• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.153-160
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• 2005

In this paper, modified second order slope rotatable designs are introduced and modified slope rotatable central composite designs (SRCCD) are constructed for $2 {\le} v {\le} 17$ (v: the number of factors). Further, it can be shown for certain values of 'v', the modified SRCCD can be viewed as SRCCD constructed as with the technique of augmentation of second order rotatable design (SORD) using central composite design to SRCCD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.

• Journal of Korean Society for Atmospheric Environment
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• v.24 no.E2
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• pp.83-91
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• 2008

This work investigated the methodology to simultaneously optimize the ozone and relative humidity composition for the $NO_x$ degradation using soil biofilter. Experiments were made as a function of inlet ozone concentration ($0{\sim}1,770\;ppb$) and relative humidity ($38{\sim}81%$). Factorial design ($2^2+3$) and response surface methodology by central composite designs were used to examine the role of two factors and optimal response condition on $NO_x$ degradation. It was found that a second-order response surface model can properly interpret the experimental data with an $R^2$-value of 0.9730 and F-value of 71.83, based on which the maximum $NO_x$ degradation was predicted up to 92.8% within our experimental conditions.

• Journal of Korean Society for Quality Management
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• v.40 no.4
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• pp.431-440
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• 2012

Purpose: In this paper we propose modified Notz designs which are useful to experimenters who want to adopt the sequential experimentation strategy and to estimate second-order regression model with as few experimental points as possible. Methods: We first present the design matrices and design points in two or three dimensional spaces for such small sized second-order designs as small composite, hybrid, and Notz designs. Modified Notz designs are proposed and compared with some response surface designs in terms of the total number of experimental points, the estimation capability criteria such as D- and A-optimality. Results: When sequential experimentation is necessary, the modified Notz designs are recommendable. Conclusion: The result of this paper will be beneficial to experimenters who need to do experiments more efficiently, especially for those who want to reduce the time of experimentation as much as possible to develop cutting-edge products.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.337-357
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• 2003

This paper introduces new measures for the stability of slope estimation on the second order response surface at a point and on a sphere. As a measure of point stability of slope estimation, we suggest a point dispersion measure of slope variances over all directions at a point. A spherical dispersion measure is also proposed as a measure of spherical stability of slope estimation on each sphere. Some designs are studied to explore the usefulness of the proposed measures. Using the point dispersion measure, another concept of slope rotatability called equally-stable slope rotatability is proposed as a useful property of response surface designs. We provide a set of conditions for a design to have equally-stable slope rotatability.

• Journal of Korean Society for Quality Management
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• v.14 no.1
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• pp.26-32
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• 1986

A class of multi-factor designs for estimating the slope of second order response surfaces is presented. For multi-factor designs the variance of the estimated slope at a point is a function of the direction of measurement of the slope and the design. If we average the variance over all possible directions, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the design origin. This property is called "slope-rotatability over all directions", and the necessary and sufficient conditions for a design to have this property are given and proved. The class of design with this property is mainly discussed.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.580-593
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• 1998

The small composite design for second order response surface might be appropriate when experimentation is expensive, difficult, or time-consuming, especially when an independent estimate of experimental error is available. It is important that the small composite designs for response surface analysis would be rotatable and slope-rotatable. Therefore the small composite designs are studied from the viewpoint of rotatability and slope-rotatability, and the optimal values of a(the distance of axial points from the center) are investigated as k(the number of independent variables) and $n_0$(the number of center points) are changed.

• Food Engineering Progress
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• v.15 no.2
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• pp.97-115
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• 2011

A review about the application of response surface methodology in the optimization of food technology is presented. The theoretical principles of response surface methodology and steps for its application are described. The response surface methodologies : three-level full factorial, central composite, Box-Behnken, and Doehlert designs are compared in terms of characteristics and efficiency. Furthermore, recent references of their uses in food technology are presented. A comparison between the response surface designs (three-level full factorial, central composite, Box-Behnken and Doehlert design) has demonstrated that the Box-Behnken and Doehlert designs are slightly more efficient than the central composite design but much more efficient than the three-level full factorial designs.

• Honam Mathematical Journal
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• v.6 no.1
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• pp.45-58
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• 1984

• Journal of Korean Society for Quality Management
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• v.47 no.3
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• pp.523-535
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• 2019

Purpose: We research on the efficient response surface methodology(RSM) design to develop a design space in Quality by Design(QbD). We propose practical designs for the successful construction of the design space in QbD by allowing different number of replicates at the box points, star points, and the center point in the rotatable central composite design(CCD). Methods: The fraction of design space(FDS) plot is used to compare designs efficiency. The FDS plot shows the fraction of the design space over which the relative standard error of predicted mean response lies below a given value. We search for practical designs whose minimal half-width of the tolerance interval per a standard deviation is less than 4.5 at 0.8 fraction of the design space. Results: The practical designs for the number of factors between two and five are listed. One of the designs in the list could be chosen depending on the experimental budget restriction. Conclusion: The designs with box points replications are more efficient than those with the star points replication. The sequential method to establish a design space is illustrated with the simulated data based on the two examples in RSM.

• Journal of the Korean Statistical Society
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• v.35 no.2
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• pp.179-192
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• 2006

In this paper, a new method of modified second order slope rotatable designs (SOSRD) using balanced incomplete block designs (BIBD) for $4{\le}v{\le}16$ is presented. In this method the number of design points required is in some cases less than the number required in Victorbabu (2305) modified slope rotatable central composite designs. Further, a new method of construction of three level modified SOSRD using BIBD is presented. The modified SOSRD can be viewed as SOSRD constructed with the technique of augmentation of second order rotatable design (SORD) using BIBD to SOSRD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.