• Journal of 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.

• Journal of Korean Society for Quality Management
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• v.40 no.3
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• pp.327-336
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• 2012

Purpose: In this study, we research the hurdle rate method to suggest the robust control chart for a contaminated process less vulnerable to fault values than existing control charts. Methods: We produce the results of p, ARL values to compare the performance of two control charts, $\bar{x}-s$ that has been used typically and TM-TS that is suggested by this paper. We implement the simulation focusing on three cases, change of deviation, mean and both of them. Results: We draw a conclusion that the TM-TS control chart has better efficiency than $\bar{x}-s$ control chart over the three cases. Conclusion: We insist that applying TM-TS control chart for a polluted process is more effective than $\bar{x}-s$ control chart.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.4
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• pp.114-120
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• 2008

The control chart is widely used statistical process control(SPC) tool that searches for assignable cause of variation and detects any change of process. Generally, ${\bar{X}}-R$ control chart and ${\bar{X}}-S$ are most frequently used. When the production run is short and process parameter changes frequently, it is difficult to monitor the process using traditional control charts. In such a case, the coefficient of variation (CV) is very useful for monitoring the process variability. The CV control chart is an effective tool to control the mean and variability of process simultaneously. The CV control chart, however, is not sensitive at small shift in the magnitude of CV. In this paper, we propose an CV-EWMA (exponentially weighted moving average) control chart which is effective in detecting a small shift of CV. Since the CV-EWMA control chart scheme can be viewed as a weighted average of all past and current CV values, it is very sensitive to small change of mean and variability of the process. We suggest the values of design parameters and show the results of the performance study of CV-EWMA control chart by the use of average run length (ARL). When we compared the performance of CV-EWMA control chart with that of the CV control chart, we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.11a
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• pp.195-198
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• 2006

In this paper, we propose a 2dimension Control Chart. Suggested which Control chart augments Schwart Control chart which is 1-dimensional and Independent variable and dependent variable interrelationship by using control chart. Schwart control chart cannot use input variable and output variable together. In this paper, we try to analysis input variable and output variable dependent and effect. So called 2-dimensional control char.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.29 no.2
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• pp.97-103
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• 2006

Recently, the control chart is developed for monitoring processes with normal short production runs by the coefficient of variation(CV) characteristic for a normal distribution. This control chart does not work well in non-normal short production runs. And most of industrial processes are known to follow the non-normal distribution. Therefore, the control chart is required to be developed for monitoring the processes with non-normal short production runs by the CV characteristics for a non-normal distribution. In this paper, we suggest the control chart for monitoring the processes with a gamma short runs by the CV characteristics for a gamma distribution. This control chart is denoted by the gamma CV control chart. Futhermore evaluated the performance of the gamma CV control chart by average run length(ARL).

• Industrial Engineering and Management Systems
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• v.16 no.1
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• pp.109-117
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• 2017

In this article, a control chart based on multiple dependent (or deferred) state sampling for the gamma distributed quality characteristic is proposed using the gamma to normal transformation. The proposed control chart has two pairs of control limits, which can be determined by considering the in-control average run length (ARL). The shift in the scale parameter of a gamma distribution is considered and the out-of-control ARL is evaluated. The performance of the proposed chart has been shown for different levels of the parameters of the proposed control chart. It is also shown that the proposed chart is better than the Shewhart chart in terms of ARLs. A case study with a real data has been included for the practical usage of the proposed scheme.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.2
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• pp.50-56
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• 2002

In this study, we establish bootstrap control limits for EWMA chart by applying the bootstrap method, called resampling, which could not demand assumptions about pre-distribution when the process is skewed and/or the normality assumption is doubt. The results obtained in this study are summarized as follows : bootstrap EWMA control chart is developed for applying bootstrap method to EWMA chart, which is more sensitive to small shifts of process. With the purpose of eliminating a skewness of the resampling distribution, the bootstrap control limits are established by using a modified residual, and its performance is analyzed by ARL. It is shown that the bootstrap EWMA control chart developed in this study includes the properties of standard EWMA control chart that is sensitive to a small shift, and detects process in out of control more quickly than standard EWMA chart.

• 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.

• 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 of Industrial and Systems Engineering
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• v.28 no.4
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• pp.85-93
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• 2005

This paper is designed a VSI ${\overline{X}}$-CRL synthetic control chart in aspect of economy. We found the optimal sampling interval and various control limit factors under various cost parameters using cost function, proposed Lorenzen and Vance. Optimal design parameters include the sample size, control limit width, sampling interval, CRL/S chart control limit; L. Comparison and analysis of cost parameters are applied between synthetic VSI ${\overline{X}}$-CRL chart and FSI ${\overline{X}}$-CRL chart. The result of this paper shows that VSI ${\overline{X}}$-CRL chart brings cost-cutting effect of 3.04% control expense less than FSI control chart. It may not be difficult to establish the optimal economic control parameters to apply the practical cost parameters in the field.