• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.385-401
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• 1997

Cumulative sum (CUSUM) control charts are widely used in industry for the statistical process control. The statistical design procedure in CUSUM charts tells how to choose the decision interval value. The decision interval is primarily determied by the desired in - control ARL - that is, by the acceptable frequency of false out-of-control signals. In this paper we propose a new approximation method for calculating the ARL and determining the decision interval. The performance of the proposed method is examined by evaluating the accuracy of estimated ARLs and decision intervals in normal and exponential cases.

• Industrial Engineering and Management Systems
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• v.8 no.3
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• pp.139-147
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• 2009

Control charts are used to distinguish between chance and assignable causes in the variability of quality characteristics. When a control chart signals that an assignable cause is present, process engineers must initiate a search for the assignable cause of the process disturbance. Identifying the time of a process change could lead to simplifying the search for the assignable cause and less process down time, as well as help to reduce the probability of incorrectly identifying the assignable cause. The change point estimation by likelihood theory and the built-in change point estimation in a control chart have been discussed until now. In this article, we discuss two kinds of process change point estimation when the CUSUM ($\bar{x}$, s) control chart for monitoring process mean and variance simultaneously is operated. Throughout some numerical experiments about the performance of the change point estimation, the change point estimation techniques in the CUSUM ($\bar{x}$, s) control chart are considered.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.11-14
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• 1996

Performance of the group cumulative sum(CUSUM) control scheme using multiple univariate CUSUM charts is more sensitive to the change of quality control(QC) characteristics than the control chart scheme based on the Hotelling statistics. We examine three group charts for multivariate normal data sets simulated with various correlation structures and shift directions in the mean vector. These group schemes apply the orginal measurement vectors, the scaled residual vectors from the regression of each variable on all others and the principal component vectors respectively to calculating the CUSUM statistics. They are also compared to the multivariate QC charts based on the Hotelling statistic by estimating average run lengths, coefficients of variation of run length and ranks in signaling order. On the basis of simulation results, we suggest a control chart scheme appropriate for specific quality control environment.

• Proceedings of the Korean Society Of Semiconductor Equipment Technology
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• 2006.10a
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• pp.90-95
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• 2006

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 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.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.367-382
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• 2017

We consider an infinite-order long-memory heterogeneous autoregressive (HAR) model, which is motivated by a long-memory property of realized volatilities (RVs), as an extension of the finite order HAR-RV model. We develop bootstrap tests for structural mean or variance changes in the infinite-order HAR model via stationary bootstrapping. A functional central limit theorem is proved for stationary bootstrap sample, which enables us to develop stationary bootstrap cumulative sum (CUSUM) tests: a bootstrap test for mean break and a bootstrap test for variance break. Consistencies of the bootstrap null distributions of the CUSUM tests are proved. Consistencies of the bootstrap CUSUM tests are also proved under alternative hypotheses of mean or variance changes. A Monte-Carlo simulation shows that stationary bootstrapping improves the sizes of existing tests.

• Management Science and Financial Engineering
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• v.5 no.1
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• pp.51-71
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• 1999

Performance of the group cumulative sum (CUSUM) control scheme using multiple univariate CUSUM charts is more sensitive to the change of quality control (QC) characteristics than the control chart schemes based on the Hotelling statistic We vexamine three group charts for multivariate normal data sets simulated with various correlation structures and shift directions in the mean vector. These group schemes apply the original measurement vectors, the scaled residual vectors from the re-gression of each variable on all others and the principal component vectors respectively to calculat-ing the CUSUM statistics. They are also compared to the multivariate QC charts based on the Ho-telling statistic by estimating average run lengths, coefficients of variation of run length and ranks in signaling order. On the basis of simulation results, we suggest a control chart scheme appropriate for specific quality control environment.

• 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 for Quality Management
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• v.34 no.4
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• pp.102-109
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• 2006

This paper investigates the effects of non-normality on the performance of univariate and multivariate cumulative sum(CUSUM) control charts for monitoring the process mean. In-control and out-of-control average run lengths of the charts are examined for the univariate/multivariate lognormal and t distributions. The effects of the reference value and the correlation coefficient under the non-normal distributions are also studied. Simulation results show that the CUSUM charts with small reference values are robust to non-normality but those with moderate or large reference values are sensitive to non-normal data especially to process data from skewed distributions. The performance of the chart to detect mean shift of a process is not invariant to the direction of the shift for skewed distributions.

• Proceedings of the Safety Management and Science Conference
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• 2013.11a
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• pp.147-160
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• 2013

이 논문은 공정변화를 보다 잘 감지할 수 있는 관리도의 개발동향에 주안점을 두고 있으며, 경제적 접근법으로 관리모수를 설정하여 공정관리 메카니즘을 사용하는데 있어서 최소의 비용을 가지도록 하여 품질 향상 비용을 절감시킬 수 있는 설계 접근방법을 조사 연구했다. 또한 CUSUM 관리도를 기존의 다양한 관리도와 결합하여 개발된 새로운 관리도를 비교했다. 비교된 관리도의 경제적 모형설계를 통하여 공정 품질에서의 경제적인 영향의 최적화를 위한 관리모수를 제시했다. 이는 공정평균의 이동을 감지하기 위한 결합 관리도를 개발하는 경제적설계 절차를 제시했다.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1565-1572
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• 2015

In this paper, we analyze the polio incidence data based on the Poisson autoregressive models, focusing particularly on change-point detection. Since the data include some strongly deviating observations, we employ the robust cumulative sum (CUSUM) test proposed by Kang and Song (2015) to perform the test for parameter change. Contrary to the result of Kang and Lee (2014), our data analysis indicates that there is no significant change in the case of the CUSUM test with strong robustness and the same result is obtained after ridding the polio data of outliers. We additionally consider the comparison of the forecasting performance. All the results demonstrate that the robust CUSUM test performs adequately in the presence of seemingly outliers.