• 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 the Ergonomics Society of Korea
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• v.15 no.2
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• pp.1-13
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• 1996

The purpose of this study is to suggest a brassiere sizing chart for elderly women. 2 control dimensions(under bust girth and cup size) were chosen as 2 axes of brassiere size chart. A loss function was used to determined intervals of under bust girth and cup size of size chart, because the loss function introduces the concept of frequency to size chart for better customer's satisfaction. From the dual distribution table whose intervals had been determined by a loss function. The 15 sizs, which had more than 2% of appearance were suggested for brassiere size chart. The suggested brassiere sizes covered 87.6% of all subjects. Considering that KS brassiere size chart consisting of 32 sizes covers 88.5%, the suggested brassiere size chart would be considered quite feasible. Also it is suggested supply reference measurement chart relevant to brassiere manufacturing for 10 most frequent sizes.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.129-142
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• 2024

In various industries, especially manufacturing and chemical industries, it is often observed that the distribution of a specific process, initially having followed a normal distribution, becomes skewed as a result of unexpected causes. That is, a process deviates from a normal distribution and becomes a skewed distribution. The skew-normal (SN) distribution is one of the most employed models to characterize such processes. The shape of this distribution is determined by the asymmetry parameter. When this parameter is set to zero, the distribution is equal to the normal distribution. Moreover, when there is a shift in the asymmetry parameter, the mean and variance of a SN distribution shift accordingly. In this paper, we propose procedures for monitoring the asymmetry parameter, based on the statistic derived from the noncentral t-distribution. After applying the statistic to Shewhart and the exponentially weighted moving average (EWMA) charts, we evaluate the performance of the proposed procedures and compare it with previously studied procedures based on other skewness statistics.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.52
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• pp.347-354
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• 1999

Statistical Process Control(SPC) which uses control charts is widely used to inspect and improve manufacturing process as a effective method. A parametric method is the most common in statistical process control. Shewhart chart was made under the assumption that measurements are independent and normal distribution. In practice, this assumption is often excluded, for example, in case of (equation omitted) chart, when the subgroup sample is small or correlation, it happens that measured data have bias or rejection of the normality test. A bootstrap method can be used in such a situation, which is calculated by resampling procedure without pre-distribution assumption. In this study, applying bootstrap percentile method to (equation omitted) chart, it is compared and evaluated standard process control limit with bootstrap percentile control limit. Also, under the normal and non-normal distributions, where parameter is 0.5, using computer simulation, it is compared standard parametric with bootstrap method which is used to decide process control limits in process quality.

• Industrial Engineering and Management Systems
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• v.4 no.1
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• pp.75-81
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• 2005

Borror et al. discussed the EWMA(Exponentially Weighted Moving Average) chart to monitor the count of defects which follows the Poisson distribution, referred to the $EWMA_c$ chart, as an alternative Shewhart c chart. In the $EWMA_c$ chart, the Markov chain approach is used to calculate the ARL (Average Run Length). On the other hand, in order to monitor the process fraction defectives P in high-yield processes, Xie et al. presented the CCC(Cumulative Count of Conforming)-r chart of which quality characteristic is the cumulative count of conforming item inspected until observing $r({\geq}2)$ nonconforming items. Furthermore, Ohta and Kusukawa presented the $CS(Confirmation Sample)_{CCC-r}$ chart as an alternative of the CCC-r chart. As a more superior chart in high-yield processes, in this paper we present an $EWMA_{CCC-r}$ chart to detect more sensitively small or moderate shifts in P than the $CS_{CCC-r}$ chart. The proposed $EWMA_{CCC-r}$ chart can be constructed by applying the designing method of the $EWMA_C$ chart to the CCC-r chart. ANOS(Average Number of Observations to Signal) of the proposed chart is compared with that of the $CS_{CCC-r}$ chart through computer simulation. It is demonstrated from numerical examples that the performance of proposed chart is more superior to the $CS_{CCC-r}$ chart.

