• Title, Summary, Keyword: CUSUM

### A Selectively Cumulative Sum(S-CUSUM) Control Chart (선택적 누적합(S-CUSUM) 관리도)

• Lim, Tae-Jin
• Journal of the Korean Society for Quality Management
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• v.33 no.3
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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.

### Design of Variance CUSUM

• Lee, Eun-Kyung;Hong, Sung-Hoon;Lee, Yoon-Dong
• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1131-1142
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• 2009
• We suggest a fast and accurate algorithm to compute ARLs of CUSUM chart for controling process variance. The algorithm solves the characteristic integral equations of CUSUM chart (for controling variance). The algorithm is directly applicable for the cases of odd sample sizes. When the sample size is even, by using well-known approximation algorithm combinedly with the new algorithm for neighboring odd sample sizes, we can also evaluate the ARLs of CUSUM charts efficiently and accurately. Based on the new algorithm we consider the optimal design of upward and downward CUSUM charts for controling process variance.

### A New Performance Criterion for Cusum Control Chart (누적합 관리도에 대한 새로운 성능 평가 기준)

• Lee, Yoon-Dong;Ahn, Byoung-Jin
• Journal of the Korean Society for Quality Management
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• v.33 no.4
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• pp.96-102
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• 2005
• Cusum control chart is an efficient method to detect the change of process status. Many variants of cusum have considered, and the effects of design parameters have reviewed. To find the best cusum out of variants and to decide the best values of the design parameters, we need a criterion measuring the performance of the cusum control chart. People used and suggested several criterions which appear to be similar, but those have quite different properties. In this paper we review the properties of performance measure of cusum and its variants. Our goal is to provide fair and impartial criterion for comparison of cusums when the decision boundaries of the cusums are much different each other. We comparatively tested newly suggested measure and traditional measure with the examples of cumulative scored chart as a special case of cusum chart.

### A Selectively Cumulative Sum (S-CUSUM) Control Chart with Variable Sampling Intervals (VSI) (가변 샘플링 간격(VSI)을 갖는 선택적 누적합 (S-CUSUM) 관리도)

• Im, Tae-Jin
• Proceedings of the Korean Operations and Management Science Society Conference
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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.

### Plasma Processing Supervision Using CUSUM Control Chart (CUSUM 제어차트를 이용한 플라즈마 공정감시)

• Kim, Woo-Suk;Kim, Byung-Whan
• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• pp.460-461
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• 2007
• 본 연구에서는 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 임피던스 정합에 관여하는 정합변수에 대한 실시간 데이터를 수집하였으며, 여기에는 임피던스와 상위치에 대한 전기적 정보, 그리고 반사전력에 대한 정보가 포함된다. 평가결과, 설계변수의 조합에 대하여 감시 성능이 크게 달랐지만, 각 센서 정보의 감시 성능을 증진시키는 설계변수의 조합이 있었음을 확인하였으며, 이는 각 종 다양한 센서정보별 CUSUM 제어 차트의 설계가 필요함을 의미한다. 연구에서는 Raw 데이터 대비 성능 분석을 위해 CUSUM 제어 차트의 설계변수를 변수인 d와 ${\Theta}$값의 변화를 주어 다수의 (d, ${\Theta}$)의 조합에 따른 감시 성능을 평가하였으며, 평가에 이용된 데이터는 소스전력이 750 W, 압력이 15 mTorr, Ar 유량이 50 seem일 때 수집하였다.

### A GLR Chart for Monitoring a Zero-Inflated Poisson Process (ZIP 공정을 관리하는 GLR 관리도)

• Choi, Mi Lim;Lee, Jaeheon
• The Korean Journal of Applied Statistics
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• v.27 no.2
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• pp.345-355
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• 2014
• The number of nonconformities in a unit is commonly modeled by a Poisson distribution. As an extension of a Poisson distribution, a zero-inflated Poisson(ZIP) process can be used to fit count data with an excessive number of zeroes. In this paper, we propose a generalized likelihood ratio(GLR) chart to monitor shifts in the two parameters of the ZIP process. We also compare the proposed GLR chart with the combined cumulative sum(CUSUM) chart and the single CUSUM chart. It is shown that the overall performance of the GLR chart is comparable with CUSUM charts and is significantly better in some cases where the actual directions of the shifts are different from the pre-specified directions in CUSUM charts.

