• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.253-264
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• 2005

Hader and Park(l978) suggested the concept of slope-rotatability in axial directions for second order response surface designs. In this paper, the moment conditions for slope-rotatability in axial directions are shown and the measures for evaluating slope-rotatability in axial directions are proposed.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.415-426
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• 2000

Hader and Park (1978) introduced the idea of slope rotatability, and Park (1987) introduced the concept of slope rotatability over all directions, and gave necessary and sufficient conditions. Park and Kim (1992) proposed a measure that represent the extent of slope rotatability for a given response surface design. Kim (1993) proposed a measure that represent the extent of slope rotatavility over all directions. In this paper, we embodied the measure of slope rotatability over all directions. Examples of applying this measure to some response surface designs are also given. In this response surface design of slope rotatavility over all directions, we obtain the mean slope variances on the spherical surface to select better experimental design varying the number of center points and radius.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.157-173
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• 2007

In this article it is considered that how the slope-rotatability property of a second order design for response surface model is affected by block effects and how the design points are assigned into the blocks so that the blocked design may have the property of slope-rotatability. If an unblocked design is blocked properly, it could be a slope-rotatable design with block effects and this property is named as block slope-rotatability. We approach this problem from the moment matrix of the blocked design, which plays an important role to get the variances of the estimates, and suggest conditions of block slope-rotatability.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.95-100
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• 2005

In this paper a class of multifactor designs for estimating the slope of second order response surface regression models with correlated errors is considered. General conditions for second order slope rotatability over all directions and also with respect to the maximum directional variance in case of k=2 have been derived assuming errors have a general correlated error structure. And we consider the measures for evaluating slope rotatability with correlated errors similar to in case of uncorrelated error structures.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.745-755
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• 2007

The concept of slope rotatability introduced by Hader and Park(1978) is available when we are interested in the difference of the responses. Since there can be constraints on the factor levels in mixture experiments, there arises a need for adaptation of the concept of slope rotatability and the measure to assess it. In this article, measures of slope rotatability in mixture experiments are proposed to quantify the amount of slope rotatability for a given design. Measures for a restricted region design as well as for an unrestricted region design are presented. Then, the designs having different optimalities are compared with respect to these measures by some examples.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.36-44
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• 1982

A new design concept, called axis-slope-rotatability, is presented for the design of experiments with mixtures. This is an analogue of the Box-Hunter (1957) rotatability for second order response surface designs. By choice of design, it is possible to make the variance of the estimated slopes along the component axes constant for all axial points equidistant from the center point of the factor space. This property is called axis-slope-rotatability for mixture experiments. When the Scheffe's second degree polynomial is used, it is shown that some symmetry conditions are sufficient for axis-slope-rotatability. Several designs having this property are illustrated.

• The Korean Journal of Applied Statistics
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• v.32 no.6
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• pp.867-878
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• 2019

In this paper, we applied modified slope rotatability introduced by Victorbabu (2005) to the central composite design of second type, and studied related content. We suggested methods of constructing central composite designs of second type which have modified slope rotatability. Especially, this property has the advantage that it can be used to sequential experiments, because we can obtain central composite designs of second type which have modified slope rotatability by adding experimental points without changing the axial values to central composite designs of second type having Box-Hunter rotatability. We explained central composite designs of second type which have modified slope rotatability by using two examples.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.563-574
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• 2004

Slope rotatability of response surface designs is a desirable property when we are interested in estimating slopes of response surfaces. In this paper, we derive a simplified measure of slope rotatability from new viewpoints for response surface designs that are frequently used in response surface methodology.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.121-137
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• 2004

Kim(2002) proposed a second type of central composite design (CCD2), in which the positions of the axial points are indicated by two numbers. In this paper, we study properties of CCD2 when we are interested in estimating the slope of a response surface. Conditions are obtained for CCD2 to be slope-rotatable over axial directions, and some CCD2's are presented that have slope rotatability over axial directions. Also values of a measure of slope rotatability over axial directions are tabulated for various CCD2's. Finally, it is shown that CCD2 is always slope-rotatable over all directions.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.519-536
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• 1995

In the design of experiments for response surface analysis, sometimes it is of interest to estimate the difference of responses at two points. If differences at points close together are involved, the design that reliably estimates the slope of response surface is important. This idea was conceptualized by slope rotatability by Hader & Park (1978) and Park (1987). Until now, second order polynomial models were only studied for slope ratatability. In this paper, we will propose the necessary and sufficient conditions for slope rotatability over all directions for the thired order polynomial models in two, three and four independent variables. Also practical slope rotatable designs over all directions for two independent variables are suggested.