• Journal of Korean Society of Industrial and Systems Engineering
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• v.26 no.3
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• pp.39-49
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• 2003

Statistical process cintrol is intended to assist operators of a stable system in monitoring whether a change has occurred in the process, and it uses several control charts as main tools. In design and use of control chart, it is rational that probability of false alarm is minimized in stable process and probability of detecting shifts is maximized in out-of-control. In this study, we establish bootstrap control limits for robust M-estimator chart by applying the bootstrap method, called resampling, which could not demand assumptions about pre-distribution when the process is skewed and/or the normality assumption is doubt. The results obtained in this study are summarized as follows : bootstrap M-estimator control chart is developed for applying bootstrap method to M-estimator chart, which is more robust to keep ARL when process contain contaminate quality characteristic.

• Journal of the Korean GEO-environmental Society
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• v.18 no.3
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• pp.31-38
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• 2017

The purpose of this study is to propose a chart that can easily estimate the seismic failure probability of small and medium sized earthfill dams with little geotechnical information. By considering the existing method and procedure for estimating the seismic failure probability of a dam, the zero seismic failure probability curve, on which the seismic probability is zero regardless of the geotechnical properties of the dam, was determined in the form of hyperbola in the dam height and freeboard ratio plane. It was confirmed that the dam height-freeboard ratio distribution pattern of the Korean small and medium sized dams was shaped like a hyperbola like the zero seismic failure probability curve. Therefore, a estimation chart was constructed in which a number of seismic failure probability contours are represented by a number of hyperbolas at regular intervals in the dam height-freeboard ratio plane. The proposed chart was applied to the calculation of the seismic failure probability of two small and midium sized dams with relatively well-managed geotechnical properties and the validity of the chart was confirmed by comparison with the results obtained by the existing procedures and methods. In the future, the proposed chart is expected to be useful in considering investment priorities for maintenance and reinforcement of small and medium sized dams in preparation for earthquakes.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.160-170
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• 1990

A new approximation method is proposed for the ARL of CUSUM chart which is based on the log probability ratio statistic. This method uses the condition of before-stopping time to derive the expectation of excess over boundaries. The proposed method is compared to some other approximation methods in normal and exponential cases.

• 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.

• 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 of Industrial and Systems Engineering
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• v.20 no.43
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• pp.205-209
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• 1997

One objective of the u control chart is to detect changes of mean nonconformities per unit occurred owing to various causes. This paper shows the detection probability using the Poisson distribution for various parameters, that is, subsample size n, mean nonconformities per unit $u_o$, and $u_o's$ change ratio k. We find that (1) as $u_o$ increases the smaller n is required for the same detection probability and the same change ratio; (2) as k gets away from 1 the smaller n is required; (3) the bigger n is required for the bigger detection probability. Several tables are given from our findings and are hoped to be used as guidelines for u chart users.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.198-207
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• 1998

The p chart approximate to the normal distribution has a difficulty to analyze the process condition precisely when the negative LCL is occurred. Furthermore, the probability of Type I error increases compared with using its original binomial distribution. For a long time the p chart has been used as approximated to the normal distribution because of its easy use. However, it becomes rapid and convenient to calculate the binomial distribution through the development of computer and software, so it is strongly suggested to use the binomial distribution determining control limits to reduce the probability of Type I error. In this study, I suggest that the control limits can be designed in use of binomial distribution and they can be utilized without special software by illustrating the certain work for establishing p-chart with the commercial one(EXCEL).

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.74-85
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• 1997

In this paper we calculate the subgroup size necessary for detecting the change of percent defective with several detection probabilities for orginal population fraction nonconforming p, changed population fraction nonconforming $p^*$, and the ratio k=$p^*$/p in the usage of p control charts. From our calculation we can know the error level of normal a, pp.oximation in detection probability calculation and recommend the subgroup size with lower error levels of normal a, pp.oximation, and then we show the reasonable subgroup size necessary for p, $p^*$, k, and the detection probability of the change of fraction nonconforming in a process. The information that we here show in tables will be useful when p control chart users decide the subgroup size in the p control chart users decide the subgroup size in the p control chart.

• Journal of Integrative Natural Science
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• v.13 no.4
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• pp.152-157
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• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.3
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• pp.22-29
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• 2010

Six sigma has been the most influential management innovation tool in order to achieve the customer's satisfaction and keep the competition in the age of limitless competition. The success in six sigma is to find the correct CTQ (Critical to Quality). QFD (Quality function deployment) is the efficient too ever created to tie product and service design decisions directly to customer wants and needs. One of the mistakes in QFD is to analyze using an inconsistent HOQ (House of quality) chart. An inconsistent HOQ chart is one in which the information from the correlation matrix is inconsistent with that from the relationship matrix. This study presents the consistency check and inconsistency check in case of failing the consistency check. Also we propose the procedures using the Limiting Probability in correlation matrix and the Median Rank in relationship matrix in order to be consistent in HOQ chart.