• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.587-600
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• 2008

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all $1{\leq}i<j{\leq}4$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• International Journal of Quality Innovation
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• v.6 no.2
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• pp.31-45
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• 2005

The target costing technique, mathematically discussed by Sauers, only uses the $C_p$ index along with Taguchi loss function and ${\bar{X}}-R$ control charts to set up goal control limits. The new specification limits derived from Taguchi loss function is linked through the $C_p$ value to ${\bar{X}}-R$ control charts to obtain goal control limits. This study further considers the reflected normal loss function as well as the $C_{pk}$ index along with its lower confidence interval in forming goal control limits. With the use of lower confidence interval to replace the point estimator of the $C_{pk}$ index and reflected normal loss function proposed by Spiring to measure the loss to society, this modified and improved target costing technique would become more robust and applicable in practice. Finally, an example is provided to illustrate how this modified and improved target costing technique works.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.1-16
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• 2000

This paper considers the problem of determining the optimal process mean and screening specification limits of a surrogate variable associated with product quality under two-stage screening procedure. In two-stage screening, the surrogate variable is inspected first to decide whether an item should be accepted, rejected or additional observations should be taken. If additional observations are required, the performance variable of interest is then observed to classify the undecided items. Assuming that the performance variable and the surrogate variable are jointly normally distributed, the optimal process mean and the screening limits are obtained by maximizing the expected profit which includes selling price, production, reprocessing, inspection and penalty costs. A numerical example is presented and numerical studies are performed to compare the proposed two-stage screening procedure with single-stage screening procedures.

• Journal of Korean Society for Quality Management
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• v.34 no.4
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• pp.125-132
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• 2006

An adjusted control limit of the $\overline{X}$ chart is proposed for monitoring the continually improving processes. The continual improvement of the process implies the decrease of the process variance, which is represented by a logistic curve. The process standard deviation is estimated by the exponentially weighted moving average of the sample standard deviations from the past to the current times. The control limits are adjusted by the estimated standard deviation at every sampling time. The performance of the adjusted control limit is compared with that of the standard control limits for various cases of the decreasing speed and size of the variance. The results show that the $\overline{X}$ chart with the adjusted control limits provides better performances for monitoring the small and moderate shifts in continually improving processes.

• Korean Journal of Optics and Photonics
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• v.15 no.5
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• pp.405-408
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• 2004

In this paper, we used a split-lens speckle shear interferometer using a double speckle interferometer, which enables continuous measurement of the deformation. We made two identical specklegrams corresponding to an object. With this method we could detect the measuring limits of the deformation for various shears. This experimental results showed that the measuring limits of a split-lens speckle shear interferometer are similar to the measuring limits of a double exposure speckle interferometer.

• Proceedings of the KIEE Conference
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• 2003.07a
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• pp.98-100
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• 2003

This paper presents the method for computing the power economic dispatch with an optimal power flow (OPF) computation algorithm, considering the power factor limits constraint. Efficient reactive power planning enhances economic operation as well as system security. Accordingly, an adequate level of power factor limits for the load buses should be evaluated for economic operation. The power factor limits are included and described into the OPF's objective function. The proposed method is applied to IEEE 26 buses system.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.1
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• pp.151-159
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• 2008

The parameter-based cardiovascular impedance simulator that is able to overcome the limits of conventional mock circulatory systems is critical for the development and test of biomedical devices including artificial heart. The concept of impedance simulator was validated mathematically in a previous study using high-gain feedback linearization control which, however, may cause serious difficulties and limits for practical implementation. In this study, therefore, practical applicability of the impedance simulator is investigated considering the physical limits such as motor speed and torque. Simple PID controller which do not require complex model of the simulator is used considering the practical implementation. Design guidelines of the impedance simulator are also provided based on the results.

• Journal of the Korean Society of Safety
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• v.25 no.2
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• pp.35-40
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• 2010

Explosion limit and flash point are the major combustion properties used to determine the fire and explosion hazards of the flammable substances. In this study, in order to predict upper explosion limits(UEL), the upper flash point of n-alcohols were measured under the VLE(vapor-liquid equilibrium) state by using Setaflash closed cup tester(ASTM D3278). The UELs calculated by Antoine equation using the experimental upper flash point are usually lower than the several reported UELs. From the given results, using the proposed experimental and predicted method, it is possible to research the upper explosion limits of the other flammable substances.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.189-192
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• 2015

An experimental study was conducted to find the effect of DBD plasma on the flammability limits of inert-gas-diluted fuel. The results showed that the concentration of diluting nitrogen at flammability limit increased when nitrogen-diluted methane and propane were reformed by plasma, while it decreased when nitrogen-diluted ethylene was reformed by plasma. Gas chromatography results suggested that the fuel type dependence of flammability limits is due to the difference in the concentrations of hydrogen and hydrocarbon species in reformed fuel.