• 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.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.685-696
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• 2012

These days the interest of quality leads to the necessity of control charts for monitoring the process in various fields of practical applications. The $\overline{X}$ chart is one of the most widely used tools for quality control that also performs well under the normality of quality characteristics. However, quality characteristics tend to have nonnormal properties in real applications. Numerous recent studies have tried to find and explore the performance of $\overline{X}$ chart due to non-normality; however previous studies numerically examined the effects of non-normality and did not provide any theoretical justification. Moreover, numerical studies are restricted to specific type of distributions such as Burr or gamma distribution that are known to be flexible but can hardly replace other general distributions. In this paper, we approximate the false alarm rate(FAR) of the $\overline{X}$ chart using the Edgeworth expansion up to 1/n-order with the fourth cumulant. This allows us to examine the theoretical effects of nonnormality, as measured by the skewness and kurtosis, on $\overline{X}$ chart. In addition, we investigate the effect of skewness and kurtosis on $\overline{X}$ chart in numerical studies. We use a skewed-normal distribution with a skew parameter to comprehensively investigate the effect of skewness.

• Journal of Korean Society for Quality Management
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• v.34 no.4
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• pp.125-132
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• 2006

An adjusted control limit of the $\overline{X}$ chart is proposed for monitoring the continually improving processes. The continual improvement of the process implies the decrease of the process variance, which is represented by a logistic curve. The process standard deviation is estimated by the exponentially weighted moving average of the sample standard deviations from the past to the current times. The control limits are adjusted by the estimated standard deviation at every sampling time. The performance of the adjusted control limit is compared with that of the standard control limits for various cases of the decreasing speed and size of the variance. The results show that the $\overline{X}$ chart with the adjusted control limits provides better performances for monitoring the small and moderate shifts in continually improving processes.

• Journal of Korean Society for Quality Management
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• v.29 no.3
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• pp.79-85
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• 2001

Estimation of the process deviation is an important problem in statistical process control, especially in the control chart, process capability analysis or measurement system analysis. In this paper we suggest the use of the Gini's mean difference for the estimation of the process deviation when we design the control limits in construction of the control charts. The efficiency of the Gini's mean difference was well explained in Nam, Lee and Jung(2000). In this paper we propose an $\overline{X}$ control chart which use the control limits based on the Gini's mean difference. In various classes of distributions, the proposed control chart shows food performance.

• 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.

• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.10-19
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• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the $\overline{X}$-chart, X-chart, $\widetilde{X}$-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In the Shewhart $\overline{X}$-chart, which is the most widely used one in Korea, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for the more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, and Truncated-normal distributions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.2
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• pp.56-62
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• 2013

Control chart is representative tool of Statistical Process Control (SPC). But, it is not given information about the economic loss that occurs when a product is produced characteristic value does not match the target value of the process. In order to manage the process, we should consider not only stability of the variation also produce products with a high degree of matching the target value that is most ideal quality characteristics. There is a need for process control in consideration of economic loss. In this paper, we design a new control chart using the quadratic loss function of Taguchi. And we demonstrate effectiveness of new control chart by compare its ARL with ${\overline{x}}-R$ control chart.

• 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.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.39-56
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• 2000

${\overline{X}}$ control chart has proven to be an effective tool to improve the product quality. Shewhart charts assume that the observations are independent and normally distributed. Under the presence of positive autocorrelation and severe skewness, the control limits are not accurate because assumptions are violated- Autocorrelation in process measurements results in frequent false alarms when standard control chats are applied in process monitoring. In this paper, Threshold Bootstrap and Moving Block Bootstrap are used for constructing a confidence interval of correlated observations. Monte Carlo simulation studies are conducted to compare the performance of the bootstrap methods and that of standard method for constructing control charts under several conditions.