### Poisson GLR Control Charts (Poisson GLR 관리도)

• Lee, Jaeheon;Park, Jongtae
• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.787-796
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• 2014
• Situations where sample size is not constant are common when monitoring a process with Poisson count data. In this paper, we propose a generalized likelihood ratio(GLR) control chart to detect shifts in the Poisson rate when the sample size varies. The performance of the proposed GLR chart is compared with the performance of several cumulative sum(CUSUM) type charts. It is shown that the overall performance of the GLR chart is comparable with CUSUM type charts and is significantly better in cases where the actual value of the shift is different from the pre-specified value in CUSUM type charts.

### A Study of Demerit-CUSUM Control Chart and Interpretation Method (Demerit-CUSUM 관리도와 해석방법에 관한 연구)

• 나상민;강창욱;심성보
• Journal of the Korean Society for Quality Management
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• v.31 no.1
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• pp.132-141
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• 2003
• As the technology has improved and demands of customers have varied, a lot of products are getting diverse and intricate. Consequently, the enterprise that produce products have to simultaneously consider the various variables for the very products. There are some scheme, such as Multivariate control chart and Demerit control chart, designed to simultaneously monitor the variables in the process. In this paper, we present an effective method for process control using the Demerit-CUSUM control chart in the process where nonconforming units or nonconformities are occured by various types. In addition, we show interpretation method for abnormal signal in order to quickly detect the assignable causes as Demerit-CUSUM control chart signals abnormality. we compare performance of Demerit control chart and Demerit-CUSUM control chart using example again used in the existing studies, and present result of performance accoriding to changing sample size and parameter.

### Detection of Plasma Variation Using CUSUM Control Chart (CUSUM 제어차트를 이용한 플라즈마 변이의 탐지)

• Kim, Woo-Suk;Kim, Byung-Whan
• Proceedings of the KIEE Conference
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• pp.139-140
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• 2007
• 본 연구에서는 반도체 플라즈마 장비 감시를 위한 CUSUM 제어 차트 설계기법에 관해 연구하였다. CUSUM 제어 차트에 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. 평가결과, 설계변수의 조합에 대하여 감시 성능이 크게 달랐지만, 각 센서 정보의 감시 성능을 증진시키는 설계변수의 조합이 있었음을 확인하였으며, 이는 각 종 다양한 센서정보 별 CUSUM 제어 차트의 설계가 필요함을 의미한다. 연구에서는 Raw 데이터 대비 성능 분석을 위해 CUSUM 제어 차트의 설계 변수를 변수인 d와 $\Theta$값의 변화를 주어 다수의 (0, $\Theta$)의 조합에 따른 감시 성능을 평가하였으며, 평가에 이용된 데이터는 소스전력이 750 W, 압력이 15 mTorr, $O_2$ 유량이 50 sccm일 때 수집 하였다.

### A note on CUSUM design for autocorrelated processes (자기상관 공정에 대한 누적합관리도에서 설계모수 값의 결정)

• Lee, Jae-June;Lee, Jong-Seon
• Journal of the Korean Society for Quality Management
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• v.36 no.4
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• pp.87-92
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• 2008
• It is common to use CUSUM charts for detecting small level shifts in processes control, in which reference value(k) and decision interval(h) are the design parameters to be determined. To control process with autocorrelation, CUSUM charts could be applied to residuals obtained from fitting ARIMA models. However, constant level shifts in processes lead to varying mean shifts in residual processes and thus standard CUSUM charts may need to be modified. In this paper, we study the performance of CUSUM charts with various design parameters applied to autocorrelated processes, especially focussing on ARMA(1,1) models, and propose how they can be determined to get better performance in terms of the average run length.