• Industrial Engineering and Management Systems
• /
• v.4 no.2
• /
• pp.158-164
• /
• 2005

Kusukawa and Ohta presented the $CS_{CQ-r}$ chart to monitor the process defect $rate{\lambda}$ in high-yield processes that is derived from the count of defects. The $CS_{CQ-r}$ chart is more sensitive to $monitor{\lambda}$ than the CQ (Cumulative Quantity) chart proposed by Chan et al.. As a more superior chart in high-yield processes, we propose a Synthetic chart that is the integration of the CQ_-r chart and the $CS_{CQ-r}$chart. The quality characteristic of both charts is the number of units y required to observe r $({\geq}2)$ defects. It is assumed that this quantity is an Erlang random variable from the property that the quality characteristic of the CQ chart follows the exponential distribution. In use of the proposed Synthetic chart, the process is initially judged as either in-control or out-of-control by using the $CS_{CQ-r}$chart. If the process was not judged as in-control by the $CS_{CQ-r}$chart, the process is successively judged by using the $CQ_{-r}$chart to confirm the judgment of the $CS_{CQ-r}$chart. Through comparisons of ARL (Average Run Length), the proposed Synthetic chart is more superior to monitor the process defect rate in high-yield processes to the stand-alone $CS_{CQ-r}$ chart.

• Proceedings of the Safety Management and Science Conference
• /
• 2011.11a
• /
• pp.535-549
• /
• 2011

Control chart is most widely used in SPC(Statistical Process Control), Recently it is a critical issue that the standard control chart is not suitable to non-normal process with very small percent defective. Especially, this problem causes serious errors in the reliability procurement, such as semiconductor, high-precision machining and chemical process etc. Procuring process control technique for non-normal process with very small percent defective and perturbation is becoming urgent. Control chart technique in non-normal distribution become very important issue. In this paper, we investigate on research trend of control charts under non-normal distribution with very small percent defective and perturbation, and propose some variable-transformation methods applicable to CUSUM control charts in non-normal process.

• Proceedings of the Safety Management and Science Conference
• /
• 2013.04a
• /
• pp.547-556
• /
• 2013

Control chart is most widely used in SPC(Statistical Process Control), Recently it is a critical issue that the standard control chart is not suitable to non-normal process with very small percent defective. Especially, this problem causes serious errors in the reliability procurement, such as semiconductor, high-precision machining and chemical process etc. Procuring process control technique for non-normal process with very small percent defective and perturbation is becoming urgent. Control chart technique in non-normal distribution become very important issue. In this paper, we investigate on research trend of control charts under non-normal distribution.

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

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.10a
• /
• pp.31-39
• /
• 1993

This paper considers a procedure for the economic design of a cumulative score(CUSCORE) control chart and more sensitive than X-type control chart for small shift to control the mean of a process with a exponentially distributed quality characteristic. An expected loss - cost model as a function of design variables(sample size, sampling interval, scoring limit and decision limit) is derived. Direct search techniques are used to optimize the model subject to ARL in control. Numerical examples and sensitivity analysis of the model are presented. For selected values of situation parameters a comparison study with CUSUM charts is given. CUSCORE control charts compare favourably with CUSUM charts in cost for speedy production process. The proposed control chart can be directly applied for controlling the lifetime characteristics.

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

• Proceedings of the Safety Management and Science Conference
• /
• 2010.11a
• /
• pp.35-39
• /
• 2010

The research classifies three types of asymptotic tail distributions such as long(heavy, thick) tailed distribution, medium tailed distribution and short(light, thin) tailed distribution. The extreme value distributions(EVD) classified in this paper can be used in SPC(Statistical Process Control) control chart and reliability engineering.

• Proceedings of the Safety Management and Science Conference
• /
• 2000.11a
• /
• pp.217-234
• /
• 2000

Approximately normalized control charts, called Q charts, have been given Quesenberry(1991) for charting in process of short-run, job-shop, etc. We consider a Q chart with inspection error for job-shop floor under geometric distribution, which can be used for processes when a fraction nonconforming is very small. Our results would be applied for designing other control charts with inspection error.

• Journal of Korean Society for Quality Management
• /
• v.51 no.4
• /
• pp.663-675
• /
• 2023

Purpose: Skewness is an indicator used to measure the asymmetry of data distribution. In the past, product quality was judged only by mean and variance, but in modern management and manufacturing environments, various factors and volatility must be considered. Therefore, skewness helps accurately understand the shape of data distribution and identify outliers or problems, and skewness can be utilized from this new perspective. Therefore, we would like to propose a statistical quality control method using skewness. Methods: In order to generate data with the same mean and variance but different skewness, data was generated using normal distribution and gamma distribution. Using Minitab 18, we created 20 sets of 1,000 random data of normal distribution and gamma distribution. Using this data, it was proven that the process state can be sensitively identified by using skewness. Results: As a result of the analysis of this study, if the skewness is within ± 0.2, there is no difference in judgment from management based on the probability of errors that can be made in the management state as discussed in quality control. However, if the skewness exceeds ±0.2, the control chart considering only the standard deviation determines that it is in control, but it can be seen that the data is out of control. Conclusion: By using skewness in process management, the ability to evaluate data quality is improved and the ability to detect abnormal signals is excellent. By using this, process improvement and process non-sub-stitutability issues can be quickly identified and improved.

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