• Industrial Engineering and Management Systems
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• v.4 no.2
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• pp.158-164
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• 2005

Kusukawa and Ohta presented the $CS_{CQ-r}$ chart to monitor the process defect $rate{\lambda}$ in high-yield processes that is derived from the count of defects. The $CS_{CQ-r}$ chart is more sensitive to $monitor{\lambda}$ than the CQ (Cumulative Quantity) chart proposed by Chan et al.. As a more superior chart in high-yield processes, we propose a Synthetic chart that is the integration of the CQ_-r chart and the $CS_{CQ-r}$chart. The quality characteristic of both charts is the number of units y required to observe r $({\geq}2)$ defects. It is assumed that this quantity is an Erlang random variable from the property that the quality characteristic of the CQ chart follows the exponential distribution. In use of the proposed Synthetic chart, the process is initially judged as either in-control or out-of-control by using the $CS_{CQ-r}$chart. If the process was not judged as in-control by the $CS_{CQ-r}$chart, the process is successively judged by using the $CQ_{-r}$chart to confirm the judgment of the $CS_{CQ-r}$chart. Through comparisons of ARL (Average Run Length), the proposed Synthetic chart is more superior to monitor the process defect rate in high-yield processes to the stand-alone $CS_{CQ-r}$ chart.

• Industrial Engineering and Management Systems
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• v.7 no.2
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• pp.101-112
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• 2008

As charts to monitor the process fraction defectives, P, in the high-yield processes, Mishima et al. (2002) discussed a synthetic chart, the Synthetic CS chart, which integrates the CS (Confirmation Sample)$_{CCC(\text{Cumulative Count of Conforming})-r}$ chart and the CCC-r chart. The Synthetic CS chart is designed to monitor quality characteristics in real-time. Recently, Kotani et al. (2005) presented the EWMA (Exponentially Weighted Moving-Average)$_{CCC-r}$ chart, which considers combining the quality characteristics monitored in the past with one monitored in real-time. In this paper, we present an alternative chart that is more superior to the $EWMA_{CCC-r}$ chart. It is an integration of the $EWMA_{CCC-r}$ chart and the CCC-r chart. In using the proposed chart, the quality characteristic is initially judged as either the in-control state or the out-of-control state, using the lower and upper control limits of the $EWMA_{CCC-r}$ chart. If the process is not judged as the in-control state by the $EWMA_{CCC-r}$ chart, the process is successively judged, using the $EWMA_{CCC-r}$ chart. We compare the ANOS (Average Number of Observations to Signal) of the proposed chart with those of the $EWMA_{CCC-r}$ chart and the Synthetic CS chart. From the numerical experiments, with the small size of inspection items, the proposed chart is the most sensitive to detect especially the small shifts in P among other charts.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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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.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.7 no.2
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• pp.151-156
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• 2012

In this paper, we gave 3 suitable modified control chart at the same time shows. First control chart is plot analysis control chart by sampling data, Second control chart is including Upper Spec and Lower Spec in first control chart. Third control chart is including target value and new calculated upper/lower control line by using known average and standard deviation of long term data. If 3 control charts are seen at the same time, there is advantage that can see problem of process at a look. We hope this method proposed in this treatise give many help in spot.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.2
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• pp.1-8
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• 2011

This paper proposes a variable sampling interval multivariate $T^2$ control chart with sampling at fixed times, where samples are taken at specified equally spaced fixed time points and additional samples are allowed between these fixed times when indicated by the preceding $T^2$ statistics. At fixed sampling points, the $T^2$ statistics are composed of all quality characteristics and a part of quality characteristics are selected to obtain $T^2$ statistics at additional sampling points. A Markov chain approach is used to evaluate the performance of the proposed chart. Numerical studies for the performance of the proposed chart show that the proposed chart reduces the observations obtained from a process and detects the assignable cause of a process with low correlated quality characteristics quickly.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.1
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• pp.15-20
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• 2015

Control charts are generally used for process control, but the role of traditional control charts have been limited in case of a non-contaminated process. Traditional ${\bar{x}}$-s control chart has not been activated well for such a problem because of trying to control processes as center line and control limits changed by the contaminated value. This paper suggests modified ${\bar{x}}$-s control chart based on robust estimation. In this paper, we consider the trimmed mean of the sample means and the trimmed mean of the sample standard deviations. By comparing with ARL value, the responding results are decided. The comparison resultant results of traditional control chart and modified control chart are contrasted.

• Korean Management Science Review
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• v.31 no.3
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• pp.27-39
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• 2014

We derive a generalized statistic form of Q control chart, which is especially suitable for short run productions and start-up processes, for the detection of process mean shifts. The generalization means that the derived control chart statistic concurrently uses within lot variability and between lot variability to explain the process variability. The latter variability source is noticeably prevalent in lot type production processes including semiconductor wafer fabrications. We first obtain the generalized Q control chart statistic when both the process mean and process variance are unknown, which represents the case of implementing statistical process control charting for short run productions and start-up processes. Also, we provide the corresponding generalized Q control chart statistics for the rest of three cases of previous Q control chart statistics : (1) both the process mean and process variance are known (2) only the process mean is unknown and (3) only the process variance is unknown.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.233-241
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• 1999

Control chart is a very extensively used tool in testing whether a process is in a state of statistical control or not. In this paper, we propose a robust EWMA(exponentially weighted moving averages) control chart for variables, which is based on the Huber's M-estimator. The Huber's M-estimator is a well-known robust estimator in sense of distributional robustness. In the proposed chart, the estimation of the process deviation is modified to have a s table level and high power. To compare the performances of the proposed control chart with other charts, some Monte Carlo simulations we performed. The simulation results show that the robust EWMA control chart has good performance.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.4
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• pp.53-58
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• 2002

This paper presents a adjustment synthetic control chart that is an integration of the Shewhart X chart and the conforming run length(CRL) chart. The application of the adjustment synthetic control chart my therefore substantially enhance the effectiveness process control for manufacturing. In the synthetic control chart, denotes the average number of the X sample required to detect a process shift. The synthetic control chart outperforms the EWM chart and the X chart when σ is greater than 0.75σ. And the X-CRL charts suggested above evaluate using the conditional probability.

• Industrial Engineering and Management Systems
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• v.12 no.2
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• pp.112-117
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• 2013

The $\overline{x}$ control chart for the process mean and either the R or s control chart for the process dispersion have been used together to monitor the manufacturing processes. However, it has been pointed out that this procedure is flawed by a fault that makes it difficult to capture the behavior of process condition visually by considering the relationship between the shift in the process mean and the change in the process dispersion because the respective characteristics are monitored by an individual control chart in parallel. Then, the ($\overline{x}$, s) control chart has been proposed to enable the process managers to monitor the changes in the process mean, process dispersion, or both. On the one hand, identifying which process parameters are responsible for out-of-control condition of process is one of the important issues in the process management. It is especially important in the ($\overline{x}$, s) control chart where some parameters are monitored at a single plane. The previous literature has proposed the multiple decision method based on the statistical hypothesis tests to identify the parameters responsible for out-of-control condition. In this paper, we propose how to identify parameters responsible for out-of-control condition using the information criterion. Then, the effectiveness of proposed method is shown through some numerical experiments.