• The Korean Journal of Applied Statistics
• /
• v.37 no.2
• /
• pp.177-189
• /
• 2024

The run length is defined as the number of samples or subgroups taken before the control chart statistic exceeds the control limits. Because the distribution of run length is typically asymmetric and has a large variability, it may not be appropriate to use ARL (average run length) alone to design control charts and evaluate performance. In this paper, we introduce the concept of percentile (PL)-based design of control charts, and propose the procedure for PL-based design of EWMA (exponentially weighted moving average) charts. For the PL-based design of EWMA, we present a fitted function for the control chart coefficient, given specific percentile parameters. Additionally, we perform simulations to compare the proposed design with the ARL-based design. The simulation results show that the proposed design yields improvements in monitoring in-control processes while maintaining the ability to detect out-of-control performance.

• Communications for Statistical Applications and Methods
• /
• v.27 no.1
• /
• pp.65-77
• /
• 2020

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

• International Journal of Quality Innovation
• /
• v.2 no.1
• /
• pp.30-49
• /
• 2001

This paper considers a recent environment in the manufacturing process in which data in large amounts can be obtained on-line in real-time. Under this environment an on-line real-time Statistical Process Control (SPC) scheme equipped with detection of a process change, change-point estimation, and recognition of the change pattern is proposed. The proposed SPC scheme is composed of a Cusum chart, filtering methods and Akaike Information Criterion (AIC). We examine the performance of this scheme by Monte Carlo simulation and show its usefulness.

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

• International Journal of Quality Innovation
• /
• v.2 no.2
• /
• pp.127-135
• /
• 2001

Personnel engaged in the medical field have implemented continual improvement by team activities in an effort to construct a system that reduces the risks involved in medical care. Knowledge in total quality management (TQM), especially statistical quality control (SQC) developed for industry, seems to be applicable to medical care. This paper describes the application of SQC to continual improvement in medical care.

• Journal of the Korean Statistical Society
• /
• v.29 no.3
• /
• pp.319-336
• /
• 2000

A mixed model with a white noise process and an IMA(0,1,1) process is considered as a process model. It is assumed that the process is a white noise in the absence of a special cause and the process changes to an IMA(0,1,1) due to a special cause. One useful scheme in measuring the process level is to use the variable measurement interval (VMI) between measurement times according to the value of the previous chart statistic. The advantage of the VMI scheme is to measure the process level infrequently when in control to save the measurement cost and to measure frequently when out of control to save the off-target cost. This paper considers the VMI scheme in order to detect changes in the process model from a white noise to an IMA(0,1,1). The VMI scheme is shown to be effective compared to the standard fixed measurement interval (FMI) scheme in both statistical and economic contexts.

• Journal of Korean Society for Quality Management
• /
• v.40 no.4
• /
• pp.467-480
• /
• 2012

Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

• Korean Management Science Review
• /
• v.12 no.1
• /
• pp.111-124
• /
• 1995

With the increasing interest of reducing process variation, statistical process control has served the pivotal tool in most industrial quality programs. In this study, system analyses have been performed associated with a cost incorporated version of a process control, a quadratic loss-based X over bar control chart model. Specifically, two issues, the capital/research investments for improvement of a system and the precision of a parameter estimation, have been addressed and discussed. Through the analysis of experimental results, we show that process variability is seen to be one of the most important sources of loss and quality improvement efforts should be directed to reduce this variability. We further derive the results that, even if the optimal designs may be sensitive, the model appears to be robust with regard to misspecification of parameters. The approach and discussion taken in this study provide a meaningful guide for proper process control. We conclude this study with providing general comments.

• Journal of Radiation Protection and Research
• /
• v.44 no.2
• /
• pp.64-71
• /
• 2019

Background: It is very difficult to distinguish between a radioactive contamination source and background radiation from natural radionuclides in the marine environment by means of online monitoring system. The objective of this study was to investigate a statistical process for triggering abnormal level of count rate data measured from our on-line seawater radioactivity monitoring. Materials and Methods: Count rate data sets in time series were collected from 9 monitoring posts. All of the count rate data were measured every 15 minutes from the region of interest (ROI) for $^{137}Cs$ ($E_{\gamma}=661.6keV$) on the gamma-ray energy spectrum. The Shewhart ($3{\sigma}$), CUSUM, and Bayesian S-R control chart methods were evaluated and the comparative analysis of determination methods for count rate data was carried out in terms of the false positive incidence rate. All statistical algorithms were developed using R Programming by the authors. Results and Discussion: The $3{\sigma}$, CUSUM, and S-R analyses resulted in the average false positive incidence rate of $0.164{\pm}0.047%$, $0.064{\pm}0.0367%$, and $0.030{\pm}0.018%$, respectively. The S-R method has a lower value than that of the $3{\sigma}$ and CUSUM method, because the Bayesian S-R method use the information to evaluate a posterior distribution, even though the CUSUM control chart accumulate information from recent data points. As the result of comparison between net count rate and gross count rate measured in time series all the year at a monitoring post using the $3{\sigma}$ control charts, the two methods resulted in the false positive incidence rate of 0.142% and 0.219%, respectively. Conclusion: Bayesian S-R and CUSUM control charts are better suited for on-line seawater radioactivity monitoring with an count rate data in time series than $3{\sigma}$ control chart. However, it requires a continuous increasing trend to differentiate between a false positive and actual radioactive contamination. For the determination of count rate, the net count method is better than the gross count method because of relatively a small variation in the data points.

• Proceedings of the Safety Management and Science Conference
• /
• 2010.04a
• /
• pp.509-517
• /
• 2010

The paper proposes the misuse types of statistical quality tools according to the kind of data and the number of population in DMAIC process of six sigma. The result presented in this paper can be extended to the QC story 15 steps of QC circle. The study also provides the improvement methods about control chart, measurement system analysis, statistical difference, and practical equivalence.