• Industrial Engineering and Management Systems
• /
• v.8 no.3
• /
• pp.139-147
• /
• 2009

Control charts are used to distinguish between chance and assignable causes in the variability of quality characteristics. When a control chart signals that an assignable cause is present, process engineers must initiate a search for the assignable cause of the process disturbance. Identifying the time of a process change could lead to simplifying the search for the assignable cause and less process down time, as well as help to reduce the probability of incorrectly identifying the assignable cause. The change point estimation by likelihood theory and the built-in change point estimation in a control chart have been discussed until now. In this article, we discuss two kinds of process change point estimation when the CUSUM ($\bar{x}$, s) control chart for monitoring process mean and variance simultaneously is operated. Throughout some numerical experiments about the performance of the change point estimation, the change point estimation techniques in the CUSUM ($\bar{x}$, s) control chart are considered.

• 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 Society for Quality Management
• /
• v.35 no.2
• /
• pp.37-44
• /
• 2007

Today, the statistical process control (SPC) in manufacture environment is an important role at the process by the productivity improvement of the manufacturing systems. The control chart in this statistical method is widely used as an important statistical tool to find the assignable cause that provoke the change of the process parameters such as the mean of interest or standard deviation. But the traditional SPC don't grasp the change of process according to the points fallen the near control limits because of monitoring the variance of process such as the fixed sampling interval and the sample size and handle the cost of the aspect of these sample point. The control chart can be divided into the statistical and economic design. Generally, the economic design considers the cost that maintains the quality level of process. But it is necessary to consider the cost of the process improvement by the learning effects. This study does the economic design in the VSI $\bar X$ control chart and added the concept of loss function of Taguchi in the cost model. Also, we preyed that the VSI $\bar X$ control chart is better than the FSI $\bar X$ in terms of the economic aspects and proposed the standard of the process improvement using the VSI $\bar X$ control chart.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.27 no.2
• /
• pp.114-122
• /
• 2004

In statistical process control applications, variable sample size (VSS) $\bar{X}$ chart is often used to detect the assignable cause quickly. However, it is usually assumed that only one assignable cause results in the out-of-control in the process. In this paper, we propose the algorithm to minimize the function of cost per unit time and compare the economic design and the statistical design by use of the value of cost per unit time. We consider double assignable causes to occur with compound in the process and adopt the Markov chain approach to investigate the statistical properties of VSS $\bar{X}$ chart. A procedure that can calculate the control chart's parameters is proposed by the economic design.

• Journal of Korean Society for Quality Management
• /
• v.40 no.2
• /
• pp.176-185
• /
• 2012

After a work of Derman and Ross(1997) that considered simple main runs rules and derived ARL (Average Run Length) using Markov chain modeling, $\bar{X}$ control chart based on diverse alternative main and supplementary runs rules that is the most popular control chart for monitoring the mean of a process are proposed. This paper reviews and discusses the-state-of-art researches for these runs rules and classifies according to several properties of runs rules. ARL derivation for a proposed runs rule is also illustrated.

• Communications for Statistical Applications and Methods
• /
• v.5 no.2
• /
• pp.373-381
• /
• 1998

In this paper a new control chart which accounts for correlation between process subgroups will be proposed. We consider the case where the process fluctuations are autocorrelated by a stationary AR(1) time series and where n($\geq1$) items are sampled from the process at each sampling time. A simulation study is presented and shows that for correlated subgroups, the proposed control chart makes a significant improvement over the traditionally employed X-bar chart which ignores subgroup correlations. Finally, we illustrate the proposed chart by comparing the standardized residuals and X-bar chart on a data set of motor shaft diameters.

• Journal of Korean Society for Quality Management
• /
• v.32 no.4
• /
• pp.252-264
• /
• 2004

Variable sampling Interval (VSI) control charts vary the sampling interval according to value of the control statistic while the sample size is fixed. It is known that control charts with 2-state VSI scheme, which uses only two sampling intervals, give good statistical properties. Variable sample size (VSS) control charts vary the sample size according to value of the control statistic while the sampling interval is fixed. In the VSS scheme no optimal results are known for the number of sample sizes. It is also known that the variable sampling rate (VSR) $\bar{X}$ control chart with 2-state VSS and 2-state VSI scheme leads to large improvements In performance over the fixed sampling rate (FSR) $\bar{X}$ chart, but the optimal number of states for sample size Is not known. In this paper, the VSR Χ charts with multi-state VSS and 2-state VSI scheme are designed and compared to 2-state VSS and 2-state VSI scheme. The multi-state VSS scheme is considered to, achieve an additional improvement by switching from the 2-state VSS scheme. On the other hand, the multi-state VSI scheme is not considered because the 2-state scheme is known to be optimal. The 3-state VSS scheme improves substantially the sensitivity of the $\bar{X}$ chart especially for small and moderate mean shifts.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.37 no.1
• /
• pp.151-156
• /
• 2014

Control charts are generally used for process control, but the role of traditional control charts have been limited in case of a contaminated process. Traditional $\bar{x}$ control charts have not been activated well for such a problem because of trying to control processes as center line and control limits changed by the contaminated value. This paper is to propose robust $\bar{x}$ control charts which is considering a location parameter in order to respond to contaminated process. In this paper, we consider $\bar{x}_{\alpha}$, that is trimmed rate; typically ten percent rate is used. By comparing with p, ARL value, the responding results are decided. The comparison resultant results of proposed two control charts are shown and are well contrasted.

• Journal of Korean Society for Quality Management
• /
• v.28 no.3
• /
• pp.44-52
• /
• 2000

In this paper we apply VSS X chart to the case when two assignable causes effect the process mean shift. We compare the case when two compound assignable causes effect the process mean with another one which effects individually. For the practical use of VSS $\bar{X}$ chart we propose the sample size which minimizes the average number of samples until the signal is given in out-of-control state.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.23 no.57
• /
• pp.123-129
• /
• 2000

The Bootstrap method proposed by Efron is non-parametric method which doesn't depend on the estimation of prior distribution refer to population. A typical statistical process control chart which is generally used is developed under the assumption that observations follow mutually independent and identically distributed within a sample and between samples. However, autocorrelation greatly affect the developed control chart under the assumption that observations are mutually independent. Many researchers showed that the result which was analyzed by using a typical control chart for the observations which has the correlation violated to the independence assumption can not be true. Therefore, we compared the standard method with bootstrap method and then evaluated them for x control chart and EWMA control chart by using bootstrap method which was proposed by Efron in the AR(1) model when the observations have correlation.