• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.10 no.16
• /
• pp.101-106
• /
• 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 Institute of Industrial Engineers
• /
• v.34 no.3
• /
• pp.328-336
• /
• 2008

This research proposes a method for economic-statistical design of adaptive moving average (A-MA) charts. The basic idea of the A-MA chart is to accumulate previous samples selectively in order to increase the sensitivity. The A-MA chart is a kind of adaptive chart such as the variable sampling size (VSS) chart. A major advantage of the A-MA chart over the VSS chart is that it is easy to maintain rational subgroups by using the fixed sampling size. A steady state cost rate function is constructed based on Lorenzen and Vance (1986) model. The cost rate function is optimized with respect to five design parameters. Computational experiments show that the A-MA chart is superior to the VSS chart as well as to the Shewhart $\bar{X}$ chart in the economic-statistical sense.

• International Journal of Quality Innovation
• /
• v.2 no.1
• /
• pp.69-86
• /
• 2001

The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts [9]. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensitivity analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.

• Journal of Integrative Natural Science
• /
• v.5 no.4
• /
• pp.246-252
• /
• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.

• Journal of Integrative Natural Science
• /
• v.5 no.3
• /
• pp.151-156
• /
• 2012

Because of the equivalence between control chart procedures and hypothesis testing, we propose to use likelihood ratio test (LRT) statistic $Z_i^2$ as the multivariate control statistic for simultaneous monitoring means of the multivariate normal process. Properties and comparisons of the proposed control charts are explored and conducted for matched fixed sampling interval (FSI) and variable sampling interval (VSI) with two sampling interval charts. The result of numerical comparisons shows that EWMA chart with two sampling interval procedure is more efficient than the corresponding FSI chart for small or moderate changes. When large shift of the process has occurred, we also found that Shewhart chart is more efficient than EWMA chart.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1996.04a
• /
• pp.15-18
• /
• 1996

Shewhart control chart is a basic technique to monitor the state of a process. We observe observations of a group of size four or five in a rational way and plot some statistics (e.g., means and ranges) on the chart. When setting up the control chart, the control limits are calculated based on preliminary 20-40 samples, which were supposedly obtained from stable operating conditions. But it may be hard to believe, especially at the beginning of constructing the chart for the first time, whether the process is stable and hence all samples were generated under the homogeneous operating conditions. In this report we suggest a mechanism to obtain robust control limits under self-criticism. When outliers are present in the sample, we obtain tighter control limits and hence increase the sensitivity of the chart. Examples will be given via simulation study.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.3
• /
• pp.729-738
• /
• 2015

In this paper, we compare the robustness to the assumption of normality of the single control charts to control the mean and variance simultaneously. The charts examined were semicircle control chart, max chart and MSE chart with Shewhart individuals control charts. Their in-control and out-of-control performance were studied by simulation combined with computation. We calculated false alarm rate to compare among single charts by changing subgroup size and shifting mean of quality characteristics. It turns out that max chart is more robust than any of the others if the process is in-control. In some cases max chart and MSE chart are more robust than others if the process is out-of-control.

• International Journal of Quality Innovation
• /
• v.1 no.1
• /
• pp.81-88
• /
• 2000

• Journal of the military operations research society of Korea
• /
• v.22 no.2
• /
• pp.126-138
• /
• 1996

The statistical control chart has been proven to be the effective tool most widely used in the manufacturing industry for monitoring and controlling the manufacturing processes. However, the Shewhart chart sometimes gives us false information when the distribution of quality characteristics is skewed. Therefore, it cannot serve as the universal quality control chart if there exist odd events in the manufacturing process. The objective of this study is thus to develop the new technique for constructing the limits of quality control chart based on a sample median and range when the distribution of the underlying population is skewed. This new control chart can effectively solve and manage the processes which have the non-normally distributed quality characteristics frequently occurring in the practical situation.

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