Construction of second order slope rotatable designs through balanced incomplete block designs

Babu, B. Re. Victor; Narasimhant, V. L.

doi:10.1080/03610929108830644

Cited by 18 publications

(25 citation statements)

References 5 publications

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“…A second-order response surface design D is said to be a SOSRD if the design points satisfy the following conditions (cf. Hader and Park (1978), Victorbabu (2005Victorbabu ( , 2006 and Victorbabu and Narasimham (1991)):…”

Section: Conditions For Modified Sosrdmentioning

confidence: 99%

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Modified second-order slope rotatable designs with equi-spaced levels

Victorbabu

2009

Journal of the Korean Statistical Society

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Section: Conditions For Modified Sosrdmentioning

confidence: 99%

“…Park (1987) introduced a class of multifactor designs for estimating the slope of response surfaces. Victorbabu and Narasimham (1991) constructed secondorder slope rotatable designs (SOSRD) using BIBD. Victorbabu (2002) suggested SOSRD with equi-spaced levels.…”

Section: Introductionmentioning

confidence: 99%

Modified second-order slope rotatable designs with equi-spaced levels

Victorbabu

2009

Journal of the Korean Statistical Society

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“…Following [2], [3], [5], equations (2 − 3) give the necessary and sufficient conditions for a measure of slope rotatability for any general second order response surface designs. Further, from the above equation (2.2), it can be seen that the necessary and sufficient conditions are: [5] proposed that, if the following conditions below are met, that is i.…”

Section: Conditions Of Measure Of Second Order Slope Rotatable Designsmentioning

confidence: 99%

“…For the central composite designs, they altered [1] rotatability to slope rotatability essentially by altering the axial point distance (a), so that the variance of the assessed unadulterated quadratic coefficients is one-fourth the variance of the assessed mixed second order coefficients. [3] examined in detail the conditions to be satisfied by a common second-order slope rotatable designs (SOSRD) and developed SOSRD using balanced incomplete block designs (BIBD). [3] constructed SOSRD through a pair of incomplete block designs.…”

Section: Introductionmentioning

confidence: 99%

“…[3] examined in detail the conditions to be satisfied by a common second-order slope rotatable designs (SOSRD) and developed SOSRD using balanced incomplete block designs (BIBD). [3] constructed SOSRD through a pair of incomplete block designs. The slope-rotatable design is that of which the variance of partial derivative is only a functions of ρ: distance from the design center.…”

Section: Introductionmentioning

confidence: 99%

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A Measure for Evaluating the Degree of Slope Rotatability in Three Level Second Order Slope Rotatable Designs

Ednah

Mutiso

Nyamwala

2019

JAMCS

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Response surface methodology (RSM) often deals with a natural and desirable property rotatability, which requires that, the variance of the predicted response at a point remains constant at all such points that are equidistant from the design center. To achieve stability in prediction variance, this important property of rotatability was developed. Analogous to rotatability, the concept of slope-rotatability has been progressed. The idea of slope - rotatability is an important design criterion for response surface design. Recently, in the design of experiments for response surface analysis, attention has been focused on the estimation of dierences in response rather than absolute value of the response mean itself. The slope-rotatable design is that of which the variance of partial derivative is only a functions of : distance from the design center. If circumstances are such that exact slope rotatability is unattainable because of more cost and time, and more important restrictions such as orthogonal blocking it is still a good idea to make the design as slope rotatable as possible. Thus, it is important to measure the extent of deviation from slope rotatability. In this study, a new measure of the degree of slope-rotatability for three level second-order slope rotatable designs using a pair of a partially balanced incomplete block design is suggested that enables us to assess the degree of slope-rotatability for a given response surface design. This determines the degree slope rotatability for the design when subjected to existing conditions of measure. The measure takes the value zero when the design is exact slope-rotatable, and becomes larger as the design deviates from being slope-rotatable design.

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