• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.65-77
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• 2020

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.1027-1034
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. When the joint distribution of the process variables is multivariate normal, multivariate Shewhart control charts using the function of the maximum likelihood estimator for monitoring the dispersion matrix are considered for the simultaneous monitoring of the dispersion matrix. The performances of the multivariate Shewhart control charts based on the proposed control statistic are evaluated in term of average run length (ARL). The performance is investigated in three cases, where the variances, covariances, and variances and covariances are changed respectively. The numerical results show that the performances of the proposed multivariate Shewhart control charts are not better than the control charts using the trace of the covariance matrix in the Jeong and Cho (2012) in terms of the ARLs.

• Proceedings of the Safety Management and Science Conference
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• 2000.11a
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• pp.217-234
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• 2000

Approximately normalized control charts, called Q charts, have been given Quesenberry(1991) for charting in process of short-run, job-shop, etc. We consider a Q chart with inspection error for job-shop floor under geometric distribution, which can be used for processes when a fraction nonconforming is very small. Our results would be applied for designing other control charts with inspection error.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.3
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• pp.289-296
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• 2001

This paper proposes multivariate control chart for autocorrelated data which are common in chemical and process industries and lead to increase in the number of false alarms when conventional control charts are applied. The effect of autocorrelated data is modeled as a vector autoregressive process, and canonical analysis is used to reduce the dimensionality of the data set and find the canonical variables that explain as much of the data variation as possible. Charting statistics are constructed based on the residual vectors from the canonical variables which are uncorrelated over time, and therefore the control charts for these statistics can attenuate the autocorrelation in the process data. The charting procedures are illustrated with a numerical example and Monte Carlo simulation is conducted to investigate the performances of the proposed control charts.

• 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.

• Journal of Korean Society for Quality Management
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• v.38 no.2
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• pp.190-201
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• 2010

This research proposes a method for designing VSI (Variable Sampling Interval) control charts with supplementary run rules. The basic idea is to apply various run rules and the VSI scheme to a control chart in order to increase the sensitivity. The sampling process of the VSI run rules chart is constructed by Markov chain approach. A procedure for designing the VSI run rules chart is proposed based on Lorenzen and Vance's model. Sensitivity study shows that the VSI run rules charts outperform the FSI (Fixed Sampling Interval) run rules charts for wide range of process mean shifts. A major advantage of the VSI run rules chart over other charts such as CUSUM, EWMA, and adaptive charts is it's simplicity in implementation. Some useful guidelines are proposed based on the sensitivity study.

• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.819-829
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• 2010

Properties of multivariate variable sampling interval (VSI) Shewhart and CUSUM charts for monitoring mean vector of related quality variables are investigated. To evaluate average time to signal (ATS) and average number of switches (ANSW) of the proposed charts, Markov chain approaches and simulations are applied. Performances of the proposed charts are also investigated both when the process is in-control and when it is out-of-control.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.6
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• pp.521-529
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• 2015

Statistical process control techniques have been greatly implemented in industries for improving product quality and saving production costs. As a primary tool among these techniques, control charts are widely used to detect the occurrence of assignable causes. In most works on the control charts it considered the problem of monitoring the mean and variance, and the quality characteristic of interest is normally distributed. In some situations monitoring of the minimum and maximum values is more important and the quality characteristic of interest is the Weibull distribution rather than a normal distribution. In this paper, we consider the statistical design of minimum and maximum control charts when the distribution of the quality characteristic of interest is Weibull. The proposed minimum and maximum control charts are applied to the wind data. The results of the application show that the proposed method is more effective than traditional methods.

• Journal of Integrative Natural Science
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• v.9 no.3
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• pp.215-222
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• 2016

When the linear correlation of the quality variables are considerably high, multivariate control charts may be a more effective way than univariate charts which operate quality variables and process parameters individually. Performances and efficiencies of the multivariate control charts under multivariate normal process has been considered. Some numerical results are presented under small scale of the shifts in the process to see the improvement of the efficiency of EWMA chart and CUSUM chart, which use past quality information, comparing to Shewart chart, which do not use quality information. We can know that the decision of the optimum value of the smoothing constant in EWMA structure or the reference value in CUSUM structure are very important whether we adopt combine-accumulate technique or accumulate-combine technique under the given condition of process.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.223-232
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• 1999

Multivariate quality control charts with combine-accumulate approach and accumulate-combine apprach for monitoring both means and variances under multivariate normal process are investigated. Numerical performances of the charts show that multivariate EWMA chart with accumulate-combine approach can be recommended for all kinds of shift in means and variances.