• Proceedings of the ESK Conference
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• 1995.10a
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• pp.268-279
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• 1995

The purpose of this study is to suggest a brassiere sizing chart for elderly women. It is found that there is no direct linear relationship between cup size and under bust girth from the analsis of breast measurements. These 2 factors(under bust girth and cup size) were chosen as 2 axes of brassiere size chart. A loss function was used to determined intervals of bust girth and cup size of size chart, because the loss function introduces the concept of frequency to size chart for better customer's satisfaction. From the dual distribution table whose intervals had been determinde by a loss function. The 15 sizes, which had more than 2% of appearance were suggested for brassiere size chart. The suggested brassierc sizes covened 87.6% of all subjects. Considering that KS brassiere size thart consisting of 32 sizes covers 88.5%, the suggested brassiere size chart would be considered quite feasible. Also is suggested supply reference measurement chart relevant to brassiere manufacturing for 10 most frequent sizes.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.4
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• pp.1-7
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• 2002

Statistical process control is used widely as an effective tool to solve the quality problems in practice fields. All the control charts used in statistical process control are parametric methods, suppose that the process distributes normal and observations are independent. But these assumptions, practically, are often violated if the test of normality of the observations is rejected and/or the serial correlation is existed within observed data. Thus, in this study, to screening process, the Combined Shewhart - CUSUM quality control chart is described and evaluated that used bootstrap method. In this scheme the CUSUM chart will quickly detect small shifts form the goal while the addition of Shewhart limits increases the speed of detecting large shifts. Therefor, the CSC control chart is detected both small and large shifts in process, and the simulation results for its performance are exhibited. The bootstrap CSC control chart proposed in this paper is superior to the standard method for both normal and skewed distribution, and brings in terms of ARL to the same result.

• 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 Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.116-122
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• 2016

Recently, the production cycle in manufacturing process has been getting shorter and different types of product have been produced in the same process line. In this case, the control chart using coefficient of variation would be applicable to the process. The theory that random variables are located in the three times distance of the deviation from mean value is applicable to the control chart that monitor the process in the manufacturing line, when the data of process are changed by the type of normal distribution. It is possible to apply to the control chart of coefficient of variation too. ${\bar{x}}$, s estimates that taken in the coefficient of variation have just used all of the data, but the upper control limit, center line and lower control limit have been settled by the effect of abnormal values, so this control chart could be in trouble of detection ability of the assignable value. The purpose of this study was to present the robust control chart than coefficient of variation control chart in the normal process. To perform this research, the location parameter, ${\bar{x_{\alpha}}}$, $s_{\alpha}$ were used. The robust control chart was named Tim-CV control chart. The result of simulation were summarized as follows; First, P values, the probability to get away from control limit, in Trim-CV control chart were larger than CV control chart in the normal process. Second, ARL values, average run length, in Trim-CV control chart were smaller than CV control chart in the normal process. Particularly, the difference of performance of two control charts was so sure when the change of the process was getting to bigger. Therefore, the Trim-CV control chart proposed in this paper would be more efficient tool than CV control chart in small quantity batch production.

• Journal of the Korean Home Economics Association
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• v.33 no.6
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• pp.199-211
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• 1995

The purpose of this study was to provide a brassiere size chart for making the well-fitted brassiere. The subjects are 2811 women whose range of age is 12 to 59. These woman were classified into 5 age groups by seniority ; age group 1(12~19), age group 2(20~29), age group 3(30~39), age group 4(40~49), age group 5(50~59). statistical differences of measurements were analyzed among 5 age groups through ANOVA. Correlation between measurements were analyzed by correlation analysis. In addition, new brassiere size chart and production rate tables were proposed in this study. The results of the study were as follows. 1) Most of the body measurements were significantly different among 5 age groups. The height was decreasing by getting older while weight was increasing significantly. The 3 girth measurements(top bust, bust, under bust girth) in breast, bust width, bust depth were apt to increase definitely. The 3 girth measurements had high Correlation coefficients among 3 girth mesurements. Therefore, it is valid to pick out cup size and under bust girth for representative items of size chart. 2) Under bust girth and cup size were chosen as 2 axes of brassiere size chart. From the dual distribution table whose intervals had been determined by KS size chart, 17 sizes, which had more than 2% of appearance, were suggested for brassiere size chart. Through these new size charts, the suggested brassiere sizes covered 82.5% of all subjects. The suggested brassiere size chart would be more helpful than KS size chart in making the well-fitted brassiere.