• Title, Summary, Keyword: Combined chart

### Multiparameter CUSUM charts with variable sampling intervals

• Im, Chang-Do;Cho, Gyo-Young
• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.593-599
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• 2009
• We consider the problem of using control charts to monitor more than one parameter with emphasis on simultaneously monitoring the mean and variance. The fixed sampling interval (FSI) control charts are modified to use variable sampling interval (VSI) control charts depending on what is being observed from the data. In general, approaches of monitoring the mean and variance simultaneously is to use separate charts for each parameter and a combined chart. In this paper, we use three basic strategies which are separate Shewhart charts for each parameter, a combined Shewhart chart and a combined CUSUM chart. We showed that a combined VSI CUSUM chart is comparatively more efficient than any other chart if the shifts in both mean and variance are small.

### Performance of the combined ${\bar{X}}-S^2$ chart according to determining individual control limits (관리한계 설정에 따른 ${\bar{X}}-S^2$ 관리도의 성능)

• Hong, Hwi Ju;Lee, Jaeheon
• The Korean Journal of Applied Statistics
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• v.33 no.2
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• pp.161-170
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• 2020
• The combined ${\bar{X}}-S^2$ chart is a traditional control chart for simultaneously detecting mean and variance. Control limits for the combined ${\bar{X}}-S^2$ chart are determined so that each chart has the same individual false alarm rate while maintaining the required false alarm rate for the combined chart. In this paper, we provide flexibility to allow the two charts to have different individual false alarm rates as well as evaluate the effect of flexibility. The individual false alarm rate of the ${\bar{X}}$ chart is taken to be γ times the individual false alarm rate of the S2 chart. To evaluate the effect of selecting the value of γ, we use the out-of-control average run length and relative mean index as the performance measure for the combined ${\bar{X}}-S^2$ chart.

### Design of Combined Shewhart-CUSUM Control Chart using Bootstrap Method (Bootstrap 방법을 이용한 결합 Shewhart-CUSUM 관리도의 설계)

• 송서일;조영찬;박현규
• Journal of the Society of Korea 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.

### Procedures for Monitoring the Process Mean and Variance with One Control Chart (하나의 관리도로 공정 평균과 분산의 변화를 탐지하는 절차)

• Jung, Sang-Hyun;Lee, Jae-Heon
• The Korean Journal of Applied Statistics
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• v.21 no.3
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• pp.509-521
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• 2008
• Two control charts are usually required to monitor both the process mean and variance. In this paper, we introduce control procedures for jointly monitoring the process mean and variance with one control chart, and investigate efficiency of the introduced charts by comparing with the combined two EWMA charts. Our numerical results show that the GLR chart, the Omnibus EWMA chart, and the Interval chart have good ARL properties for simultaneous changes in the process mean and variance.

### An Effective Control Chart for Monitoring Mean Shift in AR(1) Processes (AR(1) 공정에서의 효과적인 공정평균 관리도)

• 원경수;강창욱;이배진
• Journal of the Society of Korea Industrial and Systems Engineering
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• v.24 no.67
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• pp.27-36
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• 2001
• A standard assumption when using a control chart to monitor a process is that the observations from the process output are statistically independent. However, for many processes the observations are autocorrelated and this autocorrelation can have a significant effect on the performance of the control chart. In this paper, we consider combined control chart of monitoring the mean of a process in which the observations can be modeled as a first-order autoregressive process. The Shewhart control chart of residuals-EWMA control chart of the observations is considered and the method of combination is recommended. The performance of the proposed control chart is compared with the performance of other control charts using a simulation.

### A comparison of single charts for non-normal data (비정규성 데이터에 대한 단일 관리도들의 비교)

• Kang, Myunggoo;Lee, Jangtaek
• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.729-738
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• 2015
• In this paper, we compare the robustness to the assumption of normality of the single control charts to control the mean and variance simultaneously. The charts examined were semicircle control chart, max chart and MSE chart with Shewhart individuals control charts. Their in-control and out-of-control performance were studied by simulation combined with computation. We calculated false alarm rate to compare among single charts by changing subgroup size and shifting mean of quality characteristics. It turns out that max chart is more robust than any of the others if the process is in-control. In some cases max chart and MSE chart are more robust than others if the process is out-of-control.

### 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.

### Economic Design of Three-Stage $\bar{X}$ Control Chart Based on both Performance and Surrogate Variables (성능변수와 대용변수를 이용한 3단계 $\bar{X}$ 관리도의 경제적 설계)

• Kwak, Shin-Seok;Lee, Jooho
• Journal of the Korean Society for Quality Management
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• v.44 no.4
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• pp.751-770
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• 2016
• Purpose: Two-stage ${\bar{X}}$ chart is a useful tool for process control when a surrogate variable may be used together with a performance variable. This paper extends the two-stage ${\bar{X}}$ chart to a three stage version by decomposing the first stage into the preliminary stage and the main stage. Methods: The expected cost function is derived using Markov-chain approach. The optimal designs are found for numerical examples using a genetic algorithm combined with a pattern search algorithm and compared to those of the two-stage ${\bar{X}}$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the two-stage ${\bar{X}}$ chart in terms of the expected cost per unit time unless the correlation between the performance and surrogate variables is modest and the shift in process mean is smallish. Conclusion: Three-stage ${\bar{X}}$ chart may be a useful alternative to the two-stage ${\bar{X}}$ chart especially when the correlation between the performance and surrogate variables is relatively high and the shift in process mean is on the small side.

### Multivariate control charts for monitoring correlation coefficients in dispersion matrix

• Chang, Duk-Joon;Heo, Sun-Yeong
• Journal of the Korean Data and Information Science Society
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• v.23 no.5
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• pp.1037-1044
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• 2012
• Multivariate control charts for effectively monitoring every component in the dispersion matrix of multivariate normal process are considered. Through the numerical results, we noticed that the multivariate control charts based on sample statistic $V_i$ by Hotelling or $W_i$ by Alt do not work effectively when the correlation coefficient components in dispersion matrix are increased. We propose a combined procedure monitoring every component of dispersion matrix, which operates simultaneously both control charts, a chart controlling variance components and a chart controlling correlation coefficients. Our numerical results show that the proposed combined procedure is efficient for detecting changes in both variances and correlation coefficients of dispersion matrix.

### A Study on The Optimal Design of Combined CUSUM Control Chart for Low Cost (저비용을 위한 Combined CUSUM 관리도의 최적설계 조사연구)

• Kim, Jong-Geol;Eom, Sang-Jun;Kim, Hyeong-Man;Choe, Seong-Won
• Proceedings of the Safety Management and Science Conference
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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.