• The Korean Journal of Applied Statistics
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• v.31 no.4
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• pp.485-495
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• 2018

The CCC-r chart is more effective than traditional attribute control charts for monitoring high-quality processes. In-control process parameters are typically unknown and should be estimated when implementing a CCC-r chart. Phase II control chart performance can deteriorate due to the effect of the estimation error. In this paper, we used the standard deviation of average run length (ARL) as well as the average of ARL to quantify the between-practitioner variability in the CCC-r chart performance. The results indicate that the CCC-r chart requires larger Phase I data than previously recommended in the literature in order to have consistent chart in-control performance among practitioners.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.82-95
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• 1994

When independent individual measurements are taken both $S/c_4$ and $\bar{R}/d_2$ are unbiased estimators of the process standard deviation. However, with dependent data $\bar{R}/d_2$ is not an unbiased estimator of the process standard deviation. On the other hand $S/c_4$ is an asymptotic unbiased estimator. If there exists correlation in the data, positive(negative) correlation tends to increase(decrease) the ARL. The effect of using $\bar{R}/d_2$ is greater than $S/c_4$ if the assumption of independence is invalid. Supplementary runs rule shortens the ARL of X control charts dramatically in the presence of correlation in the data.

• 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.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.645-657
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• 1998

During the start-up of a process or in a job-shop environment conventional use of control charts may lead to erroneous results due to the limited number of subgroups used for the construction of control limits. This article considers the effect of using estimated control limits based on a limited number of subgroups. Especially we investigate the performance of $\overline{X}$ and R control charts when the data are independent, and X control chart when the data are serially correlated in terms of average run length(ARL) and standard deviation run length(SDRL) using simulation. It is found that the ARL and SDRL get larger as the number of subgroups used for the construction of the chart becomes smaller.

• 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.

• Journal of Korea Society of Industrial Information Systems
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• v.5 no.4
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• pp.55-59
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• 2000

In start up process control, it may be necessary to use appropriate scheme in monitoring processes with individual observations. In these situation individual observations are periodically drawn from the process. In this paper, using modifying statistics with individual measurement, we suggest a simple technique which operating control chart for monitoring the process. And compare individual observation control procedures that are X, an exponentially weighted moving(EWM), adjusted EWM and adjusted MCEWM charts. And estimate the ARL to detection of shifts in the process mean and standard deviation using simulation.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.108-125
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• 1998

The EWMA(Exponentially Weighted Moving Average) has recently received a great deal of attention in the quality control literature as a process monitoring tool on the shop floor of manufacturing industires, since it is easy to plot, to interpret, and its control limits are easy to obtain. Most a, pp.ications of the EWMA for process monitoring have concentrated on the problem of detecting shifts of a process mean and a process standard deviation with ARL(Average Run Length) properties. But there may be the necessity of controlling linearity on product quality such as the correlation coefficient to the process operator. Control managers may want to protect the increase of a process correlation coefficient value, such as 0, between two variables of interest. However, there are few studies concerned on this part. Therefore, we propose EWMA models for a process correlation coefficient using two transformed statistics, T-statistic and (Fisher's) Z-statistic. We also present some results of simulation by SAS/IML and compare two models.

• Journal of Korean Society for Quality Management
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• v.40 no.4
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• pp.467-480
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• 2012

Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.2
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• pp.37-45
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• 2016

Control chart is representative tools of statistical process control (SPC). It is a graph that plotting the characteristic values from the process. It has two steps (or Phase). First step is a procedure for finding a process parameters. It is called Phase I. This step is to find the process parameters by using data obtained from in-controlled process. It is a step that the standard value was not determined. Another step is monitoring process by already known process parameters from Phase I. It is called Phase II. These control chart is the process quality characteristic value for management, which is plotted dot whether the existence within the control limit or not. But, this is not given information about the economic loss that occurs when a product characteristic value does not match the target value. In order to meet the customer needs, company not only consider stability of the process variation but also produce the product that is meet the target value. Taguchi's quadratic loss function is include information about economic loss that occurred by the mismatch the target value. However, Taguchi's quadratic loss function is very simple quadratic curve. It is difficult to realistically reflect the increased amount of loss that due to a deviation from the target value. Also, it can be well explained by only on condition that the normal process. Spiring proposed an alternative loss function that called reflected normal loss function (RNLF). In this paper, we design a new control chart for overcome these disadvantage by using the Spiring's RNLF. And we demonstrate effectiveness of new control chart by comparing its average run length (ARL) with ${\bar{x}}-R$ control chart and expected loss control chart (ELCC).