• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.127-133
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• 2001

In this article we establish multivariate cumulative sum (CUSUM) control charts based on residual vector with correlated observations. We first find the residual vector and its expectation and variance-covariance matrix and then evaluate the average run length (ARL) of the control charts.

• 한국데이터정보과학회:학술대회논문집
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• 2002.06a
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• pp.141-149
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• 2002

In this paper, we propose EWMA control charts using the life time data for the system with the constant failure rate, which were drawn from the fixed sampling interval without replacement (with replacement), and investigate the power of detection of EWMA by comparing ARL of EWMA control charts with one of Shewhart control charts.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.793-801
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• 2004

In this paper, we propose control charts for failure rate using the number of failures based on the fixed interval inspection with replacement. And we investigate the power of detection of the proposed control charts by the ARL.

• Journal of Korean Society for Quality Management
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• v.26 no.2
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• pp.51-60
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• 1998

Exponetially weighted moving average(EWMA) control chart to simultaneously monitor correlation coefficients of several correlated quality variables under multivariate normal process are proposed. Performances of the proposed control charts are measured in terms of average run length(ARL) by simulation. Numerical results show that smaller values of smoothing constant are more efficient in terms of ARL.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.265-273
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• 2005

In this paper, we proposed multivariate EWMA control charts for both combine-accumulate and accumulate-combine approaches to monitor dispersion matrix of multiple quality variables. Numerical performance of the proposed charts are evaluated in terms of average run length(ARL). The performances show that small smoothing constants with accumulate-combine approach is preferred for detecting small shifts of the production process.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.313-318
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• 2006

Many control charting methods for both i.i.d and autocorrelated data can be viewed as charting the output of a linear filter applied to the process data. We propose a generalization of this concept, in which the filter parameters are optimally selected to minimize the out-of-control ARL while constraining the in-control ARL to some desired value. A number of interesting characteristics of the optimal fitters are discussed.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1487-1498
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• 2016

In monitoring a process, in-control process parameters must be estimated from the Phase I data. When we design the control chart based on the estimated process parameters, the control limits are usually chosen to satisfy a specific in-control average run length (ARL). However, as the run length distribution is skewed when the process is either in-control or out-of-control, the median run length (MRL) can be used as alternative measure instead of the ARL. In this paper, we evaluate the performance of Shewhart $\bar{X}$ chart with estimated parameters in terms of the average of median run length (AMRL) and the standard deviation of MRL (SDMRL) metrics. In simualtion study, the grand sample mean is used as a process mean estimator, and several competing process standard deviation estimators are used to evaluate the in-control performance for various amounts of Phase I data.

• 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.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.519-530
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• 2015

The geometric chart has proven more effective than Shewhart p or np charts to monitor the proportion nonconforming in high-quality processes. Implementing a geometric chart commonly requires the assumption that the in-control proportion nonconforming is known or accurately estimated. However, accurate parameter estimation is very difficult and may require a larger sample size than that available in practice in high-quality process where the proportion of nonconforming items is very small. Thus, the error in the parameter estimation increases and may lead to deterioration in the performance of the control chart if a sample size is inadequate. We suggest adjusting the control limits in order to improve the performance when a sample size is insufficient to estimate the parameter. We propose a linear function for the adjustment constant, which is a function of the sample size, the number of nonconforming items in a sample, and the false alarm rate. We also compare the performance of the geometric charts without and with adjustment using the expected value of the average run length (ARL) and the standard deviation of the ARL (SDARL).

• Journal of the Korea Society of Computer and Information
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• v.25 no.12
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• pp.187-194
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• 2020

In today's process-oriented industries, such as semiconductor and petrochemical processes, autocorrelation exists between observed data. As a management method for the process where autocorrelation exists, a method of using the observations is to construct a batch so that the batch mean approaches to independence, or to apply the EWMA (Exponentially Weighted Moving Average) statistic of the observed value to the EWMA control chart. In this paper, we propose a method to determine the batch size of UBM (Unweighted Batch Mean), which is commonly used as a management method for observations, and a method to determine the optimal batch size based on ARL (Average Run Length) We propose a method to estimate the standard deviation of the process. We propose an improved control chart for processes in which autocorrelation exists.