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. 
View via Publisher
math.uni-augsburg.de
67 Citations
Highly Influential Citations
2
Background Citations
22
Methods Citations
12

Figures and Tables from this paper

67 Citations

A measure of rotatability for second order response surface designs

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

Box and Hunter [1] introduced very important concept of rotatability for response surface designs. Measure of rotatability that enable us to assess the degree of rotatability for a given response…

Measure of rotatability of modified five-level second-order rotatable design using supplementary difference sets

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

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

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

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…

Small, balanced, efficient and near rotatable central composite designs

On third order rotatability

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

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

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…
...

References

SHOWING 1-9 OF 9 REFERENCES

A measure of rotatability for response-surface designs

A measure that quantifies the amount of rotatability in a given response-surface design is introduced in this article. The measure, which is expressible as a percentage, takes the value 100 if and…

An index of rotatability

An index of rotatability is suggested that will enable the experimenter to obtain an immediate appreciation of the overall shape of specified variance contours for symmetrical second-order designs.…

“Repairing” Response Surface Designs

This note considers a method, recently described by Dykstra, for augmenting existing data in response surface experiments. Examples are given to show how this relatively simple approach can be…

First and second order rotatability of experimental designs, moment matrices, and information surfaces

SummaryWe place the well-known notion of rotatable experimental designs into the more general context of invariant design problems. Rotatability is studied as it pertains to the experimental designs…

Hybrid Designs for Quadratic Response Surfaces

Hybrid designs were created to achieve the same degree of orthogonality as central composite or regular polyhedral designs, to be near-minimum-point, and to be near-rotatable. They resemble central…

A Measure of Rotatability for ResponseSurface

  • Designs," Technometrics,
  • 1988

Empirical Model‐building and Response Surfaces.

Multi-Factor Experimental Designs for Exploring Response Surfaces

" Schlaflian Rotatability

  • Journal of the Royal Statistical Society , Ser . B
  • 1984