• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.911-925
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• 2017

We investigate the properties of multivariate Shewart control charts with VSI procedure for monitoring simultaneous monitoring mean vector and covariance matrix in term of ANSW (average number of switches), probability of switch and ASI (average sampling interval), ATS (average time to signal). From examining the ANSW values, we know that it does not switch frequently. The VSI control charts are superior to the corresponding FSI control charts in terms of ATS. And, it can be also seen that the VSI procedures have substantially fewer switches for small or moderate shifts of the mean vector and variances.

• Journal of Integrative Natural Science
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• v.13 no.4
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• pp.152-157
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• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

• 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 the Korean Data and Information Science Society
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• v.16 no.3
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• pp.639-650
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• 2005

Theoretical and numerical comparison have shown that variable sampling interval (VSI) charts are substantially more efficient than fixed sampling interval(FSI) charts in term of ATS(average time to signal). But the frequency of switching between different sampling intervals is a complicating factor in VSI procedures. VSI EWMA charts for monitoring mean vector of related qualify characteristics are investigated. To compare the efficiencies of the proposed charts, the performances are evaluated for matched FSI and VSI charts in terms of average time to signal(ATS) and average number of samples to signal(ANSS). For the switching behavior of the proposed VSI charts, average number of switches(ANSW) are also investigated.

• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.819-829
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• 2010

Properties of multivariate variable sampling interval (VSI) Shewhart and CUSUM charts for monitoring mean vector of related quality variables are investigated. To evaluate average time to signal (ATS) and average number of switches (ANSW) of the proposed charts, Markov chain approaches and simulations are applied. Performances of the proposed charts are also investigated both when the process is in-control and when it is out-of-control.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.181-197
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• 2001

A heuristic method TABU-CSP using Tabu Search (TS) is described for solving Constraint Satisfaction Problems (CSPs). The method is started with a complete but inconsistent solution of a binary CSP and obtained in prespecified number of iterations either a consistent solution or a near optimal solution with an acceptable number of conflicts. The repair in the solution at each iterative step is done by using two heuristics alternatively. The first heuristic is a min-conflicts heuristic that chooses a variable with the maximum number of conflicts and reassigns it the value which leads to the minimum number of conflicts. If the acceptable solution is not reached after the search continued for a certain number of iterations, the min-conflict heuristic is changed and the variable selected least number of times is chosen for repair. If an acceptable solution is not reached, the method switches back to the min-conflict heuristic and proceeds further. This allowed the method to explore a different region of search space space for the solution as well as to prevent cycling. The demonstration of the method is shown on a toy problem [9]which has no solution. The method is then tested on various randomly generated CSPs with different starting solutions. The performance of the proposed method in terms of the average number of consistency is checked and the average number of conflicts is conflicts is compared with that of the Branch and Bound(BB) method used to obtain the same solution. In almost all cases, the proposed method moves faster to the acceptable solution than BB.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.859-866
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• 2012

Some switching properties of multivariate control charts are investigated when the interval between two consecutive sample selections is not fixed but changes according to the result of the previous sample observation. Many articles showed that the performances of variable sampling interval control charts are more efficient than those of fixed sampling interval control charts in terms of average run length (ARL) and average time to signal (ATS). Unfortunately, the ARL and the ATS do not provide any information on how frequent a switch is being made. We evaluate several switching properties of two sampling interval Shewhart and CUSUM procedures for controlling mean vector of correlated quality variables.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.451-459
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• 2017

There are many researches showing that when a process change has occurred, variable sampling intervals (VSI) control chart is better than the fixed sampling interval (FSI) control chart in terms of reducing the required time to signal. When the process engineers use VSI control procedure, frequent switching between different sampling intervals can be a complicating factor. However, average number of samples to signal (ANSS), which is the amount of required samples to signal, and average time to signal (ATS) do not provide any control statistics about switching performances of VSI charts. In this study, we evaluate numerical switching performances of multivariate VSI EWMA chart including average number of switches to signal (ANSW) and average switching rate (ASWR). In addition, numerical study has been carried out to examine how to improve the performance of considered chart with accumulate-combine approach under several different smoothing constant and sample size. In conclusion, process engineers, who want to manage the correlation coefficients of related quality variables, are recommended to make sample size as large and smoothing constant as small as possible under permission of process conditions.

• Journal of Integrative Natural Science
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• v.12 no.3
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• pp.78-84
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• 2019

In many cases, the quality of a product is determined by several correlated quality variables. Control charts have been used for a long time widely to control the production process and to quickly detect the assignable causes that may produce any deterioration in the quality of a product. Numerical switching performances of multivariate cumulative sum control chart for simultaneous monitoring all components in the dispersion matrix ${\Sigma}$ under multivariate normal process $N_p({\underline{\mu}},{\Sigma})$ are considered. Numerical performances were evaluated for various shifts of the values of variances and/or correlation coefficients in ${\Sigma}$. Our computational results show that if one wants to quick detect the small shifts in a process, CUSUM control chart with small reference value k is more efficient than large k in terms of average run length (ARL), average time to signal (ATS), average number of switches (ANSW).

• The KIPS Transactions:PartA
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• v.9A no.4
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• pp.547-554
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• 2002

This paper proposes an efficient dynamic routing algorithm for Multistage Bus Networks(MBN's) in distributed shared memory environment. Our algorithm utilizes extra paths available on MBN and determines routing paths adaptively according to switch traffic in order to distribute traffic among switches. Precisely, a packet is transmitted to the next switch on an extra path having a lighter traffic. As a consequence the proposed algorithm reduces the mean response time and the average number of waiting tasks. The results of simulations, carried out with varying numbers of processors and varying switch sizes, show that the proposed algorithm improves the mean response time by 9% and the average number of waiting tasks by 21.6%, compared to the existing routing algorithms which do not consider extra paths on MBN.