• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.413-422
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• 1999

Multivariate EWMA control charts to simultaneously monitor correlation coefficients of correlated quality characteristics under multivariate normal process are proposed. Performances of the proposed charts are measured in terms of average run length(ARL). Numerical results show that smalle values for smoothing constant with accumulate-combine approach are preferred for detecting smalle shifts.

• International Journal of Quality Innovation
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• v.4 no.2
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• pp.65-72
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• 2003

This paper mainly studies to build control charts under different alarm rule. For different alarm rule, the control limit parameters of a control chart should be changed, then some kinds of control schemes under different alarm rule were compared and the methods of calculating ARL for different control schemes were given.

• Journal of Korean Society for Quality Management
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• v.40 no.2
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• pp.176-185
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• 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
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• v.23 no.6
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• pp.497-515
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• 2016

Modern processes often monitor more than one quality characteristic that are referred to as multivariate statistical process control (MSPC) procedures. The MSPC is the most rapidly developing sector of statistical process control and increases interest in the simultaneous inspection of several related quality characteristics. Most multivariate detection procedures based on a multi-normality assumptions are independent, but there are many processes that assume non-normality and correlation. Many multivariate control charts have a lack of related joint distribution. Copulas are tool to construct multivariate modelling and formalizing the dependence structure between random variables and applied in several fields. From copula literature review, there are a few copula to apply in MSPC that have multivariate control charts, and represent a successful tool to identify an out-of-control process. This paper presents various types of copulas modelling for the multivariate control chart. The performance measures of the control chart are the average run length (ARL) and the average number of observations to signal (ANOS). Furthermore, a Monte Carlo simulation is shown when the observations were from an exponential distribution.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1593-1600
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. We construct bivariate Shewhart control charts based on the trace of the product of the estimated variance-covariance matrix and the inverse of the in-control matrix and investigate the properties of bivariate Shewart control charts with VSI procedure for monitoring covariance matrix in term of ATS (Average time to signal) and ANSW (Average number of switch) and probability of switch, ASI (Average sampling interval). Numerical results show that ATS is smaller than ARL. From examining the properties of switching in changing covariances and variances in ${\Sigma}$, ANSW values show that it does not switch frequently and does not matter to use VSI procedure.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.1
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• pp.87-98
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• 2005

This research investigates economic-statistical characteristics of variable sampling size and interval (VSSI)$\bar{X}$charts under two assignable causes. A Markov chain approach is employed in order to calculate average run length (ARL) and average time to signal (ATS). Six transient states are derived by carefully defining the state. A steady state cost rate function is constructed based on Lorenzen and Vance(1986) model. The cost rate function is optimized with respect to six design parameters for designing the VSSI $\bar{X}$ charts. Computational experiments show that the VSSI $\bar{X}$ chart is superior to the Shewhart $\bar{X}$ chart in the economic-statistical sense, even under two assignable causes. A comparative study shows that the cost rate may increase up to almost 30% by overlooking the second cause. Critical input parameters are also derived from a sensitivity study and a few guideline graphs are provided for determining the design parameters.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.54-65
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• 1994

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. Two basic approaches, "combine-accumulate" approach and "accumulate-combine" approach, for using past sample information in the developement of multivariate EWMA control charts are considered. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average run length (ARL) performances. The numerical results show that multivariate EWMA control charts based on the accumulate-combine approach are more efficient than corresponding multivariate EWMA control charts based on the combine-accumulate approach.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.919-929
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• 2013

We compared two basic methods, combine-accumulate method and accumulate-combine method, using the past quality information in multivariate quality control procedure for monitoring mean vector of multivariate normal process. When small or moderate shifts have occurred, accumulate-combine method yields smaller average run length (ARL) and average time to signal (ATS) than combine-accumulate method. On the other hand, we have found from our numerical results that combine-accumulate method has better performances in terms of switching behavior than accumulate-combine method. In industry, a quality engineer could select one of the two method under the comprehensive consideration about the required time to signal, switching behavior, and other physical factors in the production process.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.108-125
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• 1998

The EWMA(Exponentially Weighted Moving Average) has recently received a great deal of attention in the quality control literature as a process monitoring tool on the shop floor of manufacturing industires, since it is easy to plot, to interpret, and its control limits are easy to obtain. Most a, pp.ications of the EWMA for process monitoring have concentrated on the problem of detecting shifts of a process mean and a process standard deviation with ARL(Average Run Length) properties. But there may be the necessity of controlling linearity on product quality such as the correlation coefficient to the process operator. Control managers may want to protect the increase of a process correlation coefficient value, such as 0, between two variables of interest. However, there are few studies concerned on this part. Therefore, we propose EWMA models for a process correlation coefficient using two transformed statistics, T-statistic and (Fisher's) Z-statistic. We also present some results of simulation by SAS/IML and compare two models.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.823-833
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• 2016

The lifetime is a key characteristic of product quality. It is best to obtain the lifetime data of all samples, but they are often censored due to time or expense limitations. In this paper, we propose a binomial cumulative sum (CUSUM) chart to monitor the mean of type I right-censored Weibull lifetime data, for a xed value of the Weibull shape parameter. We compare the performance of the proposed binomial CUSUM chart with CUSUM charts studied previously using the steady-state average run length (ARL). The results show that the performance of the binomial CUSUM chart is better when the censoring rate is high and/or the sample size is small.