are, however, less effective in detecting for recurring cycles or frequent small shifts in the processes. 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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2004년도 품질경영모델을 통한 가치 창출
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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.

• Journal of Radiation Protection and Research
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• 제44권2호
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• pp.64-71
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• 2019

Background: It is very difficult to distinguish between a radioactive contamination source and background radiation from natural radionuclides in the marine environment by means of online monitoring system. The objective of this study was to investigate a statistical process for triggering abnormal level of count rate data measured from our on-line seawater radioactivity monitoring. Materials and Methods: Count rate data sets in time series were collected from 9 monitoring posts. All of the count rate data were measured every 15 minutes from the region of interest (ROI) for $^{137}Cs$ ($E_{\gamma}=661.6keV$) on the gamma-ray energy spectrum. The Shewhart ($3{\sigma}$), CUSUM, and Bayesian S-R control chart methods were evaluated and the comparative analysis of determination methods for count rate data was carried out in terms of the false positive incidence rate. All statistical algorithms were developed using R Programming by the authors. Results and Discussion: The $3{\sigma}$, CUSUM, and S-R analyses resulted in the average false positive incidence rate of $0.164{\pm}0.047%$, $0.064{\pm}0.0367%$, and $0.030{\pm}0.018%$, respectively. The S-R method has a lower value than that of the $3{\sigma}$ and CUSUM method, because the Bayesian S-R method use the information to evaluate a posterior distribution, even though the CUSUM control chart accumulate information from recent data points. As the result of comparison between net count rate and gross count rate measured in time series all the year at a monitoring post using the $3{\sigma}$ control charts, the two methods resulted in the false positive incidence rate of 0.142% and 0.219%, respectively. Conclusion: Bayesian S-R and CUSUM control charts are better suited for on-line seawater radioactivity monitoring with an count rate data in time series than $3{\sigma}$ control chart. However, it requires a continuous increasing trend to differentiate between a false positive and actual radioactive contamination. For the determination of count rate, the net count method is better than the gross count method because of relatively a small variation in the data points.

• 응용통계연구
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• 제27권5호
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• pp.787-796
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• 2014

Poisson 분포를 따르는 결점수를 관측하여 공정을 관리할 때 표본 크기를 동일하게 유지하기가 힘든 경우가 많다. 이 논문은 표본 크기가 동일하지 않은 경우 Poisson 공정모수의 변화를 탐지하는 GLR(generalized likelihood ratio) 관리도 절차를 제안하고 있다. 또한 제안된 GLR 관리도의 효율을 모의실험을 통하여 기존에 연구된 CUSUM 관리도들과 비교하였다. 모의실험 결과, 제안된 GLR 관리도는 공정모수의 다양한 변화에 대해 효율이 대체적으로 양호했으며, CUSUM 관리도에서 실제 공정모수의 변화값이 미리 지정한 값과 차이가 많이 날 경우 CUSUM 관리도에 비해 효율이 월등히 좋음을 알 수 있었다.

• 응용통계연구
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• 제27권2호
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• pp.345-355
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• 2014

단위 영역의 결점수는 일반적으로 Poisson 분포를 가정한다. 이 Poisson 분포의 확장된 형태로 ZIP(zero-inflated Poisson) 분포를 고려할 수 있는데, 이 모형은 데이터에 0이 많이 관측되는 경우 잘 적합된다고 알려져 있다. 이 논문에서는 ZIP 분포를 따르는 공정을 관리하는 GLR(generalized likelihood ratio) 관리도 절차를 제안하고 있다. 또한 제안된 GLR 관리도의 효율을 기존에 제안된 CUSUM 관리도들과 비교하였다. 그 결과 제안된 GLR 관리도는 모수의 다양한 변화에 대해 효율이 좋거나 또는 효율이 크게 떨어지지 않았고, 특히 CUSUM 관리도에서 모수가 미리 설정한 방향과 다르게 변화했을 때 효율이 크게 나빠지는 문제를 해결할 수 있는 대안이라는 결론을 얻을 수 있었다.

• 한국표면공학회:학술대회논문집
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• 한국표면공학회 2009년도 추계학술대회 초록집
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• pp.231-232
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• 2009

공정의 질 (Quality)과 장비생산성을 향상시키기 위해서는 플라즈마를 엄격히 감시해야 하며, 본 연구에서는 플라즈마 색 정보와 신경망을 결합한 감시 기법을 보고한다. 본 기법은 인-시추 색 정보 수집, 시계열 신경망 모델링, 그리고 CUSUM 제어로 구성된다. 제안한 기법을 소스전력을 변화시켜 발생한 색 정보에 적용하였으며, 신경망 모델은 비정상 플라즈마를 정확하게 탐지할 수 있음을 확인하였다.

• 품질경영학회지
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• 제33권3호
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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.

• 품질경영학회지
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• 제9권2호
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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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 춘계학술대회
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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.