# Another look at rotatability

@article{Draper1990AnotherLA, title={Another look at rotatability}, author={Norman R. Draper and Friedrich Pukelsheim}, journal={Technometrics}, year={1990}, volume={32}, pages={195-202} }

Rotatability is one of many desirable characteristics of a response-surface design. Recent work (Draper and Guttman 1988; Khuri 1988) has, for the first time, provided ways to measure “how rotatable” a design may be when it is not perfectly rotatable. This had previously been assessed by the viewing of tediously obtained contour diagrams. This article provides a criterion that is easy to compute and is invariant under design rotation. It also easily extends to higher degree models.

## 67 Citations

### A measure of rotatability for second order response surface designs

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- 1993

The concept of rotatability introduced by Box and Hunter (1957,Ann. Math. Statist.,28, 195–241) is an important design criterion for response surface design. Recently, a few measures of rotatability…

### A NOTE ON MEASURE OF ROTATABILITY FOR SECOND ORDER RESPONSE SURFACE DESIGNS USING INCOMPLETE BLOCK DESIGNS

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ABSTRACT Rotatability is a desirable quality of fitting response surface experimental designs. The property states that the variance of the estimated response made from the Taylor’s series expansion…

### Rotatable Designs and Rotatability

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Choosing a suitable experimental design is an important step in the investigations of the factors that may influence one or more response variables. There are several criteria to keep in mind when…

### A General Construction Method for Five-Level Second-Order Rotatable Designs

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A method for constructing second-order rotatable designs in order to explore and optimize response surfaces based on an infinite class of supplementary difference sets and achieve both properties of rotatability and estimation efficiency.

### Measure of Rotatability for Second Order Response Surface Designs Using a Pair of Balanced Incomplete Block Designs

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In this paper, measure of rotatability for second order response surface designs using a pair of balanced incomplete block designs without any additional set of designs points is suggested which…

### On third order rotatability

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Third order rotatability of experimental designs, moment matrices and information surfaces is investigated, using a Kronecker power representation. This representation complicates the model but…

### Repairing Non-rotatable Central Composite Designs

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A different and new approach to repairing non-rotatable central composite designs has been proposed. Some other authors, like Khuri (Technometrics 30(1):95–104) and Draper and Pukelsheim…

### ROBUST ROTATABLE CENTRAL COMPOSITE DESIGNS

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Das [3] studied robust second order rotatable designs (RSORD) and constructed second order rotatable designs with correlated errors (SORDWCE) under the auto correlated structure using central…

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