• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.21-29
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• 2002

Several different control statistics to simultaneously monitor dispersion matrix of several quality variables are presented since different control statistics can be used to describe variability. Multivariare cumulative sum (CUSUM) control charts are proposed and the performances of the proposed CUSUM charts are evaluated in terms of average run length (ARL). Multivariate Shewhart charts are also proposed to compare the properties of the proposed CUSUM charts. The numerical results show that multivariate CUSUM charts are more efficient than multivariate Shewhart charts for small or moderate shifts. And we also found that small reference value of the CUSUM chart is more efficient for small shift.

• 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.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.203-215
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• 2022

In this paper, we consider the control charts applicable to monitoring the change of the population mean for sequentially observed individual data. The most representative control charts are Shewhart's individual control chart, the exponential weighted moving average (EWMA) control chart, and their combined control chart. We compare their performance based on a simulation study, and also, through real data analysis, we present how to apply control charts in practical application and investigate the problems of each control chart.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.67
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• pp.27-36
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• 2001

A standard assumption when using a control chart to monitor a process is that the observations from the process output are statistically independent. However, for many processes the observations are autocorrelated and this autocorrelation can have a significant effect on the performance of the control chart. In this paper, we consider combined control chart of monitoring the mean of a process in which the observations can be modeled as a first-order autoregressive process. The Shewhart control chart of residuals-EWMA control chart of the observations is considered and the method of combination is recommended. The performance of the proposed control chart is compared with the performance of other control charts using a simulation.

• Journal of the Korean Statistical Society
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• v.14 no.2
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• pp.76-86
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• 1985

Shewhart X-chart, which is most widely used in practice, is shown to be inappropriate for the cases where the process distribution is one-sided asymmetrical, and thus some nonparametric Shewhart type charts are developed instead. These schemes may be applied usefully when there is not enough information in determining the process distribution. The average run lengths are obtained to compare the efficiency of control charts for various shifts of the location parameter and for some typical one-sided asymmetrical distributions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.56
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• pp.83-92
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• 2000

This paper presents a study on control schemes for gradual increases (drifts) in a process variance. A new control chart, the Drifting Variance Control Chart (DVCC) is designed using Likelihood Ratio Test (LRT), and the ARL performance of the chart is evaluated for different subgroup sizes. The performance of this chart is then compared to some of the popular control schemes for the process dispersion, like the Shewhart S$^2$chart, the CUSUM chart and the EWMA chart. Results are presented and discussed. Also included is a sensitivity analysis that investigates how the DVCC performs when applied to a stepped change in process variance.

• The Korean Journal of Applied Statistics
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• v.35 no.6
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• pp.725-737
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• 2022

In the standard assumption of statistical process monitoring (SPM) under consideration, the in-control region of the control parameter of quality characteristic consists of a single point. However, if small deviations from the ideal situation may not be of practical importance, the parametric space can consist of three regions: In-control, indifference, and out-of-control. In this paper, we propose two exponentially weighted moving average (EWMA) charting procedures applicable to the situation with three parameter regions, and compare the efficiency of the proposed procedures with the Shewhart chart and the cumulative sum (CUSUM) chart.

• Journal of Korean Society for Quality Management
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• v.12 no.2
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• pp.15-24
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• 1984

Since W.A. Shewhart (1931) developed the quality control method using the control chart, many theoretical and empirical works about such an analytical method have been done. However there are two major methods relating to the control chart analysis; the conventional 3 sigma control method and the warning limit method which has been suggested as a modification of the former. The conventional 3 sigma method requires to take a remedial action only when a quality characteristic is beyond the control limit (3 sigma). However, once a quality characteristic is over the control limit, searching and repairing an assignable cause requires time consuming job and high costs. Therefore if we set the warning limit between the central line and the control limit, we will be able to take remedial measures before too late. In spite of its advantage, much attention has not been paid to use the control chart with warning limit in Korean industries. The main object of this study is to examine improvement of quality and productivity when the control chart with warning limit is used.

• Journal of Korean Society for Quality Management
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• v.14 no.2
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• pp.2-8
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• 1986

This thesis is concerned with the design of control chart based on the sample median which is easy to use in practical situations and to analyze the properties for non-normally distributed Weibull process. In this cases are use to the quality characteristics of the process are not normally distributed but skewed due to the intermitted production, small lot size and sample size is small one n=3 or n=5, etc. And when it relates unsymmetrically distributed process, model designed median control chart is more effective than Shewhart $\bar{x}$-chart which assumed on normal distribution, when we exactly should be known Weibull distribution or estimated. The median control chart in this thesis is more robustness compared with other conventionally developed control chart.

• Journal of the Korean Professional Engineers Association
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• v.20 no.3
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• pp.15-25
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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 X-chart, X-chart, 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 Shewhart 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 tile more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the X-chart, the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the X-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based on a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $X^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the propose4 median chart and the X chart was also performed with these examples and the median chart turned out to be superior to the X-chart.