• The Korean Journal of Applied Statistics
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• v.33 no.2
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• pp.161-170
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• 2020

The combined ${\bar{X}}-S^2$ chart is a traditional control chart for simultaneously detecting mean and variance. Control limits for the combined ${\bar{X}}-S^2$ chart are determined so that each chart has the same individual false alarm rate while maintaining the required false alarm rate for the combined chart. In this paper, we provide flexibility to allow the two charts to have different individual false alarm rates as well as evaluate the effect of flexibility. The individual false alarm rate of the ${\bar{X}}$ chart is taken to be γ times the individual false alarm rate of the S² chart. To evaluate the effect of selecting the value of γ, we use the out-of-control average run length and relative mean index as the performance measure for the combined ${\bar{X}}-S^2$ chart.

• Journal of Korean Society for Quality Management
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• v.31 no.2
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• pp.117-130
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• 2003

This paper investigates the economic design of synthetic control charts. The synthetic control chart has been proven to be statistically superior to the $\bar{X}$-control chart, but its economic characteristics have not been known. We develop an economic model of the synthetic control chart, based on Duncan's model. The synthetic chart has one more decision variable, the lower control limit for the conforming run length. In addition to this, the significance level and the power of the synthetic chart are more complicated than those of the $\bar{X}$-chart. These features make the optimization problem more difficult. We propose an optimization algorithm by adapting the congruent gradient algorithm. We compare the optimal cost of the synthetic chart with that of (equation omitted)-control chart, under the same input parameter set of Duncan’s. For all cases investigated, the synthetic chart shows superior to the $\bar{X}$-chart. The synthetic control chart is easy to implement, and it has better characteristics than the $\bar{X}$-chart in economical sense as well as in statistical sense, so it will be a good alternative to the traditional control charts.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.2
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• pp.114-122
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• 2004

In statistical process control applications, variable sample size (VSS) $\bar{X}$ chart is often used to detect the assignable cause quickly. However, it is usually assumed that only one assignable cause results in the out-of-control in the process. In this paper, we propose the algorithm to minimize the function of cost per unit time and compare the economic design and the statistical design by use of the value of cost per unit time. We consider double assignable causes to occur with compound in the process and adopt the Markov chain approach to investigate the statistical properties of VSS $\bar{X}$ chart. A procedure that can calculate the control chart's parameters is proposed by the economic design.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.101-106
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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 $\bar{X}$-chart, $\bar{X}$-chart, $\bar{X}$-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 $\bar{X}$-chart. which is the most widely used one in Kora, 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, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the $\bar{X}$-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 $\bar{X}$-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 oh 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, $\chi$$^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the proposed median chart and the $\bar{X}$ chart was also performed with these examples and the median chart turned out to be superior to the $\bar{X}$-chart.

• Journal of Korean Society for Quality Management
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• v.29 no.1
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• pp.1-10
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• 2001

We consider the problem of detecting special variations in multivariate $T^2$-control chart when two or more multivariate outliers are present. Since a multivariate outlier may reflect slippage in mean, variance, or correlation, it can distort the sample mean vector and sample covariance matrix. Damaged sample mean vector and sample covariance matrix have difficulty in examining special variations clearly, An alternative to detection outliers or special variations is to use robust estimators of mean vector and covariance matrix that are less sensitive to extreme observations than are the standard estimators $\bar{x}$ and $\textbf{S}$. We applied popular minimum volume ellipsoid(MVE) and minimum covariance determinant(MCD) method to estimate mean vector and covariance matrix and compared its results with standard $T^2$-control chart using simulated multivariate data with outliers. We found that the modified $T^2$-control chart based on the above robust methods were more effective in detecting special variations clearly than the standard $T^2$-control chart.

• 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).

• The Korean Journal of Nuclear Medicine Technology
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• v.16 no.1
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• pp.115-118
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• 2012

Purpose: The Levey-Jennings chart controlled measurement values that deviated from the tolerance value (mean ${\pm}2SD$ or ${\pm}3SD$). On the other hand, the upgraded Westgard Multi-Rules are actively recommended as a more efficient, specialized form of hospital certification in relation to Internal Quality Control. To apply Westgard Multi-Rules in quality control, credible quality control substance and target value are required. However, as physical examinations commonly use quality control substances provided within the test kit, there are many difficulties presented in the calculation of target value in relation to frequent changes in concentration value and insufficient credibility of quality control substance. This study attempts to improve the professionalism and credibility of quality control by applying Westgard Multi-Rules and calculating credible target value by using a commercialized quality control substance. Materials and Methods : This study used Immunoassay Plus Control Level 1, 2, 3 of Company B as the quality control substance of Total T3, which is the thyroid test implemented at the relevant hospital. Target value was established as the mean value of 295 cases collected for 1 month, excluding values that deviated from ${\pm}2SD$. The hospital quality control calculation program was used to enter target value. 12s, 22s, 13s, 2 of 32s, R4s, 41s, $10\bar{x}$, 7T of Westgard Multi-Rules were applied in the Total T3 experiment, which was conducted 194 times for 20 days in August. Based on the applied rules, this study classified data into random error and systemic error for analysis. Results: Quality control substances 1, 2, and 3 were each established as 84.2 ng/$dl$, 156.7 ng/$dl$, 242.4 ng/$dl$ for target values of Total T3, with the standard deviation established as 11.22 ng/$dl$, 14.52 ng/$dl$, 14.52 ng/$dl$ respectively. According to error type analysis achieved after applying Westgard Multi-Rules based on established target values, the following results were obtained for Random error, 12s was analyzed 48 times, 13s was analyzed 13 times, R4s was analyzed 6 times, for Systemic error, 22s was analyzed 10 times, 41s was analyzed 11 times, 2 of 32s was analyzed 17 times, $10\bar{x}$ was analyzed 10 times, and 7T was not applied. For uncontrollable Random error types, the entire experimental process was rechecked and greater emphasis was placed on re-testing. For controllable Systemic error types, this study searched the cause of error, recorded the relevant cause in the action form and reported the information to the Internal Quality Control committee if necessary. Conclusions : This study applied Westgard Multi-Rules by using commercialized substance as quality control substance and establishing target values. In result, precise analysis of Random error and Systemic error was achieved through the analysis of 12s, 22s, 13s, 2 of 32s, R4s, 41s, $10\bar{x}$, 7T rules. Furthermore, ideal quality control was achieved through analysis conducted on all data presented within the range of ${\pm}3SD$. In this regard, it can be said that the quality control method formed based on the systematic application of Westgard Multi-Rules is more effective than the Levey-Jennings chart and can maximize error detection.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.2
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• pp.245-252
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• 2011

VoIP transmits voices over IP-based networks and it is the abbreviation of Voice over Internet Protocol. Recently, VoIP provides various services in addition to voices. Since VoIP services' provision is extending, VoIP service quality management is becoming an important issue. Therefore, in this paper, we study VoIP service quality management. We examine VoIP technology, service types, and network architecture. Then, we investigate key quality indicators(KQIs)/key performance indicators(KPIs) in terms of customers, not network service providers. Toward this, we also study the concept of general service quality management as well as the concept of telecommunication related service quality management. Moreover, we apply $\bar{x}$ and R charts to show how to use statistical quality control techniques in real telecommunication companies with one KQI.