• 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.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.101-108
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• 2005

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.257-270
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• 2006

Kim(2002) proposed a second type of central composite design in which the positionsof the axial points are indicated by two numbers, and called it CCD2. In the present paper, we have studied CCD2 further and obtained several new facts. We have obtained CCD2's that have both orthogonality and rotatability, both orthogonality and slope rotatability, and both rotatability and uniform precision. We also have applied Park and Kim's (1992) measure of slope rotatability to such CCD2's and observed some useful results.

• 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.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.25-36
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• 2006

Icosahedron and dodecahedron designs are experimental designs which can be used for response surface analysis for the case when three independent variables are involved. When we are interested in estimating the slope of a response surface, slope rot at ability is a desirable property. In this paper, we derive conditions for icosahedron and dodecahedron designs to have slope rotatability, and actually obtain some slope-rotatable icosahedron and dodecahedron designs. We also apply Park and Kim (1992)'s measure of slope rotatability to icosahedron and dodecahedron designs, and observe resultant facts.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.153-161
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• 2002

A new method of construction of second order slope rotatable designs (SOSRD) using symmetrical unequal block arrangements (SUBA) with two unequal block sizes is suggested. The proposed method may sometimes lead to designs with less number of design points than those available in the literature. Further, bounds for the parameters of SOSRD are also obtained.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.51-59
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• 1996

A measure that quantifies the amount of slope retatability for the second degree Scheffe polynomial model for mixture experiments is proposed and used to compare the several mixture designs which met the symmetric momemts conditions in this article.

• 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.

• Journal of the Korean Statistical Society
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• v.17 no.2
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• pp.121-133
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• 1988

In this paper a class of mixture designs for estimating the slope of second order Scheffe polynomial response surfaces for mixture experiments with q components is presented. The variance of the estimated directional slope at a point is a function of the direction of the slope and the design. If the variance is averaged over all possible directions in the (q-1)-dimensional simplex, 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 centroid point. This property is called "slope-rotatability over al directions in the simplex", and the necessary and sufficient conditions for mixture design to have this property are given and proved. The class of designs with this property is compared with other mixture designs and discussed.discussed.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.105-123
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• 1993

반응표면의 기울기를 추정하기 위한 실험계획법이 가질 수 있는 바람직한 성질로, Hader와 Park(1978)이 제시한 "축 방향에 걸친 기울기 회전성"과, Park(1987)이 제시한 "모든 방향에 걸친 기울기 회전성"이 있다. 또한 주어진 임의의 실험계획에 대하여 축 방향에 걸친 기울기 회전성의 정도를 수치로 나타낼 수 있는 측도(measure)가 Park과 Kim(1992)에 의해 제시된 바 있다. 본 논문에서는 반응표면 실험계획법이 가지고 있는 모든 방향에 걸친 기울기 회전성의 정도를 알 수 있게 해 주는 측도를 개발하였다. 또한 이 측도를 여러 종류의 계획들에 적용하여 결과를 관찰하였다. 이 측도의 장점 중의 하나는 어떠한 계획에도 적용이 가능하다는 점이다. 계획에도 적용이 가능하다는 점이다.